Penthouses (except when framed by and extension of the building frame). 2.5 ...... USA. Stratta,J.L., (2003), Manual of Seismic Design, Pearson Education, First ...
Int roduct ion to
Earthquake Safety of Building Contents (Non-St ruct ural Elements)
C. V. R. Murty Rupen Goswami A. R. Vijayanarayanan Vipul V. Mehta R. Pradeep Kumar
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Preface
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Countries with advanced seismic safety initiatives are managing to reduce losses due to building collapses, but the safety of building contents is still at a relatively nascent stage. In urban India, the costs of the building contents and finishes are touching about 60-70% of the building construction cost. This book is meant to provide guidance on how to secure these non-structural elements of buildings (contents of buildings, appendages to buildings, and services and utilities) to resist design earthquake shaking. This book employs exaggerated deformation shapes to emphasise the deformation and thereby understand the implications of seismic design of non-structural elements. The book does not bring any new research results, but presents under pair of covers the basics available in international literature related to seismic safety of non-structural elements. It is hoped that the book will help draw the attention of professional architects and engineers to the subject matter. Hence, the target audience of the book is practicing Architects and MEP design engineers; the book should help teachers and students also of architecture and engineering colleges get a basic understanding of the subject.
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Table of Contents Preface Table of Contents
1
Introduction
1.0 1.1
Basics of Earthquake-Resistant Design & Construction of Structural Elements Non-structural Elements 1.1.1 Mistaken as Non-Structural Elements Importance of Securing them Classificati on of Non-structural Elements Strategies to secure Non-structural Elements 1.4.1 Expected Performance of NSEs during Strong Earthquake Shaking 1.4.2 Safety from Primary Hazards 1.4.3 Safety from Secondary Hazards 1.4.4 Requirements for NSEs of Buildings 1.4.4.1 Level of shaking to be considered 1.4.4.2 Design Provisions
1.2 1.3 1.4
2
Safety from Sliding, Rocking and Toppling Hazards
2.0 2.1 2.2
2.5
Effect of Ground Movement Strategies against Sliding, Rocking and Toppling Hazards Classificati on of Sliding, Rocking and Toppling Hazard NSEs 2.2.1 NSEs anchored only to Horizontal LLRSS Elements 2.2.2 NSEs anchored only to Vertical LLRSS Elements 2.2.3 NSEs anchored to both Horizontal and Vertical LLRSS Elements Design against Sliding, Rocking and Toppling Hazards 2.3.1 Design Lateral Force for SEs 2.3.2 Design Lateral Force for NSEs 2.3.2.1 Design Lateral Force for Connection of NSEs Examples Calculation of Design Lateral Force for NSEs 2.4.1 NSEs anchored only to Horizontal LLRSS Elements 2.4.1.1 Plastic Water Storage Tanks on Roof Slab 2.4.1.2 Masonry Parapet Wall on Roof Slab 2.4.1.3 False Ceiling Hanging from Roof/Floor Slab 2.4.1.4 Machines on slabs 2.4.2 NSEs anchored only to Vertical LLRSS Elements 2.4.2.1 Book Shelf supported on Walls 2.4.2.2 Cupboards 2.4.2.3 TV and Table 2.4.2.4 Gas Cylinder on Floor 2.4.3 NSEs anchored to both Horizontal and Vertical LLRSS Elements 2.4.3.1 Large Storage Rack Earthquake performance of code-designed connections of NSEs
3
Safety from Pulling and Shearing Hazards
3.0 3.1 3.2
General Strategies against Pulling and Shearing Hazards Classificati on of Pulling and Shearing Hazard NSEs 3.2.1 NSEs having Relative Displacement with respect to Ground 3.2.2 NSEs having Inter-storey Relative Displacement 3.2.3 NSEs having Relative Displacement between two items shaking independently Design against Pulling and Shearing Hazards 3.3.1 Design Relative Lateral Displacement for SEs 3.3.2 Design Relative Lateral Displacement for NSEs Examples Calculation of Design Relative Lateral Displacement for NSEs 3.4.1 NSEs having Relative Displacement with respect to Ground 3.4.1.1 Water Mains, Fire Hydrant Supply Pipes and Gas Pipes from outside the Building
2.3
2.4
3.3
3.4
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page
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3.5
3.4.1.2 Sewage Mains from outside the Building 3.4.2 NSEs having Inter-storey Relative Displacement 3.4.2.1 Glass Windows & Partitions, and French windows 3.4.2.2 Water and Fire Hydrant Pipelines inside Building 3.4.2.3 Electric Wires inside Building 3.4.2.4 Sewage Pipelines inside Building 3.4.2.5 Exhaust Fume Pipe of Generator 3.4.3 NSEs having Relative Displacement between two items shaking independently 3.4.3.1 Electric Cables from Pole to Building 3.4.3.2 Water Pipes across Seismic Joint in a Building 3.4.3.3 Electric Wires across Seismic Joint in a Building Earthquake performance of code designed connections of NSEs
Bibliography Acknowledgements
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Chapter 1
Introduction 1.0 Basics of Earthquake-Resistant Design & Construction of Structural Elements Dynamic actions are caused on structures by both wind and earthquakes, But, design for wind forces and for earthquake effects are distinctly different. The intuitive philosophy of structural design uses force as the basis, which is consistent in wind design wherein the building is subjected to a pressure on its exposed surface area; this is force-type loading. However, in earthquake design, the structure is subjected to random motion of the ground at the base of the structure (Figure 1.1), which results in inertia forces in the structure that cause stresses; this is displacement-type loading. Another way of expressing this difference is through the load-deformation curve of the building – the demand on the structure is force (i.e., vertical axis) in force-type loading imposed by wind pressure, and is displacement (i.e., horizontal axis) in displacement-type loading imposed by earthquake shaking.
roof
Fw
ug (t)
(a)
(b)
Figure 1.1: Difference in the design effects on a building during natural actions of (a) Earthquake Ground Movement at base, and (b) Wind Pressure on exposed area
Further, wind force on the structure has a non-zero mean component superposed with a relatively small oscillating component (Figure 1.2). Thus, under wind forces, the structure may experience small fluctuations in the stress field, but reversal of stresses occurs only when the direction of wind reverses, which happens only over a large duration of time. On the other hand, the motion of the ground during the earthquake is cyclic about the neutral position of the structure. Thus, the stresses in the structure due to seismic actions undergo many complete reversals and that too over the small duration of earthquake.
time (a)
time (b)
Figure 1.2: Nature of temporal variations of design actions: (a) Earthquake Ground Motion – zero mean, cyclic, and (b) Wind Pressure – non-zero mean, oscillatory
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Moreover, since earthquake induces inertia forces, the mass of the structure being designed controls seismic design. Civil engineering structures tend to be very massive, and designing them to behave elastically during earthquakes without damage may render the project economically unviable. On the contrary, it may be necessary for the structure to undergo damage and thereby dissipate the energy input to it during the earthquake. Therefore, the ea rthquake-resistant design philosophy requires that structures should be able to resist (Figure 1.3): (a) Minor (and frequent) shaking with no damage to structural and non-structural elements; (b) Moderate shaking with no damage to structural elements, but some damage to non-structural elements; and (c) Severe (and infrequent) shaking with damage to structural elements, but with NO collapse (to save life and property inside/adjoining the structure). Therefore, structures are designed only for a fraction of the force that they would experience if they were designed to remain elastic during the expected strong ground shaking (Figure 1.4), and thereby permitting damage (Figure 1.5). But, sufficient initial stiffness is ensured to avoid structural damage under minor shaking. Thus, seismic design balances reduced cost and acceptable damage, thereby making the project viable. This careful balance is arrived based on extensive research and detailed post-earthquake damage assessment studies. A wealth of this information is translated into precise seismic design provisions. In contrast, structural damage is not acceptable under design wind forces. For this reason, design against earthquake effects are is called as earthquake-resistant design and not earthquake-proof design.
(a)
(b)
(c)
Figure 1.3: Earthquake-resistant Design Philosophy: (a) Minor (Frequent) Shaking – No/Hardly any damage, (b) Moderate Shaking – No structural damage, but some non-structural damage, and (c) Severe (Infrequent) Shaking – Structural damage, but NO collapse H, roof
Lateral Force H Maximum Force, if t he st ruct ure remains elast ic all along
Elast ic St r uct ur e Act ual St ruct ur e
Minimum Design Force, t hat codes require t o
Reduction in Design Force w hen some damage can be allow ed
be use d
0
Lateral Deflection
Figure 1.4: Basic strategy of earthquake design: Calculate maximum elastic forces and reduce by a factor to obtain design forces.
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(a)
(b)
Figure 1.5: Earthquake-Resistant and not Earthquake-Proof: Damage is expected during an earthquake in normal constructions (a) undamaged building, and (b) damaged building.
The design for only a fraction of the elastic level of seismic forces is possible, only if the structure can stably withstand large displacement demand through structural damage without collapse and undue loss of strength. This property is called ductility (Figure 1.6). It is relatively simple to design structures to possess certain lateral strength and initial stiffness by appropriately proportioning the size and material of the members, but achieving sufficient ductility is more involved. Extensive laboratory tests on full-scale specimen identified preferable methods of detailing.
H
H, roof Good Ductility
St rengt h Medium Ductility Poor Ductility
0
Deform abilit y
Figure 1.6: Ductility: Structures are designed and detailed to develop favourable failure mechanisms that possess specified lateral strength, reasonable stiffness and, above all, good post-yield deformability.
In summary, the loading imposed by earthquake shaking under the building is displacementtype and that by wind and all other hazards is of force-type. Earthquake shaking requires buildings to be capable of resisting certain relative displacement within it due to the imposed displacement at its base, while wind and other hazards require buildings to resist certain level of force applied on it (Figure 1.7). While it is possible to estimate with precision the maximum force that can be imposed on a structure, the maximum displacement imposed under the building is not as precisely known.
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roof
Fw
H u g (t)
Force Loading
Wind Demand
0 Displacement Loading
Earthquake Demand
Figure 1.7: Displacement Loading versus Force Loading: Earthquake shaking imposes displacement loading on the building, while all other hazards impose force loading on it
1.1 What are Non-Structural Elements? Structural Elements (SEs) in buildings carry all earthquake-induced inertia forces generated in the building down to foundations. But, there are many items of buildings, such as contents of buildings & appendages to buildings and services & utilities, which are supported by SEs. The inertia forces of these items are carried down to foundations by SEs. Such items are called Non-Structural Elements (NSEs) (Figure 1.8). NSEs can be listed under three groups, namely contents of (a) Contents of buildings:
Items required for functionally enabling the use of spaces, such as (i) Furniture and minor items, e.g., storage shelves, (ii) Facilities and equipment, e.g., refrigerators, washing machines, gas cylinders, TVs, multilevel material stacks, false ceilings, generators and motors, and (iii) Door and window panels and frames, large-panel glass panes with frames (as windows or infill walling material), and other partitions within the buildings; (b) Appendages to buildings:
Items projecting out of the buildings, either horizontally or vertically, such as chimneys projecting out from buildings, glass or stone cladding used as façades, parapets, small water tanks rested on top of buildings, sunshades, advertisements hoardings affixed to the vertical face of the building or anchored on top of building, and small communication antennas mounted atop buildings; (c) Services and utilities:
Items required for facilitating essential activities in the buildings, such water supply mains, electricity cables, gas pipelines, sewage pipelines and telecommunication wires from outside to inside of building and within the building, air-conditioning ducts, rainwater drain pipes, elevators, fire hydrant systems including water pipes through the buildings.
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(a)
Figure 1.8: Common non-structural elements: (a) Contents of buildings, (Photo, The EERI Annotated Slide Collection)
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(b)
Figure 1.8 (Continued): Common non-structural elements: (b) Appendages to buildings (Photo, The EERI Annotated Slide Collection)
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(c)
Figure 1.8 (Continued): Common non-structural elements: (c) Services and utilities (Photo, The EERI Annotated Slide Collection)
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1.1.1 Mistaken as Non-Structural Elements In design practice, non-structural elements are not modeled since they do not carry any forces. However, some elements assumed to be non-structural could significantly influence the seismic behaviour of the structure by inadvertently participating in the lateral force transfer. It is a practice in India to neglect a number of items in the process of structural design of buildings, assuming that these items are non-structural elements. But, these items behave more as structural elements, and not non-structural elements; they participate in the load path and transfer inertia forces to the ground. Considering the significant contribution to stiffness and strength of such elements (that lie in the load path), it should be made a practice to include them in the analytical model of the building. Thus, the design is made consistent with the conditions of the actual structure. Some of these common SEs that are assumed to be NSEs are discussed in this section. (a) Unreinforced Masonry Infill Walls
The most common items assumed by structural designers to be non-structural elements are unreinforced masonry (URM) infills provided in frame panels of three-dimensional frames of RC moment resisting frame (MRF) buildings (Figure 1.9). URM infills are filled in after the frame is built. Thus, the gravity loads of the building, namely dead load, superposed dead load and live load, are carried by the frame and not by the URM infills. For this reason, designers declare them as NSEs. But, when the building sways under horizontal earthquake shaking, the infills come in the way of the free movement of the frame members, which are SEs. They (i) resist the lateral deformation of frame members of the building, (ii) become part of the load path along which earthquake-induced inertia forces generated in the building are transferred to foundation, and (iii) contribute significantly to lateral stiffness and strength of building. Thus, URM infills may act as NSEs for resisting vertical loading on the MRF building, but are indeed SEs for resisting lateral loading on the frame. As a consequence, earthquake behaviour of buildings with URM infills is completely different from that assumed as above by designers – it can be both detrimental and beneficial to the safety of building. When infills are provided uniformly in the building frame, they add to both the strength and stiffness of the MRF building. But, when provided selectively in the building, they can affect the structural configuration of the building and make it behave poorly. For instance, (1) When URM infill walls are provided in all storeys except the ground storey, they make the building stiff and strong in the upper storeys and flexible and weak in the ground storey. Over 400 RC MRF buildings collapsed during the 2001 Bhuj Earthquake due to the flexible and weak ground storey effects (Figure 1.10). This negative effect could have been captured during the structural design of the building, if infills were considered in the analysis. Designers should consider URM infills in RC frame buildings as SEs and not as NSEs, and thereby avoid all unexpected behaviour of buildings.
(a)
(b)
(c)
Figure 1.9: Idealization of real buildings: Analysis and design must bear in mind the physical behaviour of structures during lateral shaking – (a) Analytical Model, (b) Designed Structure, and (c) Actual Structure Constructed
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(2) When URM infill walls of partial height are provided adjacent to a column to fit a window over the remaining height, then the column is restricted from freely shaking in the lateral direction. Other columns in the same storey with no walls adjoining it, do not experienc e such restriction. Consider earthquake ground movement to the left, when the beam-slab floor system moves horizontally to the right. The floor moves the top ends of all these columns (P, Q, R in Figure 1.11a) by the same horizontal displacement with respect to the floor below. But, the stiff infill walls of partial height restrict horizontal movement of the lower portion of column Q; this column deforms by the full displacement over only the remaining height adjacent to the window opening. On the other hand, columns P and R deform over the full height. Since the effective height over which column Q can freely bend is small, it offers more resistance to horizontal motion than columns P and R, and thereby attracts more force than them. But, the columns are not designed to be stronger or have higher shear resistance capacity in keeping with the increased forces that they attract, and thus fail. Now, consider the earthquake ground movement to the right, when the beam-slab floor system moves horizontally to the left. Here, column P is in jeopardy and columns Q and R are not. As a net consequence of earthquake shaking, columns P and Q are damaged due to the adjoining presenc e of the URM infill walls. This short-column effect is most severe when opening height is small. The damage is explicit in such columns (Figure 1.11b), even though the assumption is implicit of URM infill walls being considered as nonstructural elements.
Figure 1.10: Collapse of one set of RC frame buildings during 2001 Bhuj earthquake: there is no damage in the stiff upper portion, while the lower storey is completely crushed. The building in the background is completely collapsed.
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`
Beam-Slab System No connection
Opening
Column
R
Q
Wall
P
Beam-Slab System Opening
Short column
Partial Height Wall
Unrestricted Col umn
Column damage Portion of column restrained from moving
Part of column restricted to move
Column damage
(a)
(b)
Figure 1.11: Short columns effect in RC buildings when partial height walls adjoin columns: (a) Effective height of column over which it can bend is restricted by adjacent walls, and (b) damage to adjoining columns during earthquake shaking between floor beam and sill of ventilator
(b) Rooftop Water Tanks
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Two types of small capacity water tanks are normally fixed on top of RC buildings, namely high density plastic (HDP) tanks rested directly on roof slab and RC tanks rested on plain concrete pedestals or masonry piers. Of these two, the mass of RC tanks is large; they attract high seismic inertia forces. If they are not anchored, they can run loose from top of the masonry piers (Figure 1.12). Unanchored tanks are threat to life; many such tanks dislodged and some collapsed on ground and adjoining properties during 2001 Bhuj Earthquake. These tanks may be of small capacity, but their connections with the roof slab system should be formally conceived, designed and constructed. Also, such tanks behave as cantilevers and cannot mobilize large energy absorption, as a result of which they experience far more damage.
Figure 1.12: Failure of small capacity water tanks atop RC buildings during 2001 Bhuj earthquake: they need to be formally anchored to rooftops, else they can dislodge from the roof (c) Elevator Shaft Core made of RC In RC buildings, when elevator core s hafts are made of reinforced concrete, these RC shafts offer large lateral stiffness and strength to the overall lateral load resistance of the building. Hence, in the design of multi-storey buildings, the contribution of these RC shafts should be considered. During the 2001 Bhuj earthquake, RC shafts were severely damaged in some reinforced concrete multi-storey buildings with open ground storeys. Discussion with practicing engineers after the 2001 Bhuj (India) earthquake revealed that RC frame buildings were analysed and designed as bare frames; in particular, the contribution of RC elevator shaft cores was neglected. These walls were not provided with adequate strength to accommodate the large lateral force attracted by them, and hence experienced severe damage. Many RC buildings with open ground storeys collapsed. But, some of these RC buildings, which had RC elevator shaft core, did not collapse; the elevator core shafts were severely damaged but seemed to have helped inadvertently in preventing their collapse (Figure 1.13a). When these elements were not properly connected to the rest of the building frame, the building collapsed but the elevator core did not (Figure 1.13b). (d) Staircase Waist Slab and Beams Most RC buildings built in India have RC staircases built integrally with the structural system of the building. These staircases behave as un-designed braces and attract large lateral forces. The SEs associated with the staircase usually offer unsymmetrical lateral stiffness and strength to the building. Hence, when the staircase is not considered in structural analysis and design of a building system, it participates in the load path during strong shaking, attracts significant earthquake induced forces, and even gets damaged (Figure 1.14).
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(a)
(b)
Figure 1.13: Contribution of RC elevator core shafts to safety of RC buildings during 2001 Bhuj earthquake: they are structural elements, and not non-structural elements
1.2 Importance of Securing Non-Structural Elements Regulatory systems are not in place yet in many places of the world to ensure safety of the structural system. Consequently, designers and builders are getting away with being miserly about spending any money on ensuring safety of the structure. Often, structural designer is unaware of the attention to be paid to nonstructural elements in the building. On the other hand, they are spending lavishly on non-structural elements. But, it is not guaranteed that this investment on nonstructural elements is safe, because the non-structural elements are not protected against damage during earthquake shaking. It is the primary responsibility of all stakeholders to ensure that the structural system is safe against the effects of earthquake shaking, and thereby to ensure safety of life and property. While this is yet to happen, even losses due to failure of non-structural elements is on the rise in urban buildings. Today, about 60-70% of the total cost of construction in new buildings being built in urban I ndia is of the non-structural elements, and the rest of the structural elements. Learning how to secure non-structural elements also takes time, and hence should be started immediately. Experiences from countries with advanced practices of earthquake safety suggest that even though loss of life has be minimized due to structural collapses, the economic setback due to lack of non-structural element safety is still large. Loss due to an NSE can be small or substantive depending on the function it is serving and its cost. For instance, if book shelves of a library are not properly secured, they can get distorted (Figure 1.15a) or topple; the former may only dislodge books, but the latter can cause threat to life. But, on the other hand, an unreinforced masonry chimney can topple from the roof top and cause threat to life (Figure 1.15b). Similarly, if gas pipelines are pulled apart or electric wires are stretched out of the control panels toppled (Figure 1.16a), then they can cause second order disaster like fire and/or deaths due to asphyxiation. In both cases of toppling or pulling of non-structural elements, direct and indirect losses can be significant.
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(a)
(b)
Figure 1.14: (a) Cracking of staircase elements in RC frame building during 2001 Bhuj earthquake: they are structural elements, and not non-structural elements, and (c) damage to unreinforced masonry infill and floor tiles around the stairwell during 1972 Nicaragua Earthquake (Photo: The EERI Annotated Slide Collection)
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(a)
(b)
Figure 1.15: Undesirable earthquake performance of non-structural elements that topple – (a) damage to bookshelves, and (b) toppling of books from library book shelves (Photos: The EERI Annotated Slide Collection)
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(a)
(b)
Figure 1.16: Earthquake performance of non-structural elements: (a) f electric control panel pullout, and (b) failure of sprinkler pipe system (Photos: The EERI Annotated Slide Collection)
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Experiences from several past earthquakes in countries with advanced provisions for earthquake safety show that even when the building structure is made earthquake-resistant, failure of nonstructural elements can pose threat to (a) occupants of the building, and (b) severely impair the performance of critical items of the building, e.g., electric power, communication equipment, and water supply. Since non-structural elements account for significant part of the total cost of most buildings, it is recognized in counties prone to seismic hazard, that good earthquake performance of nonstructural elements also is extremely important.
1.3 Classification of Non-structural Elements There are two basic NSE items, based on their behaviour during earthquake shaking. These basic items are those that (a) topple and fall, and (b) pull and shear (Figure 1.17). The former are stiff and heavy items. They can topple or slide, if not anchored, e.g., heavy motor. And, the latter are flexible and light items. They swing, foul with adjoining objects, or pull off from supports, if not anchored properly. The former type of NSE is called as acceleration-sensitive NSE and the latter deformationsensitive NSE. Table 1.1 provides a list of NSEs and identifies if the NSE is acceleration-senstive or deformation sensitive. Some NSEs fall under both categories, with one of the effects being the more dominant (called primary effect) and the other less dominant (called secondary effect). For such NSEs, Table 1 identifies which of these two effects is the primary and which the secondary, for the design of the connection between the NSE and the SE. Acceleration sensitive NSEs are mainly affected by acceleration of the supporting structure, and the interaction between the NSE and SE due to deformation of the supporting structure is not significant. Acceleration sensitive NSEs are vulnerable to sliding, overturning, or tilting. Many consumer goods NSEs are acceleration sensitive. Hence, the connection of such NSEs to the SEs should be designed according to the force provisions contained in Chapter 2 of this document. Deformation sensitive NSEs are mainly affected by deformation of the supporting structure, and the interaction between the NSE and SE due to acceleration of the supporting structure is not significant. Deformation sensitive NSEs are vulnerable to the inter-storey drift. Many plumbing service items running between the floors are deformation sensitive. Hence, the connection of such NSEs to the SEs should be designed according to the displacement provisions contained in Chapter 3 of this document. The performance of deformation sensitive NSEs can be improved by designing the NSE to accommodate the expected lateral displacement without damage. In important NSEs, it is preferable to limit the inter-storey drift of the supporting SE to protect the NSE. Some NSEs are both acceleration and deformation sensitive, with one of these effects being dominant (Table 1.1). Their connections with the SEs must be designed according to the provisions contained in both Chapter 2 and Chapter 3 of this document.
Fp
(a) (b) Figure 1.17: Basic types of non-structural elements – (a) stiff & massive – need force design, and (b) flexible & slender – need relative displacement design.
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Table 1.1: Categorisation of NSEs Category
Sub-category
Non-Structural Element
Sensitivity Acceleration
Consumer Goods inside buildings
Furniture and minor items Appliances
Architectural finishes inside buildings
Openings
False ceilings
Appendages buildings
to
Stairs Partitions not held snugly between lateral load resisting members Vertical projections
Horizontal projections Exterior or Interior Façade
Services and utilities
Exterior Structural Glazing Systems From within and from outside to inside the building
Inside the building
Storage Vessels and Water Heaters Mechanical Equipment
1. Storage shelves 2. Multi-level material stacks 1. Refrigerators 2. Washing machines 3. Gas cylinders 4. TVs 5. Diesel generators 6. Water pumps (small) 7. Window ACs 8. Wall mounted ACs 1. Doors and windows 2. Large-panel glass panes with frames (as windows or infill walling material) 3. Other partitions Directly stuck to or hung from roof Suspended integrated ceiling system
1. Chimneys & Stacks 2. Parapets 3. Water Tanks (small) 4. Hoardings anchored on roof tops 5. Antennas communication towers on rooftops 1. Sunshades 2. Canopies and Marquees Hoardings anchored to vertical face Tiles (ceramic, stone, glass or other) (i) pasted on surface (ii) bolted to surface (iii) hung from hooks bolted to surface
1. Water supply pipelines 2. Electricity cables & wires 3. Gas pipelines 4. Sewage pipelines 5. Telecommunication wires 6. Rainwater drain pipes 7. Elevators 8. Fire hydrant systems 9. Air-conditioning ducts 1. Pipes carrying pressurized fluids 2. Fire hydrant piping system 3. Other fluid pipe systems 1. Flat bottom containers and vessels 2. Structurally Supported Vessels 1. Boilers and Furnaces 2. General manufacturing and process machinery 3. HVAC Equipment
Deformation
Both
Secondary
Primary
Secondary Primary Secondary
Primary Secondary Primary
Secondary Secondary
Primary Primary
Secondary
Primary
Primary
Secondary
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1.4 Strategies to secure Non-structural Elements The stiff and massive NSEs should be designed to resist the overturning forces generated in them (Figure 1.17a), by anchoring them to the SEs. Anchoring these NSEs to SEs causes additional forces on SEs, and the SEs should be designed to resist the forced imposed on them by the NSEs. For this reason, these NSEs are called Force Sensitive items. Expensive contents of museums fall into the first category of force design. Such objects can be secured by three simple measures, namely tie it down, bolt it down and protect it with a canopy over it (Figure 1.18).
(a)
(b)
(c)
Figure 1.18: Force design items – 3 simple steps to overcome forces and debris falling on them (a) Tie it, (b) Bolt it, and (c) Protect it with canopy
On the other hand, the flexible and slender NSEs should be designed to accommodate the large relative displacements generated between them and the adjoining objects and surfaces (Figure 1.17b) by making provision for large oscillations without pounding or extra slack in the NSE. For this reason, these NSEs are called Displacement Sensitive items. There are some NSEs can be both displacement and force sensitive, and need to be designed for both forces and relative displacements. Electric lines and gas pipelines fall into the second category of displacement design. Such items when connected to the building from the outside (either from the street or adjacent building) should be provided with adequate slack or flexible couplers to allow for relative displacement generated during earthquakes (Figure 1.19).
Communication and Electric w ires Provided adequate slack
Provide flexible connect io n Water and Gas pipes
Ground shaking
Figure 1.19: Displacement design items – allow for free relative movement at ends of items connected between outside ground and oscillating building
1.4.1 Expected Performance of NSEs during Strong Earthquake Shaking
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Normal buildings are designed to undergo elastic behaviour (with no damage) under forcetype loadings that appear on them, e.g., dead, live and wind loads. But, they are designed to undergo inelastic behaviour (with damage) under displacement-type loading, namely earthquake ground shaking. Since the latter is more severe, it is required to discuss performance levels of buildings intended to be earthquake-resistant. Thus, performance-based assessment and design draws prominence to ensure that both the building and its contents are safe during the expected strong earthquake shaking. Performance-based design recognizes four qualitative levels of performance of the building structure (SEs), which may be defined as: (a) Fully Operational (FO) Level: The building is shaken by the earthquake, but no damage occurs in it; the function of the building is not disrupted due to the occurrence of the earthquake; (b) Immediate Occupancy (IO) performance level: The building is shaken predominantly in its linear range of behavior and only minor damage may occur in it. (c) Life Safety (LS) performance level: The building is shaken severely in their nonlinear range of behavior. Significant damage occurs in them, but the building has some more reserve capacity to withstand some more shaking and does not reach the state of imminent collapse. The use of the facility is restricted after the earthquake until detailed structural safety assessment is performed to ascertain the suitability of the building for retrofitting. If found suitable for retrofitting, the building may be retrofitted. (d) Collapse Prevention (CP) performance level: The building is shaken severely in their nonlinear range of behavior. Major damage occurs in them. The building does not have any reserve capacity to withstand some more shaking; it is in the state of imminent collapse. The building cannot be used after the earthquake. Currently, there are many parameters (including the structural type) that govern the overall performance. It is not an easy task to quantitatively define the desired performance level of a building, using any or some of these parameters that can be monitored for quantitatively assessing the performance of the building. Thus, there is no ONE acceptable, quantitative definition for the FO, IO, LS and CP performance levels. The subject of Performance-Based Design of buildings is being researched, and the philosophy has not been included yet in seismic codes of most seismic countries for design and construction of structural elements (SEs). These codes largely adopt equivalent forcebased approach to design SEs in new buildings and not the displacement-based approach required by Performance-Based Design concepts. Displacement effects related to ductility are only indirectly incorporated in the structural design of SEs. A similar line of discussion as in SEs is needed in the seismic design of NSEs. The four levels of performance levels as in SEs can be thought of in NSEs also, namely FO, IO, LS and CP. In seismic design, the expected performance levels are not clarified explicitly of different NSEs at different levels of shaking. T he objectives of earthquake-resistant design philosophy (See Annexure A) require that there is no damage to NSEs during minor shaking, but admits some damage in the NSEs during moderate shaking; the performance of NSEs is not discussed during strong shaking. These are only qualitative statements of performance requirements and that too made in the context of normal buildings. Critical & lifeline buildings, that are critical in the aftermath of an earthquake, must be fully operational (FO) immediately after the earthquake. It is desirable that the following specific performance levels are satisfied under the expected design level shaking at the building: (1) Critical & Lifeline Buildings: The building structure should be within the range of IO performance level. This will help the immediate use of the building without perceiving any threat to the people in the event of aftershocks in the region. (2) Contents & Utilities of Critical & Lifeline Buildings: The contents & utilities within the building structure should be within the range of FO performance level. This will help the continuity of all the critical & lifeline building services to persons affected during the earthquake and requiring critical & lifeline services. The target performance levels are listed in Table 2, that are expected of SEs and NSEs.
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Table 2: Target performance levels of SEs and NSEs in buildings Building Normal Critical & Lifeline Building
Performance Level Expected SEs NSEs Life Safety (LS) Immediate Occupancy (IO) Immediate Occupancy (IO) Fully Operational (FO)
In general, stiffnesses of NSEs systems in buildings arises largely out of their connection with SEs of the buildings. Under differnet intensities of earthquake shaking (Intensities 1, 2, 3 and 4 in Figure 1.20), the imposed dispalcement on the NSE is differnet; largest dispalcement is imposed under most severe ground shaking (level 4 shaking). Figure 13a presents the lateral loaddeformation curves of four designs of NSEs systems, namely designs A, B, C and D, of different lateral strengths, but of same intial stiffness. And, Figure 13b presents four designs of NSEs systems of same lateral strength, but of different initial stiffness. It is sufficient, if the NSEs are operational after an earthquake. Hence, the connections of NSEs to SEs need be such that this objective is met with and the cost of securing the NSEs to the SEs is a minimum. But, too much of strength of the connections between NSEs and SEs increases the cost, and too much flexibility casuses damage to the NSEs (as well as to the building) and threat to life.
H
Design D
St rengt h Design C
H
Design B
St rengt h Design A
A
0 1
2
3
Level of earthquake shaking
(a)
4
B
C
Design D
0 1
2
3
4
Level of earthquake shaking
(b)
Figure 1.20: Earthquake design and performance of non-structural elements: (a) of different strengths, and (b) of same strength
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NSEs in buildings are to be secured with measures such that they shall not overturning or sliding under the expected strong earthquake shaking, and accrue damage under the inelastic displacement of the structure imposed on them under the expected strong shaking. Thus, design codes specify (1) the minimum lateral force with which the connections of these NSEs to SEs need to be deisgned with, and (2) the displacement requirements to prevent interference of NSEs with each other or with the SEs. The expected peformance from NSEs is depicted in Figure 1.21 alongside the correpsonding expected performance of SEs; this is shown for both normal buildings and for ciritcal & lifeline buildings. T he expected performance level of SEs in ciritcal & lifeline buildigns is higher than that of SEs in normal buildings. Similarly, the expected performance level of NSEs in ciritcal & oifeline buildigns is higher than that of NSEs in normal buildings.
H
Normal Buildings : Struct ural Ele ment s
LS CP
IO FO
0
1 2
3
4
Level of earthquake h ki
H
LS IO
Critical and Lifeline Buildings : Struct ural Ele ment s CP
FO
0
(a)
H
LS IO
Normal Buildings : Non-Struct ural Elements CP
FO
0 1 2
H
3
4
Critical and Lifeline Buildings : Non-Struct ural Elements
Level of earthquake
LS
IO FO
0 1 2
3
4
(b)
Figure 1.21: NSEs are required to be designed for higher levels of performance than SEs: Performance under four intensities of earthquake shaking by(a) SEs, and (b) NSEs
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1.4.2 Safety from primary hazards
Safety assessment of NSEs not secured to structural elements of the building should be undertaken in reinforced concrete buildings, against (a) Lateral inertia forces generated in the NSEs, that topple/overturn, slide or fall down from an elevation, under the action of design level shaking specified in the design codes, or (b) Relative lateral deformation between NSEs and between NSEs & SEs (of items spanning across two floors or connected between the building and a point outside building), that move or swing by large amounts in translation & rotation, by elastic action of NSEs under the action of inelastic deformations of the SEs imposed on them under design level shaking specified in the codes; these inelastic displacements of SEs are estimated using the displacements obtained from linear elastic analysis of the building under the action of design forces. The threat of a direct loss of an NSEs is called primary hazard, if the NSE can cause threat to life or impair the function of the NSE, under the above actions, 1.4.3 Safety from secondary hazards
Threat of failure of NSEs is called secondary hazard, if can cause loss to other items or failure of a function of the building and jeopardize safety of people, building and its contents. For instance, spill of chemicals in a laboratory can cause fires (Figure 1.22a), and toppling of unreinforced masonry parapet wall or chimney of a house can harm life of persons below (Figure 1.22b).
(a)
(b)
Figure 1.22: Earthquake performance of non-structural elements can cause second order disaster: (a) chemical spill in a laboratory can cause loss of life, and (b) toppling of masonry chimneys can cause loss of life of persons below electric (Photos: The EERI Annotated Slide Collection)
1.4.4 Requirements for NSEs of Buildings
In normal buildings, NSEs should be designed to sustain the expected severe shaking specified in the design codes for the design of SEs in buildings. And, in critical and lifeline buildings, higher levels of shaking should be designed for. The current Indian seismic code IS:18932003 does not have any provisions on seismic design of NSEs. But, the IITK-GSDMA revised draft guidelines of IS:1893 gives provisions for seismic design of NSEs in line with seismic design forces specified in IS:1893 for SEs. In this section, these provisions mentioned in Draft guidelines of IS:1893 are used to demonstrate the methodology of design of NSEs.
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1.4.4.1 Level of shaking to be considered
NSEs should be designed to resist the effects of a design shaking as defined in the codes. For this level of shaking, when force-based checks are to be undertaken, the design horizontal acceleration coefficient should be used in all computations (related to the building and its contents & utilities) as given in the codes. Under the action of forces corresponding to design event, the contents & utilities should be safe against overturning AND relative displacement. 1.4.4.2 Design Provisions
The design provisions are discussed in Chapters 2 and 3 to secure the NSEs against falling and toppling hazards through force design, and against pulling and shearing hazards through displacement design, respectively. Some NSEs are governed by both force design and displacement design. For those NSEs, first the force design should be performed and then verification should be done on the displacement issues. …
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Chapter 2
Safety from Sliding, Rocking and Toppling Hazards 2.0 Effect of Ground Movement Objects inside a building can slide, rock or topple when the building is subjected to random earthquake shaking, if the object is unanchored in either the vertical or lateral direction and if the shaking is severe (Figure 2.1). Sliding means the base of the NSE is completely in contact with the surface on which it is rested, but the NSE is horizontally translating on that surface with friction (Figure 2.1c). Rocking means the NSE is not sliding, locked at the toe (i.e., point A in Figure 2.1d) and lifts off from its heal (i.e., point B in Figure 2.1d). Toppling means the NSE is rocking, loosing balance and finally ends up sideways on the surface on which it is rested (Figure 2.1d). Which of these three actions is possible depends on (a) the intensity of shaking of the surfa ce on which the object is rested (reflected by the acceleration of the surface in the horizontal and vertical directions), and (b) the geometry of the object. In reality, in addition to the above three basic possibilities, the NSE also may simultaneously slide and rock.
Anchors
F H
CG
W
H/2
L
B
(a)
B A
B/2
(b)
(c)
A
(d)
A
(e)
Figure 2.1: Sliding, Rocking and Toppling Hazard NSEs - Tendency in unanchored NSEs to displace during earthquake shaking depends on the level of lateral shaking and on the aspect ratio (B/H) of the object (a) Geometry of NSE, (b) Forces acting on NSE, (c) Sliding, (d) Rocking, and (e) Toppling
(a) Governing Conditions
The actual behaviour of a NSE is complex and nonlinear under dynamic earthquake shaking. Also, the geometry and distribution of mass in a NSE are non-prismatic and non-uniform, respectively. In this chapter, simplified checks are presented for assessing the safety of the NSE against each of the above three basic cases. For this purpose of assessing safety of NSEs subjected to earthquake shaking, all NSEs are considered to be rectangular with their mass uniformly distributed along the entire volume of the object. Consider a prismatic object of height H and base dimensions B×H (Figure 2.1), and shaking along the breadth B of the object. Let the mass of the object be m; it weight may be represented as W. If the ground under the object moves to the left with acceleration “a”, then it is required to assess whether the object will slide, rock or topple to the right about point A.
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(a) Sliding Only Owing to vertical gravity self weight of the NSE, a frictional force of W is generated at its base, where is the coefficient of static friction. Under horizontal earthquake shaking, the object only will slide when BOTH of the following two conditions are satisfied, namely (1) The earthquake-induced lateral inertia force Feq is more than the frictional force W at the base, Feq W , and (2.1) (2) The restoring moment due to self-weight of the NSE is more than the overturning moment due to lateral inertia force (when the moments are considered about point A)
B H W Feq . 2 2
(2.2)
Using gravity force W=mg and earthquake-induced inertia force Feq=maeq, where m is the mass of the object, g the acceleration due to gravity, and aeq the lateral inertial acceleration due to earthquake shaking, the above two conditions reduce to a eq g , (2.3) and
a eq
B g. H
(2.4)
(b) Rocking Only Here the frictional force is more than the earthquake-induced inertia horizontal force. Under horizontal earthquake shaking, the object only will ro ck when BOTH of the following conditions are satisfied, namely (1) The earthquake-induced lateral inertia force Feq is less than the frictional force W at the base, Feq W , and (2.5) (2) The restoring moment due to self-weight of the NSE is less than the overturning moment due to lateral inertia force (when the moments are considered about point A)
B H W Feq . 2 2
(2.6)
Again, substituting W=mg and Feq=maeq, the above two conditions reduce to a eq g ,
(2.7)
and
a eq
B g. H
(2.8)
(c) Toppling Only Here the frictional force is more than the earthquake-induced inertia horizontal force. Under horizontal earthquake shaking, the object only will topple when BOTH of the following conditions are satisfied, namely (1) The restoring moment due to self-weight of the NSE is less than the overturning moment due to lateral inertia force (when the moments are considered about point A)
B H W Feq , and 2 2
(2.9)
(2) The condition derived from simplifying the non-linear governing differential equation for toppling ( Makris and Roussos, 1998) is satisfied
Feq W 1 3T
2 2 B H B tan 1 . 1.5g H
(2.10)
Here, the object may or may not be sliding as the rocking is happening, and hence a condition involving coefficient of friction does not arise. Again, substituting W=mg and Feq=maeq, the above condition reduces to
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a eq g 1 3T
B 2 H 2 B tan 1 . 1.5g H
(2.11)
The above equations have not been included yet in many design codes. Thus, so long as the center of gravity (CG) of the object remains within the width (say, B) of the object, inertia force F causes overturning moment about point A and gravity forc e W causes restoring moment (Figure 2.1c). But, once the CG of the object moves out of the base width of the object, both lateral inertia force and gravity forc e cause overturning moment about point A (Figure 2.1d). Thus, objects are likely to topple, if they are twice as tall as their width or more, if the earthquake acceleration exceeds 0.5g. Conversely, squat objects have a lesser likelihood of toppling by themselves. Generally, in most earthquakes, objects are less likely to topple if their heights are half of their breadth or less, since lateral earthquake acceleration is less likely to exceed 2g. In the above discussion, peak ground acceleration (PGA) value of the entire earthquake shaking is used as the measure of earthquake-induced acceleration a eq in the object.
(b) Numerical Example
Consider an cupboard placed at all floor levels of a four storey RC frame building, which is 0.45m×0.90m in plan and 2.1m tall; the mass of the cupboard is 2000 kg (Figure 2.2). the building is subjected to 1940 El Centro ground motion (S00E component; 0.31 g peak ground acceleration). The acceleration at all floor levels of the building are obtained from structural analysis of the building. These values are shown in Table 2.1. Using Eqs.(2.3) and (2.4) for sliding, Eqs.(2.7) and (2.8) for rocking, and Eq.(2.11) for toppling, the safety is assessed of the same cupboard placed on all floors. Two orientations of the cupboard are considered, namely with the narrow width in the direct ion of shaking and perpendicular to it; the latter is expected to be vulnerable. The results of the critical governing condition are listed in Table 2.1.
5 4 3
2.1m
2 1
0.45m
0.9m
Storey
Figure 2.2: Toppling and Falling Hazard NSEs – Same object is more vulnerable when placed on upper floors of a building shaken by earthquakes
2-4
Table 2.1: Safety of an Cupboard at different floors of a building subjected to 1940 El Centro Earthquake ground motion Floor Floor Acceleration Governing condition Level (m/s2 ) Sliding Rocking Smaller width of the object in the direction of shaking
Toppling
2.1m
Direction of Shaking 0.45m
5 4 3 2 1
4.76 4.36 3.32 1.73 3.42
0.9m
Not Safe Safe Safe Safe Safe
Not Safe Not Safe Not Safe Safe Not Safe
Not Safe Not Safe Safe Safe Safe
Larger width of the object in the direction of shaking
2.1m
Direction of Shaking 0.45m
5 4 3 2 1
4.76 4.36 3.32 1.73 3.42
Not Safe Safe Safe Safe Safe
0.9m
Not Safe Not Safe Safe Safe Safe
Safe Safe Safe Safe Safe
Results from Table 2.1 show that the cupboard is safe against toppling when direction of shaking matches is along its larger plan dimension. While this is an intuitive result, the equations above offer a quantitative way of the ensuring safety is reassuring. But, when the shaking is along the smaller plan dimension, the results are of importance. The ground storey receives the shaking directly from the ground, while the upper storeys receive the motion filtered by the building. Hence, the shaking acceleration at the second storey is smaller than that in the first storey. Thus, the possibility of rocking arises in the ground storey that is absent in the second storey. Otherwise, the overall observation is that floor acceleration is higher in the upper storeys, and hence there is a greater likelihood of toppling of the cupboard in the upper storeys.
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2.1 Strategies against Sliding, Rocking and Toppling
The strategy to ensure safety of NSEs from Sliding, Rocking and Toppling is to (1) prevent it from sliding, AND (2) increase its restoring moment. Theoretically, increase in restoring moment can be achieved in many ways (e.g., increasing the base dimension and increasing the weight). But, since most NSEs cannot be tampered with too much, the intervention to increase restoring moment must be kept to a minimum. One possible intervention to increase restoring moment necessarily seeks to tie the object down to the structural system that carries all loads arising in the structure during earthquake shaking, along the load path to the foundation. The tying action can be with ropes/wires/cables, double-side sticking tapes, indirect hold-down methods, or small metallic flats/angles screwed/welded to the object and the structural system. The choice of the intervention depends on the mass, geometric size, value, aesthetics and extent to which one can tamper with the object. When it is not possible to tamper with it, the object can be encased in another shroud (without jeopardizing its functionality); in turn, the shroud is tied to the structural system. Objects placed next to the walls can be held back with the help of walls. But, those in the middle of the room need to be anchored only to the floor slab. Sometimes, two adjacent objects (that are wide enough) can be tied together to ensure stability against overturning by satisfying the condition (mentioned before) that the B/H ratio of the integrated object is more than 2 (Figure 2.3). The individual objects can be integrated with each other using metallic/wooden flats that can be welded, bolted/riveted or glued to the two objects (Figure 2.3a). The choice of the connector and method of connection depends on the factors stated earlier in this section. Connect ors CG
CG
H B1
Connect ors
F W
H/2
F
W
CG
L
B2
A
B1 B2 B
(a)
(b)
(c)
(d)
Figure 2.3: Unanchored Twin NSEs – Tendency to topple during earthquake shaking can be reduced if they can be integrated with stiff and strong connectors When objects placed one over the other cannot be connected to each other, it may be necessary to tie the top object directly to the ground (Figure 2.4a). Here, the tying should be done symmetrically in both directions in plan, by keeping the ties inclined in the two perpendicular plan directions (Figure 2.4b). This tie will resist the inertia forces generated during earthquake shaking that is in all three directions in space. The choice of the connector and method of connection will depend on the factors stated above. When objects are not tied in both plan directions, they can swing in the unanchored directions (Figure 2.4c). Anchored in Perpendicular directions
Tie Tie
Unanchored direction
(a) (b) (c) Figure 2.4: Direction of Tying NSEs – In any two perpendicular plan directions the object must be tied; this will ensure that the object does not swing unrestrained in any direction
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When an object is very precious or critical and is in the neighbourhood of objects than can fall on it, it may be given a second level of protection. This can be done by providing a canopy over it (Figure 2.5). Of course, the canopy itself must be made safe to take the impact of the falling object, by designing it to resist the falling the object and preventing it from sliding or overturning during earthquake shaking. Canopy
NSE
Figure 2.5: Protection of NSEs against falling debris – This can happen when objects are stacked at elevations higher than that of this NSE. Here, both the NSE and the canopy should be individually safe and anchored.
There are small or light objects that cannot be individually anchored, e.g., crockery on a kitchen shelf and glass bottles carrying chemicals on a chemical laboratory shelf (Figure 2.6a). For these objects, strategies are necessary to stack them in a container and design to hold back the container from toppling. Strings, front panel plates and vertical spacers are commonly used to hold back such items (Figure 2.6b).
(a)
Front Panel String
(b)
Vert ical Spacer
Figure 2.6: Small and light NSEs that cannot be individually anchored – Tendency to topple during earthquake shaking can be reduced if they can be held back by indirect means
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2.2 Classification of Sliding, Rocking and Toppling NSEs
The toppling and falling hazard objects can be at any elevation of the building (Figure 2.7a). Based on their tendency to overturn, these different objects require different methods to secure them. They can be connected to any element of the lateral load resisting structural system (LLRSS) of the building, namely the vertical elements (like walls and columns), the horizontal elements (like slabs and beams), or both. In turn, these elements of the LLRSS of the building carry the inertia forces of these objects along the load path of the structural system of the building down to the foundation. For the purposes of designing the connectors between the objects and the elements of the LLRSS of the building, the toppling and falling hazard NSEs can be classified into three types, namely (1) NSEs anchored only to horizontal elements of the LLRSS of the building (Figure 2.7b), (2) NSEs anchored only to vertical elements of the LLRSS of the building (Figure 2.7c), and (3) NSEs anchored to both horizontal and vertical elements of the LLRSS of the building (Figure 2.7d). Some of the typical examples are discussed in the sub-section below.
Vert ical Element Lat eral load resist ing struct ural syst em ( LLRSS) of t he building
Load
of t he LLRSS
pat hs
Horizont al Element of t he LLRSS
(a)
(b)
(c)
(d)
Figure 2.7: Toppling and Falling Hazard NSEs – 3 ways of ensuring safety of NSEs by connecting to the LLRSS of the building, namely : (b) to horizontal elements only of the LLRSS, (c) to vertical elements only of the LLRSS, and (d) to both horizontal and vertical of the LLRSS.
2.2.1 NSEs anchored only to Horizontal LLRSS Elements Objects can topple under lateral earthquake shaking, if they are massive (but not necessarily tall) and do not have adequate width or grip at the base (Figure 2.8a), e.g., parapets on roof tops, television placed on table, plastic water storage tanks on roof tops, and machines & generators. Sometimes, these objects may not topple, but their sliding may cause other losses. Such objects can be made safe against toppling and/or sliding by just anchoring them at the base by taking support from the horizontal elements of the LLRSS (e.g., Figure 2.9). Sometimes, the NSE is hung from the LLRS (e.g., Figure 2.10). This is vulnerable under strong s haking with vertical component dominating. Vertical projections made of unreinforced masonry have proved to be a major concern during earthquake shaking (Figure 2.11); they need to be anchored formally to the horizontal LLRS elements. Mitigation measures adopted in past earthquakes have been successful in securing the NSEs (Figure 2.12).
2-8
Connect or
(a)
(b)
(c)
Figure 2.8: Toppling and Falling Hazard NSEs – Examples of NSEs connected to the LLRSS of the building, namely: (a) to horizontal elements only of the LLRSS, (b) to vertical elements only of the LLRSS, and (c) to both horizontal and vertical of the LLRSS.
(a)
(b)
Figure 2.9: Poor earthquake performance of NSEs is avoidable through design: (a) heavy battery bank collapse owing to light supports, and (b) improved performance with formal supports (Photos: The EERI Annotated Slide Collection)
(a)
(b)
Figure 2.10: Poor earthquake performance of NSEs is avoidable through design: (a) hanging light fixtures, and (b) collapse of false ceiling (Photos: The EERI Annotated Slide Collection)
2-9
(a)
(b)
Figure 2.11: Poor earthquake performance of NSEs is avoidable through design: (a) unreinforced masonry parapet collapse, and (b) unreinforced masonry boundary wall collapse (Photos: The EERI Annotated Slide Collection)
(a)
(b)
Figure 2.12: Good earthquake performance of NSEs is achievable through simple and innovative, but careful design of the anchors: (a) holding back the bottles on a rack, and (b) holding back the heavy book shelves to the wall (Photos: The EERI Annotated Slide Collection)
2.2.2 NSEs anchored only to Vertical LLRSS Elements Objects that are massive (but moderately tall) can topple under lateral earthquake shaking (Figure 2.8b), e.g., refrigerators and cupboards. Such objects can be made safe against toppling by just anchoring them at the top by taking support from the vertical elements of the LLRSS. In special cases, even light and short objects can be anchored to the vertical elements of the LLRSS, e.g., LPG cylinders. These objects do not offer proper grip to anchor them at their base to the horizontal elements of the LLRSS, but have a feature (like the top ring in a LPG cylinder).
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Some objects may have to be mounted directly on walls from functional considerations, e.g., shelves and flat televisions mounted on walls. Caution is essential to ensure that walls on which such objects are mounted, can safely carry the object and resist earthquake shaking in their out-ofplane directions. This is particularly a concern, when the object is mounted on an unreinforced masonry wall. Objects that are on shelves that are held against the wall can also be treated as wall mounted (Figure 2.13).
Figure 2.13: Poor earthquake performance of NSEs is avoidable through design: objects placed on shelves anchored to the vertical LLRS elements (Photos: The EERI Annotated Slide Collection)
2.2.3 NSEs anchored to both Horizontal and Vertical LLRSS Elements Objects that are massive (and tall) can topple under lateral earthquake shaking (Figure 2.8c), e.g., industrial storage racks stocking raw material or finished products. Such objects have a significant part of their mass at higher elevations, narrow width and large height. These factors make such objects candidates to topple, because they cannot be made safe against toppling by just anchoring them at the base by taking support from the horizontal elements of the LLRSS; supports are required at the upper elevations also by taking support from the vertical elements of the LLRSS. Some false ceilings are held by both horizontal and vertical LLRS elements (Figure 2.14). This is vulnerable more under strong vertical shaking.
Figure 2.14: Poor earthquake performance of NSES is avoidable through design: false ceiling systems require diagonal brace-like anchors also; just vertical elements alone make the NSE swing horizontally (Photos: The EERI Annotated Slide Collection)
2.3 Design against Sliding, Rocking and Toppling Hazards
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Countries faced with high earthquake hazard have internalized experiences of earthquake safety of non-structural elements over the years. On the outer surface of the building, no objects are loosely placed on higher elevations at window sills, balconies or ledges of buildings, whic h can fall down from elevations, e.g., flower pots are not precariously rested on ledges. In tall buildings of urban areas, this possibility is completely eliminated because of wind issues, e.g., cantilever overhangs cause high wind forces on buildings and hence not employed anymore by architects of those countries. This also eliminates the possibility of placing any objects on them by residents/users. Draft IS:1893 gives expressions to estimate the design lateral force for determining the adequacy of the connectors between the NSEs and the SEs to which they are connected. In Clause 7.13.1.2, the Draft IS:1893 clarifies that the clauses therein are applicable only when the NSE does not directly modify the strength or stiffness of the SEs of the building, or significantly add to the mass of the building. In general, an NSE is said to be having significant mass, if its mass exceeds 20% of that of floor on which it is anchored or 10% of total mass of building in which it is present. For the other NSEs that alter the stiffness or mass of the building, the NSE in discussion should be treated as a SE; all provisions relevant to SEs shall be applicable to this so called NSE. This element should be included in the structural analysis of the building; the forces required to connect this element to the other SEs be determined accordingly. For example, unreinforced masonry (URM) infill walls should be considered as structural elements for response under in-plane loading. When these URM infills adjoin structural columns, they can foul with the movement of the columns, cause short-column effect and seriously alter the building response. 2.3.1 Design Lateral Force for SEs When buildings shake during earthquakes, the level of accelerations in the buildings can be more than that at the ground (PGA: Peak Ground Acceleration), depending on the natural period T of the building. This is reflected in the design acceleration spectrum value Sa/g given by Eq.(2.11) (Figure 2.15):
2.5 0.00 T 0.40 1.00 0.40 T 4.00 for Soil Type I : rocky or hard soil sites T 2.5 0.00 T 0.55 Sa 1.36 . 0.55 T 4.00 for Soil Type II : medium soil sites g T 2.5 0.00 T 0.67 1.67 0.67 T 4.00 for Soil Type III : soft soil sites T
(2.11)
The design lateral force for structural elements (SEs) is given by Eq.(2.12):
VB
ZI Sa 2R g
W ,
(2.12)
where Z is the Seismic Zone Factor (Table 2.2), I the Importance Factor, R the Response Reduction Factor, and W the Seismic Weight of the Building. The factors Z, I, R and W are defined by IS:18932004. Eq.(2.11) suggests that the acceleration experienced by the building can be up to 2.5 times larger than the peak ground acceleration (PGA). This information is important in the design of NSEs also.
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Table 2.2: Seismic Zone Factor Z of the location where the building in which the NSE is present as per IS:1893-2004 Seismic Zone Z
V 0.36
IV 0.24
III 0.16
II 0.10
Design Acceleration Spectrum (S a/g)
Note: The zone in which a building is located can be identified from the Seismic Zone Map of India given in IS:1893-2004, sketched in Figure 2.16 of this document.
3.0 Soil Type I Soil Type II Soil Type III
2.0
1.0
0.0 0.0
1.0
2.0
3.0
4.0
Natural Period T
Figure 2.15: Design Acceleration Spectrum for Design of SEs: As per IS:1893-2004, design acceleration value depends on the natural period T of the building and soil type
Figure 2.16: Sketch of Seismic Zone Map of India: sketch based on the actual seismic zone of India map given in IS:1893-2004
2-13
2.3.2 Design Lateral Force for NSEs Clause 7.13.3 of Draft IS:1893 gives the design lateral force Fp for the design of the NSEs as:
Fp
Z x ap I W , 1 h Rp p p 2
(2.13)
where Z is the Seismic Zone Factor (Table 2.2), Ip the Importance Factor of the NSE (Table 2.3), Rp the Component Response Modification Factor (Table 2.4), ap the Component Amplification Factor (Table 2.4), Wp the Weight of the NSE, x the height of point of attachment of the NSE above top of the foundation of the building, and h the overall height of the building. Table 2.3: Importance Factors I p of NSEs as per Draft IS:1893 NSE Component containing hazardous contents Life safety component required to function after an earthquake (e.g., fire protection sprinklers system) Storage racks in structures open to the public All other components
Ip 1.5 1.5 1.5 1.0
The acceleration at the point of attachment of the NSE to the SE depends on peak ground acceleration, dynamic response of the building, and location of the element along the height of the building. In Eq.(2.13), the acceleration at the point of attachment is simplified and is considered to be linearly varying from the acceleration at the ground taken as 0.5Z to the acceleration at the roof taken to twice as much, i.e., Z. The component response modification factor Rp reflects the ductility, redundancy and energy dissipation capacity of the NSE and its attachment to the SE. There is not much research done on estimation of these factors. The component amplification factor ap reflects the dynamic amplification of the NSE relative to the fundamental natural period T of building in which the NSE is present. Experimental research studies using shake tables are required to evaluate fundamental natural period of the NSE, which may not be feasible for all the NSEs employed in the architectural and civil engineering practice. Hence, as a simplification of the design process, the connection of the NSE to the SE is designed without needing the value of T of the building or that of the NSE. Values of ap and Rp given in Draft IS:1893 and reproduced in this document (Table 2.2) are taken from the NEHRP provisions (FEMA 369, 2001); these empirically specified values are based on “collective wisdom and experience of the responsible committee”. The NSEs with flexible body are assigned ap of 2.5, and that with rigid body of 1.0. Values of Rp are taken as 1.5, 2.5 and 3.5 for low, limited and high deformable structures, respectively. Values of ap lower than those specified in Table 2.2 are permitted provided detailed dynamic analyses are performed to justify the same; in any case, ap shall not be less than 1.0, that is assigned for equipment that are generally rigid and are rigidly attached. ap is assigned a value of 2.5 for flexible components and flexibly attached components. The expression given in Eq.(2.13) for the design lateral force Fp is a simplified one for determining the safety of the NSE. In most NSEs, the users (Architects and Engineers) would be required to question manufacturers of the NSEs of the safety of the NSE under this force Fp applied in the random sense that earthquakes impose these forces on the NSE, and not in a static sense. Manufacturers, who are sensitive to the safety of NSEs in earthquakes, tend to conduct full scale shake table tests at their end, before releasing the NSE into the market for sale.
Table 2.4: Coefficients ap and Rp of Architectural, Mechanical and Electrical NSEs as per Draft IS:1893 S.No. 1
2
Item Architectural Component or Element Interior Nonstructural Walls and Partitions Plain (unreinforced) masonry walls All other walls and partitions Cantilever Elements (Unbraced or braced to structural frame below its center of mass) Parapets and cantilever interior nonstructural walls Chimneys and stacks where laterally supported by structures. Cantilever elements (Braced to structural frame above its center of mass) Parapets Chimneys and stacks Exterior Nonstructural Walls Exterior Nonstructural Wall Elements and Connections Wall Element Body of wall panel connection Fasteners of the co nnecting system Veneer High deformability elements and attachments Low deformability and attachments Penthouses (except when framed by and extension of the building frame) Ceilings All Cabinets Storage cabinets and laboratory equipment Access floors Special access floors All other Appendages and Ornamentations Signs and Billboards Other Rigid Components High deformability elements and attachments Limited deformability elements and attachments Low deformability elements and attachments Other flexible Components High deformability elements and attachments Limited deformability elements and attachments Low deformability elements and attachments Mechanical and Electrical Component/Element General Mechanical Boilers and Furnaces Pressure vessels on skirts and free-standing Stacks Cantilevered chimneys Others Manufacturing and Process Machinery General Conveyors (non- personnel) Piping Systems High deformability elements and attachments Limited deformability elements and attachments Low deformability elements and attachments HVAC System Equipment Vibration isolated Non-vibration isolated Mounted in-line with ductwork Other Elevator Components Escalator Components Trussed Towers (free-standing or guyed) General Electrical Distributed systems (bus ducts, conduit, cable tray) Equipment Lighting Fixtures
2-14
ap
Rp
1.0 1.0
1.5 2.5
2.5 2.5
2.5 2.5
1.0 1.0 1.0
2.5 2.5 2.5
1.0 1.0 1.25
2.5 2.5 1.0
1.0 1.0 2.5
2.5 1.5 3.5
1.0
2.5
1.0
2.5
1.0 1.0 2.5 2.5
2.5 1.5 2.5 2.5
1.0 1.0 1.0
3.5 2.5 1.5
2.5 2.5 2.5
3.5 2.5 1.5
1.0 2.5 2.5 2.5 1.0
2.5 2.5 2.5 2.5 2.5
1.0 2.5
2.5 2.5
1.0 1.0 1.0
2.5 2.5 1.5
2.5 1.0 1.0 1.0 1.0 1.0 2.5
2.5 2.5 2.5 2.5 2.5 2.5 2.5
2.5 1.0 1.0
5.0 1.5 1.5
2-15
The force values Fp arrived at using Eq.(2.13) provide a lower limit of seismic design force for the design of NSEs; one can use higher level of forces for this design, if detailed analysis performed shows the same. For NSEs of that are important or dangerous, detailed nonlinear time history analyses should be conducted of the buildings, which the NSE is present, under different ground motions, to determine the actual shaking experienced at the base of the NSE to determine the force experienced by the NSE. Alternately, seismic structural analysis can be performed using the design acceleration response spectrum at the base of the building and the design acceleration response spectrum determined at the level of the connection between the NSE and SE; this design acceleration spectrum at the base of the NSE is called the floor response spectra. The design lateral force Fp given by Eq.(2.13) is valid for NSEs that are attached to horizontal surfaces of SEs as well as to vertical surfaces of SEs. For NSEs that are projecting out of horizontal surfaces of SEs, Fp is the horizontal force tangential to horizontal surfaces of SEs to which the NSEs are attached. And, for NSEs that are projecting out of vertical surfaces, Fp is the vertical force tangential to vertical surfaces of SEs tow which the NSEs are attached. Even though the vertical and horizontal earthquake vibrations of the ground and of the building (at different levels) are different, for the purposes of design of normal SEs, no distinction is being made in the estimation of the design lateral force Fp for connecting NSEs to vertical or horizontal surfaces of SEs. This is attributed to numerous other approximations involved in the derivation of the expression for Fp . When NSEs are mounted on vibration isolation system, the Draft IS:1893 requires the connections between the NSEs and the SEs to be designed for twice the value of the design lateral force Fp . The mass of the NSE along with the flexible mounts employed in the isolation system can be visualized to have a fundamental natural mode of vibration and an associated natural period. The isolated NSE will experience amplification of its vibrations when this fundamental natural mode of its vibration experiences resonance-like condition with one or more natural modes of vibration of the building on which it is mounted. Hence, the NSE placed on a vibration isolator can experience higher seismic accelerations, than if it is rigidly mounted on the SE without the isolator. The Draft IS:1893 recognises this effect. 2.3.2.1 Design Lateral Force for Connection of NSEs
Draft IS:1893 requires that connections between nonstructural elements (NSEs) and structural elements (SEs) should be designed for twice the design seismic force Fp required for the design of the NSE given as per Eq.(2.13). This factor is drawn from the fact that when a force is applied suddenly its effect is about twice as much as that if it were applied statically (Figure 2.17). F W
t
W
F W
t
2W
W
Fmax = W
~2
Fmax ~ 2W
(a) (b) Figure 2.17: Influence of dynamic loading – Difference in the force and deformation experienced by the spring when loaded (a) gradually and (b) suddenly
2-16
The connections can be by bolting, welding or any other method that offers positive fastening without relying on frictional resistance produced by the effect of gravity. Here, friction forces induced by gravity are required to be ignored because the vertical ground vibrations during earthquake shaking may reduce the net effect of gravity and thereby the effective weight of the NSE offering restoring effects. When these connections are outdoors and exposed to elements of nature, the method of fastening should be corrosion resistant, ductile and having adequate anchorage into the SE. This is particularly a concern in façade works and exterior panels.
2.4 Examples Calculation of Design Lateral Force for NSEs
3 @ 4m
4.5m
4 @ 3m
Limited cases of typical NSEs are considered in this section to demonstrate how to calculate the forces required securing these NSEs to the SEs. There are many documents that guide the design related to earthquake safety of NSEs. In this document, these forces are calculated as per the provisions given in the Draft IS:1893 published by the Gujarat State Disaster Management Authority, Gandhinagar (Gujarat), and available on the website www.nicee.org of the National Information Center of Earthquake Engineering (NICEE), IIT Kanpur. The examples considered are categoriesed into three groups, namely (i) NSEs anchored to only Horizontal LLRSS Elements, (ii) NSEs anchored to only Vertical LLRSS Elements, and (iii) NSEs anchored to both Horizontal and Vertical LLRSS Elements. In this section, most NSE examples are studied with reference to a benchmark building (Figure 2.18) in high seismic region. Except when otherwise stated, the benchmark building is a 5storey unreinforced masonry infilled RC frame building with four bays in X-direction in plan and three in Y-direction; bay width is 4m in each direction. The height of a typical storey is 3m and that of the ground storey 4.5m, with foundation being 1.5m below ground level. Columns are considered hinged at the top of the foundation. The column size is 400×400 mm and beam size 300×550 mm; the flexural rigidity of the column section is about half that of the beam section, even though their axial areas are about the same. The thickness of the floor slabs is 150 mm. The grade of concrete used in the RC building is M25. For the purposes of studying the NSEs in this book, URM infills are not modeled in the building; only bare frame is considered. No inelasticity is considered in the building SEs; it is expected to remain elastic. But, inelasticity is considered in the NSEs.
4 @ 4m Figure 2.18: Benchmark Building – It is a 5-storey RC moment frame building with URM infills
2-17
2.4.1 NSEs anchored only to Horizontal LLRSS Elements 2.4.1.1 Plastic Water Storage tanks on Roof Slab
Consider earthquake safety of the water storage tank (Figure 2.19) placed atop the 5-storey RC frame benchmark building. The tank is made of high density plastic, and has capacity to hold 5,000L of water. Its diameter is 2m and height 2m. The mass of the empty tank is 100 kg. When the ground shakes during earthquakes, three possibilities arise, namely: (1) the tank can slide horizontally, (2) the tank can rock and eventually topple, or (3) the tank can slide as well as rock (and topple). To secure it against earthquake effects, the tank should be fastened to the roof slab.
Water Tank
1000
Fp 1000 Eart hquake Shaking of Roof Slab
Roof Slab
Fbolt
Wp 1000
1000
Figure 2.19: Plastic water tank on roof top – forces acting on it
The design of the fastener between the tank and the roof slab is governed by the design lateral force Fp given by Eq.(2.13). Considering that the building is located in Seismic Zone V in India, the Seismic Zone Factor Z is 0.36 (Table 2.1). (x/h) is 1.0, since the height x of point of attachment of the tank above top of the foundation of the building is the same as the overall height h of the building. The Component Amplification Factor ap is 1.0 (Table 2.3) for a water tank, and the Component Response Modification Factor Rp is 1.5 (Table 2.3). Further, the Importance Factor I p is 1.0 (Table 2.2). Thus, Fp
0. 36 16.5 1 1. 0 5100 9.8 0. 24 49 ,980 11,995 N 1 2 16.5 1.5
The overturning moment at the base of the tank is due to Fp acting at a height of h/2 from the base of the tank, and the restoring moment due to tank weight W p . Clearly, Fp
h 1.25 2. 0 W p 0.24W p Wp 0.85 W p 2 2 2 2
Thus, no overturning is expected to occur; no bolt is required to prevent overturning, but it may topple if the force is higher. Also, bolts are required to prevent sliding of the tank. If the coefficient of friction is 0.3, the lateral frictional resistance force is (0.3×5100×9.8=) 14,996 N. Thus, the demand is 11,995 N and the resistance is more than that. Thus, sliding is not likely to occur. In any case, friction is not to be relied up in the safety of systems during earthquake shaking, because vertical accelerations induced on the RC slabs can render the frictional resistance ineffective. Thus, positive systems are required to resist the lateral force and secure the generator from sliding. For resisting a lateral force of 11,995N, four bolts of 12mm are considered. The lateral shear carrying capacity of the four bolts available (as per Clause 8.4 of IS:800-2007) is 2 fy 1 12 250 1 59, 362N , Vn 4 A v 4 4 3 m0 3 1.1
and, the lateral force demand calculated (as per Clause 8.4 of IS:800-2007 is Vd f V 1.5 11,995 17 ,993kN . Thus, demand is less than the supply and hence, four MS bolts of 12mm diameter are sufficient to prevent the tank from sliding.
2-18
2.4.1.2 Masonry Parapet Wall on Roof Slab
Consider the earthquake safety of the masonry parapet wall on the roof of the benchmark building (described at the start of Section 2.4 of this chapter) along the entire outer perimeter. The masonry parapet wall is 250mm thick and 900mm tall. Often, these parapets are merely rested on the roof slab with no positive anchorage or connection to the roof slab (Figure 2.20) anchorage like reinforcement bars from roof slab projecting into the masonry parapet. Hence, they are vulnerable to lateral shaking generated during earthquakes. This section explains how to ensure that masonry parapet walls are made safe to resist earthquake shaking. lp hp
tp Figure 2.20: Segment of a masonry parapet wall – geometry of a small segment considered Towards ensuring safety of masonry parapets under earthquake shaking, the design lateral force Fp appearing on the parapet wall is calculated as per Eq.(2.13). For the masonry parapet wall, both x and h are same, since the parapet rests on top of the roof slab at a height x=h from the top of the foundation of the building. For performing hand-calculations, this force Fp is applied at centre of mass of parapet wall (Figure 2.21), i.e., at its mid-height, because masonry parapet is uniform in geometry along its height. This force can cause (a) sliding of the wall horizontally, (b) toppling of the masonry parapet wall, or (c) crushing of the masonry of the parapet in compression at the base of the parapet on top of the roof slab, even if items (a) and (b) are satisfied. (a) Sliding of Parapet Wall The sliding shear stress at the base of parapet (Figure 2.21b) is given by Fp l p tp ,
(2.14)
where lp and t p are length and thickness of the parapet wall segment considered. As per
Clause 5.9.1.1 of Draft IS1905 (IITK-GSDMA, 2005b), should be less than the permissible shear stress f s given by f s 0.1 f d 6 0.5MPa , where f d is the actual compressive stress under dead
load, given by f d W p l p tp . (b) Toppling of Parapet Wall Under the design lateral force Fp acting on the masonry parapet wall, the parapet wall can rotate about its bottom toe on top of roof slab and topple. The overturning moment M 0 on the parapet is caused by the horizontal force Fp acting on the masonry segment being considered for overturning check at half height h p / 2 of the parapet (Figure 2.21c), and is given by
M 0 Fp
hp 2
,
where Fp = Design Lateral Force on the parapet as defined in Eq.(1), and
hp = Full height of parapet from the top of the slab.
(2.15)
2-19
Masonry Parapet
0.5hp
Fp
Fp W p
Earthquake Shaking of Roof Slab
0.5hp
Fp W p
W p
Point of rotation
tp
Roof Slab
(a)
(b)
Fp
(c)
Fp W p
W p
Bending stresses
Compression only bending stresses fo x0
(d)
(e)
Figure 2.21: Masonry Parapet Wall on Roof Slab – (a) Forces acting on the parapet wall due to seismic force, (b) Sliding: shear stresses developed at the base of parapet wall due to seismic force, (c) Overturning: shear overturning moment causing toppling of the masonry parapet wall, (d) Loss of Contact: tensile and compressive stresses at the base of the parapet wall, and (e) Compression only contact: resistive stress assuming tensile stress to be zero at the base of the parapet wall
And, the restoring moment M r on the parapet is caused by self-weight W p of masonry parapet segment considered acting at mid-width t p / 2 of the parapet wall, and is given by
Mr Wp
tp 2
,
(2.16)
where W p = Self-weight of the parapet, and
t p = Thickness of the parapet wall. For safety against overturning, necessarily
M r ( FS ) M 0 ,
(2.17) where FS = Factor of Safety of the parapet against overturning, and may be taken as 1.5 as per Clause 4.2.2.7 of Draft IS1905.
2-20
(c) Crushing of Parapet Wall The crushing of parapet wall can occur due to rotation of the parapet about the heal/toe of the wall due to overturning moment acting about that point leading to bending compressive and tensile stresses in the masonry parapet wall (Figure 2.21d). This stress together with vertical compressive stress due to self-weight of the parapet wall, gives the net compressive stress in the masonry wall at its toe. The stresses f bc ,heal and f bc ,toe at heal and toe of the parapet wall (on top of the slab), respectively, are:
f bc ,heal f bc ,toe
Wp A
Wp A
W p 6M 0 M0 Z l p t p l p tp2 Wp 6 M0 M0 Z l p t p l p t 2p
(2.18) (2.19)
where the parameters are as defined earlier in this section. This net axial-cum-flexural compressive stresses or tensile stresses should not exceed their corresponding permissible limits specified in Draft IS1905. To verify the above, the permissible flexural stresses in compression and tension are taken from Draft IS1905. The permissible flexural compressive stress f bc ,perm for masonry wall as per Clause 5.7.1 of Draft IS1905 is f bc ,perm 1.25 f a , where f a as per Clause 5.6.2 of Draft IS1905 is
f a k s k p k a f b , in whic h fb is the permissible basic compressive stress in masonry for the grade of mortar and masonry units used, and k s is Stress Reduction Factor (Table 11 of Draft IS1905), k p Shape Modification Factor as per Clause 5.6.2.3 of Draft IS1905, and k a Area Reduction Factor as per Clause 5.6.2.2 of Draft IS1905. And, the permissible flexural tension stress f bt in masonry as per Clause 5.8 of Draft IS1905 is given in Table 2.5. Table 2.5: Permissible stress f bt in flexural tension as per Draft IS1905 Mortar Permissible Grade flexural tension stress fbt 0.07 MPa M1 or better
0.14 MPa 0.05 MPa
M2 0.10 MPa
Conditions
Bending in the vertical direction where tension developed is normal to bed joints Bending in the longitudinal direction where tension developed is parallel to bed joints provided crushing strength of masonry units is not less than 10 MPa Bending in the vertical direction where tension developed is normal to bed joints Bending in the longitudinal direction where tension developed is parallel to bed joints provided crushing strength of masonry units is not less than 7.5 MPa
Even if the parapet wall is safe under the overturning moments, it should be checked aganinst crushing of the toe at the base. This is further aggravated by net tensile stress at the heal exceeding the permissible tension values. In such a case, the base of the masonry parapet wall may be assumed to be under only varying compression (Figure 2.21e), neglecting the tensile capacity of the masonry wall. The compressive stress so calculated is compared against the permissible stress in compression. If this value exceeds the permissible value, the wall is rendered unsafe. Following are the force and moment equilibrium equations which give values of f 0 and x0 :
f 0 x0 l p W p , tp Wx 0 Wp M0 . 3 2
(2.20) (2.21)
2-21
Consider a single-brick 250mm thick 900 mm high masonry parapet at the roof of the benchmark four-storey building in seismic zone V, is unanc hored to the roof and simply rested on it. For calculations, take a 1000mm long segment of the parapet wall to assess its safety. The coefficients required for the calculation of design lateral force in Eq.(2.13) are taken as: Z = 0.36, ap = 2.5, Rp = 2.5, and Ip = 1. The design lateral force is given by:
0.36 16.5 2.5 1 4.5 1.62kN . 1 2 16.5 2.5 The shear stress due to applied design force Fp is calculated as per Eq. (2.14) to be Fp
1.62 0.001 0.0065MPa . 1 250
If the parapet has to be safe against sliding, should be smaller than the permissible shear stress f s at the base of the parapet wall. As per Eq.(3), in the calculation of permissible shear stress f s , the actual compressive stress f d is required, and is given by Eq.(4) as
fd
4.5 0.001 0.018 MPa . 1 0.25
Hence, the permissible shear stress as per Eq.(3) is
0.03 0.103MPa . 6 Since shear stress (=0.0065MPa) developed due to applied design force Fp is less than the permissible shear strength f s (=0.103MPa), no sliding is expected. f s 0.1
The design lateral force Fp can cause the masonry parapet to topple; hence, the wall is checked against overturning. Overturning moment M 0 caused due to design lateral force Fp is given by Eq.(5) as
M 0 1.62 0.450 0.73 kNm The restoring moment M r which can stop the parapet wall from toppling is generated by its selfweight. As per Eq.(6), this restoring moment M r is M r 4.5
0.25 0.56kNm 2
The factor of safety available in the unbraced masonry parapet wall is:
FS
M r 0.56 0.77 . M o 0.73
Since the Factor of Safety FS required is 1.5 against overturning as per Clause 4.2.2.7 of Draft IS1905, the parapet wall will topple. The most effective way of bracing a masonry parapet walls against out-of-plane collapse during earthquake shaking, is by providing tie-columns and tie-beams around it (Figure 2.22). The size of tie-columns and tie-beams can be obtained from the standard literature on Confined Masonry Construction (Brzev, 2006). Typically, the cross-section of the tie column has the width of the wall and the other dimension can vary from 150mm to the thickness of the masonry wall being used. These are provided in the same locations as those of the building columns. Many a time, the building columns are themselves extended, with nominal reinforcement provided in them (4 longitudinal deformed bars of 10mm diameter, with 6mm transverse ties at 200mm centres). A tie beam at the top of the parapet should be at least 75mm thick but resting over the full width of the parapet wall. At least two bars of 10mm diameter are required as longitudinal bars with 6mm transverse ties at 200mm centres.
2-22
Tie Beams
Tie Columns
Figure 2.22: Protecting the parapet wall against lateral instability during earthquake shaking, by providing tie-columns and tie-beams
2.4.1.3 False Ceiling and other object hangings from Roof/Floor Slab
Consider the false ceiling made of gypsum board hung with steel wire hangers from the roof slab of the benchmark building (described at the start of Section 2.4 of this chapter) (Figure 2.23). The gypsum board of the false ceiling is 12mm thick, and the steel wire hangars are 3mm in diameter and placed at 600mm centers in both directions in plan. Since it is hung from the roof slab, it is necessary to verify if the false ceiling system will pull out especially during the vertical shaking of the building during earthquakes. Towards ensuring safety of the false ceiling system under earthquake shaking, the design vertical force Fp appearing on the false ceiling system is calculated as per Eq.(2.5). For the false ceiling system at the roof slab level, both x and h are same, since the false ceiling system hangs from the roof slab at a height x=h from the top of the foundation of the building. For performing handcalculations, this force Fp is applied at centre of mass of false ceiling system, i.e., at its mid-width of the false ceiling, because it is uniform in geometry in its plan. This force can cause downward pullout of the hangar wires from the RC slab. Hanger Wires
RC Roof Slab
Hook
False ceiling board Vertical Roller
Hanger Wire
Gypsum False Ceiling Board
Figure 2.23: Schematic of details of hanging a false ceiling – a hook is employed to hold the hangar wire of false ceiling connection to the slab
2-23
Consider the false ceiling in one grid bay in plan, namely in an area of size 4m×4m in plan. Let the hangar wire grid be 0.6m×0.6m. Hence, about 45 wires are required to hold the false ceiling system in each grid bay. For simplicity of calculations, let there be 48 wires in all, so that there are 3 wires per square meter of the plan area. If the weight of the gypsum board is 20 kN/m 3, the weight per unit plan area of the 120mm thick gypsum board false ceiling is (20.0 × 0.12 =) 2.4kN/m2. The design vertical force is given by:
Fp
0.36 16.5 1.0 1 2.4 0.144 2.4 346 N / m 2 . 1 2 16.5 2.5
In addition to carrying the above dynamic shaking related force, the springs should be capable of carrying the weight of the gypsum board also. The weight of 1m2 of the gypsum board is 2.4kN. Hence, the total force to be carried by three hangar wires in tension in 1m2 plan area is (2,400 N + 346N) ~2,750 kN. The axial load safety of each 3mm diameter MS wire is estimated using the Indian Steel Code IS:800-2007 and the Indian Concrete Code IS:456-2000. Firstly, the design axial tension is calculated using a Partial Safety Factors f for loads of 1.5 for dead load and 1.5 for earthquake load, as per Clause 5.3.3 of IS:800-2007. Hence, the design axial tension to be carried is (1.5×2,400 + 1.5×236 =) 4,120 kN. In calculating the design tensile capacity of each wire, there are two items, namely design strength from rupture and from yielding. The design strength Tdg due to yielding of the gross section of one wire (as per Clause 6.2) is given by: 2 fy 250 3.0 Ag Tdg 1,607 N , 2 1.1 m0 and, design strength Tdn due to rupture of critical section of one wire (as per Clause 6.3) is given by 2 fu 400 3.0 0.9 An Tdn 2 ,036 N , 0.9 2 1.25 m1
Thus, for all three wires in each square meter of the plan of the gypsum board false ceiling system, the design capacity corresponds to the smaller of the two capacities (as per Clause 6.1) and is
Td 3 1,607 4 ,821 N
Since this is more than the demand of 4,120 N, the 3mm diameter wires are capable of carrying the tension. Two additional checks are required to ensure that the 3mm hangar wire screw does not pull out (Figure 2.24) due to failure of (a) direct bond between the wire and the slab, and (b) 45° conical pull-out of the concrete in the slab along with the screw of the 3mm wire.
RC Roof Slab Lp
hp Hangar wire
Pull-out force F p
(a)
Hangar wire
Pull-out force F p
(b)
Figure 2.24: Hangar wires of false ceilings – (a) direct bond failure, and (b) conical failure of concrete
2-24
There are two mitigation measures for securing the safety of false ceiling systems, namely (a) Employing large diameter MS hooks (with hooks projecting out under the soffit of the RC slab locked into the reinforcement bars of the slab prior to the casting of the roof slab) for holding the hangar wires of the false ceiling and offering positive anchorage of the false ceiling system into the RC slab (Figure 2.25a); and (b) Employing formal secondary structural members framing between the mains structural beams to carry the loads caused by the false ceiling (Figure 2.25b). These secondary beams may be made of cold-form steel sections with hinge detailing at the ends. Secondary beam
RC Roof Slab
RC Roof Slab Main beam
False Ceiling Board
Hooks
Main column
Hangar Wires
Hangar wires
(a)
(b)
Figure 2.25: Mitigation measures for securing false ceiling systems to roof/floor slabs – (a) Positive Anchorages from reinforcement bars of slab to hang the false ceiling from, and (b) Secondary structural systems running between the structural beams to carry just the false ceiling loads
2.4.1.4 Machines on Floor Slabs
Consider earthquake safety of a machine unit (Figure 2.26) placed atop the 5-storey RC frame benchmark building. The machine has 1,800 kg mass, and has size 3.2m×1.15m in plan and 1.5m in height. When the ground shakes during earthquakes, the machine can (1) slide off at the base, or (2) topple and fall sideways along its narrow dimension direction. To secure the machine unit against these earthquake effects, it should be fastened to the roof/floor slab.
Generator
Machine
750
Fp 750
Anch or Bolts Earthquake Shaking of Building
Roof Slab
Fbolt
Wp 575
Figure 2.26: Machine unit rested on roof slab – forces acting on it
575
2-25
The design of the fastener between the machine and the roof slab is governed by the design lateral force Fp given by Eq.(2.5). Considering that the building is located in Seismic Zone V in India, the Seismic Zone Factor Z is 0.36 (Table 2.1). (x/h) is 1.0, since the height x of point of attachment of the machine above top of the foundation of the building is the same as the overall height h of the building. The Component Amplification Factor ap is 1.0 (Table 2.3) for machine, and the Component Response Modification Factor Rp is 2.5 (Table 2.3). Further, the Importance Factor Ip is 1.0 (Table 2.2). Thus,
0.36 16.5 1 1.0 1800 9.8 0.144 17 ,640 2 ,541N . 1 2 16.5 2.5 The overturning moment at the base of the machine is due to Fp acting at a height of h/2 from the base of the machine, and the restoring moment due to machine weight W p . Clearly, Fp
Fp
h b 0.750 0.575 Wp 0.144W p Wp 0.23Wp 2 2 2 2
Thus, no overturning is expected to occur under the action of the design lateral force; no bolt is required to prevent overturning. But, it may topple if the force is higher. Also, it is required to prevent sliding of the machine. If the coefficient of friction is 0.45, the lateral frictional resistance force is (0.45×1800×9.8=) 7,938 N. Thus, the demand is 2,541 N and the resistance is more than that. Thus, sliding is not likely to occur. In any case, friction is not to be relied up in the safety of systems during earthquake shaking, because vertical accelerations induced on the RC slabs can render the frictional resistance ineffective. Thus, positive systems are required to resist the lateral force and secure the machine from sliding. For resisting a lateral force of 2,541N, four bolts of 12mm are considered. The lateral shear carrying capacity of the four bolts available (as per Clause 8.4 of IS:800-2007) is 2 fy 1 12 250 1 59, 362N , Vn 4 A v 4 4 3 m0 3 1.1
and, the lateral force demand calculated (as per Clause 8.4 of IS:800-2007 is Vd f V 1.5 2 ,541 3,812 kN . Thus, demand is less than the supply and hence, four MS bolts of 12mm diameter are sufficient to prevent the machine from sliding. 2.4.2 NSEs anchored only to Vertical LLRSS Elements 2.4.2.1 Book Shelf supported on Wall
Consider earthquake safety of the water storage tank (Figure 2.27) placed atop the 5-storey RC frame benchmark building. The book shelf including its contents has a mass of 150 kg. It is 1.5m long, 0.45m wide and 0.9m tall. When the ground shakes during earthquakes, two possibilities arise, namely: (1) the shelf pull out horizontally from the wall, owing to insufficient connections, or (2) the shelf can cause collapse of the wall in the out-of-plane direction, if it is made of masonry wall. To secure it against the earthquake effects, the shelf should be fastened to the roof slab with screws and the out-of-plane safety of the wall should be ensured during strong ground shaking. The design of the fastener between the shelf and the wall is governed by the design lateral force Fp given by Eq.(2.5). Considering that the building is located in Seismic Zone V in India, the Seismic Zone Factor Z is 0.36 (Table 2.1). Since the point of attachment of the shelf is 1.5m above the floor level in the fifth storey, x=15m and h=16.5m. The Component Amplification Factor a p is 2.5 (Table 2.3) for a shelf fastened to the vertical wall, and the Component Response Modification Factor Rp is 2.5 (Table 2.3). Further, the Importance Factor Ip is 1.0 (Table 2.2). Thus,
2-26 Book Shelf
Book Shelf
Fscrew
15000
Fp
450
450
Masonry Wall
Wp Eart hquake Shaking of Building
225
15000 above top of foundation level
225
Figure 2.27: Book shelf on masonry wall – forces acting on it
0.36 15.0 2.5 1.0 150 9.8 0.345 1, 470 508N 1 2 16.5 2.5 The overturning moment at the base of the shelf is due to Fp acting at its mid-height and its weight W p . And, the restoring moment is due to the bolt at the top of the shelf. Clearly, Fp
Fbolt
1 h b 1 0.900 0.450 1, 470 622 N 508 Fp Wp h 2 2 0.900 2 2
The lateral force demand calculated for the two bolts at the top (as per Clause 8.4 of IS:800-2007 is Vd f V 1.5 622 933N . Thus, the two bolts at the top of the shelf should carry a tension of 933N corresponding to Fp and the two at the bottom a shear force of 508N corresponding to Wp ; this is a simplistic but conservative estimate of forces. Consider two 6mm diameter MS bolts for resisting a lateral force of 506N by the top bolt. The axial load safety of each 6mm diameter MS bolt is estimated using the Indian Steel Code IS:8002007 and the Draft Indian Masonry Code IS:1905-2006. Firstly, the design axial tension is calculated using a Partial Safety Factors f for loads of 1.5 for dead load and 1.5 for earthquake load, as per Clause 5.3.3 of IS:800-2007. Hence, the design axial tension to be carried is 933 kN. In calculating the design tensile capacity of each wire, there are two items, namely design strength from rupture and from yielding. The design strength Tdg due to yielding of the gross section of one bolt (as per Clause 6.2) is given by: fy Tdg m0
2 A g 250 6. 0 12, 852 N , 1. 1 2
and, the design strength Tdn due to rupture of the critical section of one bolt (as per Clause 6.3) is given by f Tdn u m1
2 0.9 An 400 0.9 6. 0 16, 286 N , 1. 25 2
Thus, for the two bolts on top of the shelf, the design capacity corresponds to the smaller of the two capacities (as per Clause 6.1) and is Td 2 12 ,852 25 ,704 N
Since, this is more than the demand of 622 N, the 6mm diameter bolts are capable of carrying the tension.
2-27
The lateral shear carrying capacity available of the two bolts at the bottom of the shelf (as per Clause 8.4 of IS:800-2007) is 2 fy 1 6 250 1 7 , 420N , Vn 2 Av 2 4 3 m0 3 1.1
and, the lateral force demand calculated (as per Clause 8.4 of IS:800-2007 is Vd f V 1.5 508 762N . Thus, demand is less than the supply and hence, two MS bolts of 6mm diameter are sufficient to prevent the shelf from shearing off from the wall. It is required to ensure that the top bolts holding the shelf should not pull out in bond from the masonry wall. The potential of the shelf against toppling under lateral shaking is verified by performing time history analysis of the building with the shelf on the masonry wall in the fifth storey of the building. The shelf is modeled as a prismatic rigid mass of the same dimensions with springs connecting it to the masonry wall at its four corners (Figure 2.31). The center of mass of the object is considered to be at mid-height. The vertical and horizontal springs have linear properties; the stiffness values are corresponding to the screws used to secure them. The building base is subjected to the 1940 El Centro earthquake ground motion (S00E component; 0.31g peak ground acceleration). The time history response of the book shelf shows that the bolt develops a force of 2503 N, which is less than the design force of the bolt. Hence, the bolt design is sufficient. 2.4.2.2 Cupboards
Consider earthquake safety of a cupboard (Figure 2.28) placed on the fifth storey of the 5storey RC frame benchmark building. The cupboard including its contents has a mass of 2,000 kg. It is 0.9m long, 0.45m wide and 2.1m tall. When the ground shakes during earthquakes, (1) the cupboard can topple laterally outwards from the wall if simply rested on the floor slab without any anchorage to the adjoining masonry wall, or (2) the cupboard can cause collapse of the masonry wall in the out-of-plane direction. To secure it against earthquake effects, the cupboard should be fastened to the wall with screws and the out-of-plane safety of the wall should be ensured during strong ground shaking.
Cupboard
Fbolt
Cupboard
13500
Fp Masonry Wall
1050
Wp Slab
225
225
Eart hquake Shaking of M asonry W all
Figure 2.28: Cupboard adjacent to masonry wall – forces acting on it
1050
2-28
The design of the fastener between the cupboard and the wall is governed by the design lateral force Fp given by Eq.(2.5). Considering that the building is located in Seismic Zone V in India, the Seismic Zone Factor Z is 0.36 (Table 2.1). Since the point of attachment of the cupboard is on the floor level in the fifth storey, x=13.5m and h=16.5m. The Component Amplification Factor ap is 1.0 (Table 2.3) for a shelf fastened to the vertical wall, and the Component Response Modification Factor Rp is 1.5 (Table 2.3). Further, the Importance Factor Ip is 1.0 (Table 2.2). Thus,
0.36 13.5 1.0 1.0 2 ,000 9.8 0.216 19 ,600 4 ,234N 1 2 16.5 1.5 The overturning moment at the base of the cupboard is due to Fp acting at its mid-height and the restoring moment due to its weight W p . Clearly, h b 1.05 0.45 Fp W p 0.216 Wp Wp 0.112 Wp 2 2 2 2 Fp
Thus, cupboard is not likely to topple under the design lateral force. But, it may topple if the force is higher. Also, it is necessary to ensure that the cupboard will not slide under the same lateral force.
Consider two 6mm diameter MS bolts for resisting a lateral force of 4,234N. The axial load safety of each 6mm diameter MS bolts is estimated using the Indian Steel Code IS:800-2007 and the Draft Indian Masonry Code IS:1905-2006. Firstly, the design axial tension is calculated using a Partial Safety Factors f for loads of 1.5 for dead load and 1.5 for earthquake load, as per Clause 5.3.3 of IS:800-2007. Hence, the design axial tension to be carried is (1.5×4,234 =) 6,351 kN. In calculating the design tensile capacity of each bolt, there are two items, namely design strength from rupture and from yielding. The design strength Tdg due to yielding of the gross section of one bolt (as per Clause 6.2) is given by: fy Tdg m0
2 A g 250 6. 0 12, 852 N , 1. 1 2
and, design strength Tdn due to rupture of critical section of one bolt (as per Clause 6.3) is given by 2 f 400 6.0 16, 286 N , Tdn u 0.9 An 0.9 1. 25 2 m1
Thus, for the two bolts on top of the shelf, the design capacity corresponds to the smaller of the two capacities (as per Clause 6.1) and is Td 2 12 ,852 25 ,704 N
Since, this is more than the demand of 6,351N, the two 6mm diameter bolts are capable of carrying the tension and prevent sliding of the cupboard. Additionally, it is required to check to ensure that the top bolts holding the shelf should not fail in bond of the masonry wall. If it is not capable of resisting this out-of-plane action, a new mitigation measure is required. And, when anchors are provided (Figure 2.29), the axial force in the top bolt is 20,420 N, which is more than the design force of the bolt. Hence, the design of the bolt needs to be revised.
Cross- runn er between RC columns (hinged at ends)
NSE Cupboard
Masonry wall
Figure 2.29: Alternate mitigation measure to prevent out-of-plane collapse of cupboard and masonry wall– cupboard is connected to a cross-runner held between RC columns
2-29
2.4.2.3 TV and Table
Consider earthquake safety of a slim TV (Figure 2.30) placed on the fifth storey of the 5storey RC frame benchmark building. The TV has a mass of 10 kg. It is 0.6m long, 0.225m wide and 0.6m tall. The mass of the TV table and its contents is 50kg, and is 0.70m long, 0.45m wide and 0.9m tall. When the ground shakes during earthquakes, the TV can topple laterally in its thin direction, if simply rested on the TV table without any anchorage to the TV table or the adjoining masonry wall. To secure it against earthquake effects, the TV should be fastened to the TV table, which in turn to the masonry wall behind. TV & Table
TV
13500
Fp
600
50 Masonry Wall
TV Table
900
Slab
Eart hquake Shaking of Building
225
225
Figure 2.30: TV on TV table adjacent to masonry wall – forces acting on it
The design of the fastener between the TV and the TV table is governed by the design lateral force Fp given by Eq.(2.5). Considering that the building is located in Seismic Zone V in India, the Seismic Zone Factor Z is 0.36 (Table 2.1). Since the point of attachment of the TV is on the floor level in the fifth storey, x=13.5m+0.9m and h=16.5m. The Component Amplification Factor ap is 1.0 (Table 2.3) for a shelf fastened to the vertical wall, and the Component Response Modification Factor Rp is 1.5 (Table 2.3). Further, the Importance Factor I p is 1.0 (Table 2.2). Thus,
0.36 14.4 1.0 1.0 10 9.8 0.225 98 22 N 1 2 16.5 1.5 The overturning moment at the base of the TV is due to Fp acting at its mid-height and the restoring moment due to its weight W p . Clearly, h b 0.35 0.2 Fp W p 0.225W p Wp 0.061Wp 2 2 2 2 Fp
Thus, the TV is not likely to topple under the design lateral force. But, it may topple if the force is higher. Also, it is necessary to ensure that the TV does not slide under the same lateral force. Consider two 3mm diameter MS screws for resisting a lateral force of 22N in shear. The lateral shear carrying capacity of the two 3mm screws available (as per Clause 8.4 of IS:800-2007) is
f 1 3 2 250 1 Vn 2 Av y 2 1,855N , 4 3 m 0 3 1.1 and, the lateral force demand calculated (as per Clause 8.4 of IS:800-2007 is Vd f V 1.5 22 33N . Thus, demand is much less than the supply, and hence, two MS screws of 3mm diameter are sufficient to prevent the TV from shearing off from the TV table.
2-30
2.4.2.4 Gas Cylinder on Floor
Consider earthquake safety of a gas cylinder (Figure 2.31) placed on the fifth storey of the 5storey RC frame benchmark building. The gas cylinder including its contents has a mass of 40 kg. It is 0.3m in diameter and 0.75m in height. When the ground shakes during earthquakes, the gas cylinder can topple laterally outwards from the wall if simply rested on the floor slab without any anchorage to the adjoining masonry wall. To secure it against earthquake effects, the gas cylinder should be fastened to the wall. Gas Cylinder
13500
Wire rope
Gas Cylinder Masonry Wall
Fp
750
Slab
Wp Eart hquake Shaking of Building
~0
300
Figure 2.31: Gas cylinder rested on the floor slab adjacent to the masonry wall – forces acting on it
The design of the fastener between the gas cylinder and the wall is governed by the design lateral force Fp given by Eq.(2.5). Considering that the building is located in Seismic Zone V in India, the Seismic Zone Factor Z is 0.36 (Table 2.1). Since the point of attachment of the gas cylinder is on the floor level in the fifth storey, x=13.5m and h=16.5m. The Component Amplification Factor ap is 1.0 (Table 2.3) for a shelf fastened to the vertical wall, and the Component Response Modification Factor Rp is 1.5 (Table 2.3). Further, the Importance Factor I p is 1.0 (Table 2.2). Thus,
0.36 13.5 1.0 1.0 40 9.8 0.216 392 85N 1 2 16.5 1.5 The overturning moment at the base of the gas cylinder is due to Fp acting at its mid-height and the restoring moment due to its weight W p . Clearly, Fp
Fp
h b 0.75 0.3 Wp 0.216W p Wp 0.069 Wp 2 2 2 2
Thus, the gas cylinder is not likely to topple under design lateral force. But, it may topple, if force is higher. Also, it is necessary to ensure that the gas cylinder will not slide under same lateral force. Consider the gas cylinder chained to a hook that has a 3mm diameter MS screw for resisting a lateral force of 85N. The axial load safety of each 3mm diameter MS screws is estimated using the Indian Steel Code IS:800-2007 and the Draft Indian Masonry Code IS:1905-2006. Firstly, the design axial tension is calculated using a Partial Safety Factors f for loads of 1.5 for dead load and 1.5 for earthquake load, as per Clause 5.3.3 of IS:800-2007. Hence, the design axial tension to be carried is (1.5×85 =) 127 kN. In calculating the design tensile capacity of each screw, there are two items, namely design strength from rupture and from yielding. The design strength Tdg due to yielding of the gross section of one screw (as per Clause 6.2) is given by:
2-31
fy Tdg m0
2
Ag 250 3. 0 1,607 N , 1.1 2
and, the design strength Tdn due to rupture of the critical section of one screw (as per Clause 6.3) is given by 2 f 400 3.0 2, 036 N , Tdn u 0. 9An 0. 9 1. 25 2 m1
Thus, for the two screws on top of the shelf, the design capacity corresponds to the smaller of the two capacities (as per Clause 6.1) and is
Td 1,607 N
Since, this is more than the demand of 127N, the one 3mm diameter screws are capable of carrying the tension and prevent sliding of the gas cylinder. It is required to check and ensure that the 3mm screw holding the gas cylinder should not fail in bond at the masonry wall. 2.4.3 NSEs anchored to both Horizontal and Vertical LLRSS Elements 2.4.3.1 Large Storage Rack
Consider earthquake safety of a large storage rack (Figure 2.32) placed on the ground storey of the 5-storey RC frame benchmark building. It height exceeds that of the first storey and hence, the RC slab is removed in the building at the floor above the first storey. The storage rack including its contents has a mass of 10,000 kg. It is 2.3m long, 0.8m wide and 4.8m tall. When the ground shakes during earthquakes, the storage rack can topple laterally in its out-of-plane direction (i.e., along the 0.8 width direction) outwards from the wall, if simply rested on the floor slab without any anchorage to the adjoining structural system. To secure it against strong earthquake ground shaking effects, the storage rack should be fastened to the structural systems of the building with positive anchorage systems.
Second level RC Beams & Slab
Slab Slab Slab Storage Rack 1500
Fanchor
Slab NO Slab Slab
2400
Fanchor
First level RC Beams Only; NO Slab
Fp Structural System Storage Rack
2400
Wp Ground level RC Beams & Slab
Eart hquake Shaking of Building
Figure 2.32: Storage Rack adjacent to structural systems – forces acting on it
Filling in ground floor
2-32
The design of the fastener between the storage rack and the structural system of the building is governed by the design lateral force Fp given by Eq.(2.5). Considering that the building is located in Seismic Zone V in India, the Seismic Zone Factor Z is 0.36 (Table 2.1). Since the point of attachment of the storage rack is 1.5m above the top of the foundation level, in the ground storey area, x=1.5m and h=16.5m. The Component Amplification Factor ap is 1.0 (Table 2.3) for a shelf fastened to the vertical wall, and the Component Response Modification Factor Rp is 2.5 (Table 2.3). Further, the Importance Factor Ip is 1.5 (Table 2.2). Thus,
0.36 1.5 1.0 1.5 10 ,000 9.8 0.118 98,000 11,564 N 1 2 16.5 2.5 The overturning moment at the base of the storage rack is due to Fp acting at its mid-height and the restoring moment due to its weight W p . Clearly, Fp
Fp
h b 4.8 0.8 Wp 0.118W p Wp 0.117 W p 2 2 2 2
Thus, the storage rack is not likely to topple under the design lateral force. But, it may topple, if the force is higher. Also, it is necessary to ensure that the storage rack will not slide under the same lateral force. Consider two 12mm diameter MS bolts each at the top and mid height of the rack for resisting a lateral force of 11,564N. The axial load safety of each 12mm diameter MS bolt is estimated using the Indian Steel Code IS:800-2007. Firstly, the design axial tension is calculated using a Partial Safety Factors f for loads of 1.5 for dead load and 1.5 for earthquake load, as per Clause 5.3.3 of IS:800-2007. Hence, the design axial tension to be carried is (1.5×4,234 =) 6,351 kN. In calculating the design tensile capacity of each bolt, there are two items, namely design strength from rupture and from yielding. The design strength Tdg due to yielding of the gross section of one bolt (as per Clause 6.2) is given by: fy Tdg m0
2 A g 250 12. 0 25,704 N , 1. 1 2
and, the design strength Tdn due to rupture of the critical section of one screw (as per Clause 6.3) is given by f Tdn u m1
2 0.9 An 400 0.9 12. 0 32, 572 N , 1. 25 2
Thus, for the four bolts at the top level of the storage rack, the design capacity corresponds to the smaller of the two capacities (as per Clause 6.1) and is Td 4 25 ,704 102, 816 N
Since, this is more than the demand of 11,564N, the four 12mm diameter screws are capable of carrying the tension and prevent sliding of the storage rack.
2.5 Earthquake performance of code designed connections of NSEs The design of connections of NSEs with the SEs is based on lateral force on NSE estimated as per Eq.(2.13), which involves many simplifications. Also, there are many uncertainties in arriving at the parameters used therein. Actual earthquake shaking may induce higher level of forces than those estimated using Eq.(2.13), especially when the building is located near major active earthquake faults or when the shaking is stronger than that expected in design. When the demand on the connections between NSEs and SEs exceeds the code specified forces, the design of connections of NSEs as per the discussion in the previous sections may not suffice. …
3-1
Chapter 3
Safety from Pulling and Shearing Hazards 3.0 General During earthquake shaking, NSEs shake along with the SEs. Sometimes, the NSEs are obstructed by the SEs from freely shaking, if paths of oscillations of the SEs and NSEs foul with each other, and are not pre-rehearsed to accommodate the movements in the process of design. Since many NSEs are smaller, more brittle and/or more expensive than SEs, NSEs are damaged by SEs during earthquake shaking; sometimes, damage to NSE can lead to threat to life of the residents of the building. Hence, it is necessary to protect the NSEs, and thereby ensure life safety in the building. Thus, the main requirement in ensuring safety of the NSEs is to understand and estimate the relative movement between the SEs and NSEs (Figure 3.1). NSEs that are long may need two or more supports. Consider two adjacent supports that hold the NSE. These supports of the NSE can be resting: (i) one on ground and the other on the building, (ii) one at a certain level of a building and the other at a different level of the same building, and (iii) one on a building and the other on an adjoining building. During earthquake shaking, these support points (which are basically the SEs of the building in focus) can shake by different amounts and can lead to relative displacement in the NSE. Let one end of the NSE sustain an absolute lateral displacement of NSE1 and the other NSE2 (Figure 3.1a). For safety of the NSE, the relative deformation p to be accommodated by/within the NSE is the relative movement between the two supports. If the supports are moving away from each other, the elongation-type relative deformation p that needs to be accommodated is: p NSE 1 NSE2 ,
(3.1)
and if they move towards each other, the compression-type relative deformation p that needs to be accommodated is: p NSE1 NSE 2 .
(3.2) SE
NSE1 Support 1
Vertical Movement
NSE2 NSE
Support 2
NSE
Cantilever SE NSE
SE
SE Horizontal Movement
SE
(a)
(b)
SE
(c)
Figure 3.1: Pulling and Shearing Hazard NSEs: Movements at the ends of the NSE can be (a) both horizontal, but at the same level in adjoining buildings, (b) both horizontal, but at the different levels of the same building or adjoining buildings, and (c) both vertical and horizontal, at different levels of the same building or adjoining buildings
3-2
Understandably, when either of the supports at the two ends of the NSE has potential to move by large amounts, larger relative deformation needs to be accommodated between the ends of the NSE. Typically, the support points on flexible buildings are candidates for large lateral displacement. Thus, from point of view of safety of NSE during earthquake shaking, it is preferable to have buildings that are stiff in the lateral direction. Since the discussion in this book is largely restricted to safety of NSEs in buildings, the main concern is the lateral movement of the supports of the NSEs (Figure 3.1a and 3.1b). But, when an NSE is resting on a horizontal cantilever, even vertical movements of the support points should be considered (Figure 3.1c); likewise, if it is resting on a vertical cantilever, horizontal movements of the support points should be considered. The imposed relative displacement between the ends of the NSE can be axial type (Figure 3.1a), lateral translational type (Figure 3.1b), or both (Figure 3.1c).
3.1 Strategies against Pulling and Shearing Hazards The strategy to ensure safety from pulling and shearing hazards is to prevent the objects from fouling with each other by providing a pre-determined separation/slack in them. Increase in separation can be achieved in many ways. Some NSEs cannot accommodate much displacement within themselves, and in these NSEs, the intervention to increase separation is largely through extra spaces within the SEs. Any intervention to increase the separation necessarily must seek to ensure that the NSE is supported at all times of the earthquake shaking. Based on geometry, pulling and shearing hazard NSEs can be grouped into two types (Figure 3.2), namely Lineal NSEs (whose one dimension is much larger than the other two, e.g., water mains and pipes) and Planar NSEs (whose two dimensions are much larger than the third, e.g., glass window and façade panels). Lineal NSEs need to be supported at the ends, and need to accommodate the relative displacement imposed by the SEs between its ends. Planar NSEs are supported along all four edges of its plane, and needs to accommodate the relative displacement imposed by the SEs along all four edges.
Lineal NSE W at er M ain Pipe
Planar NSE Glass W indow Panel
Linear NSE fouls with SEs at its top and bottom ends
Planar NSE fouls with SEs on all four edges of its plane
(a) (b) Figure 3.2: Types of Displacement-Sensitive NSEs: (a) Lineal NSE with possibility of fouling with the SE only at the two ends, and (b) Planar NSE with possibility of fouling with SE along the four edges of its perimeter
3-3
3.2 Classification of Pulling and Shearing Hazard NSEs
The pulling and shearing hazard NSEs can be at any elevation of the building. Based on the displacement restraint imposed by the SEs supporting the NSEs, different approaches are required to estimate this relative displacement and ways of accommodating the same. For the purposes of designing the connections between the NSEs and SEs and of accommodating the relative displacement, the pulling and shearing hazard NSEs can be classified into three types, namely (1) NSEs having Relative Displacement with respect to Ground (Figure 3.3a), (2) NSEs having Inter-storey Relative Displacement (Figure 3.3b), and (3) NSEs having Relative Displacement between two buildings shaking independently (Figure 3.3c). Some of the typical examples are discussed in the sub-section below.
(a)
(b)
(c)
Figure 3.3: Pulling and Shearing Hazard NSEs – 3 types of relative deformations are imposed on the NSE, namely: (a) Relative Displacement with respect to Ground, (b) Inter-storey Relative Displacement, and (c) Relative Displacement between two buildings shaking independently. 3.2.1 NSEs having Relative Displacement with respect to Ground Some lineal NSEs run between the outside ground and the building, but are connected to an upper elevation of the building in contrast to the base of the building. Examples of this type of NSE are Water Mains running from outside ground to the building (for normal use or for fire hydrant purposes; Figure 3.4a), and Gas Pipes laid between the building and a ground-supported large volume gas tank (placed at some distance away form the building; Figure 3.4b). In rare instances, Sewage Mains also are run from the outside ground to an upper elevation of the building (Figure 3.4c); normally, sewage lines go down to the lowest level of the building and exit through the base of the building to the outside ground. During earthquake shaking, the ground outside shakes independent of the building at the level at which the NSE is connected. Thus, the ends of the NSE are subject to differential shaking, implying that a relative axial deformation imposed between the ends of the NSE. This relative deformation can be large, if the building is laterally flexible. Tensile strains induced in the NSE can cause failure of the function of the sewage mains, if segmented pipes are used as Sewage Mains. Compressive strains in water mains can cause buckling of the pipe, and thereby impede its function. Design of NSEs and their connections to the SEs must find ways of avoiding these strains from being generated, by accommodating the relative displacement. Another example of a lineal NSE of this kind is the Exhaust Fume Chute in generator rooms (Figure 3.4). The generator is normally anchored to its foundation that is directly constructed on ground. And, the exhaust fume chute goes from the generator to outside the generator room; it is supported by the wall of the generator room. The generator is relatively rigid, and the exhaust fume chute is flexible. Hence, when earthquake shaking occurs, the wall of the generator room shakes differentially from the generator, and all the relative deformation is accommodated only in the chute. Design of NSE must ensure that the exhaust fume chute is not restrained at the SE and accommodate the movement caused by the relative deformation.
3-4
Water Mains
Water Mains
in compression
in t ension
(a) Gas Pipe
Gas Pipe
in compression
in t ension
Gas Tank
Gas Tank
(b)
Sewage Mains
Sewage Mains
in compression
in t ension
(c) Figure 3.4: Relative Displacement with respect to Ground – Lineal NSEs need to sustain axial compression and tension strains without failure: (a) Water mains, (b) Gas pipes, and (c) Sewage mains
Exhaust Fume Chute
Exhaust Fume Chute
in compression
in t ension
Generator
Generator
Figure 3.4: Relative Displacement with respect to Ground – Exhaust fume chutes from diesel generators sustain axial compression and tension strains during earthquake shaking
3-5
3.2.2 NSEs having Inter-storey Relative Displacement Some NSEs run through the full height of the building (e.g., façade stone or glass, and water pipes and sewer pipes), and some occupy the whole of a single storey (e.g., French glass windows). Since these NSEs are supported by the floor slabs, columns and walls at different levels, they are subjected to relative deformation within each storey. This deformation is of shear type, and the NSE needs to be capable of accommodating the shear deformation imposed on it by the adjoining SEs within each storey (Figure 3.5a). When segmented ceramic pipes are used for sewage transport, the inter-storey drift can cause rupture of the sewage lines (Figure 3.5b), which is a loss of function as well as second order disaster. Manufacturers of segmented sewage pipes also indicate the maximum lateral drift that the pipe joints can be subjected without leakage. Design of these sewage lines should verify this as part of the design of the NSE.
Water Mains deformed lat erally
Water Mains undeformed original
Water Mains deformed lat erally
(a)
Sewage Pipeline deformed lat erally
Sewage Pipeline undeformed original
Sewage Pipeline deformed lat erally
(b) Figure 3.5: Inter-storey Relative Displacement – Lineal NSEs need to sustain lateral translational strains without failure: (a) Water pipelines, and (b) Sewage pipes 3.2.3 NSEs having Relative Displacement between two items shaking independently Many buildings have expansion joints or seismic joints in them, thereby separating the buildings into parts that freely shake during earthquake ground motions. In many of these buildings, lineal NSEs are continued from one part of the building to the adjoining one. Examples of such lineal NSEs (Figure 3.6), include (a) electric power wires and cables, (b) water pipelines, (c) gas pipelines in hospital and laboratory buildings, (d) air-conditioning ducts, (e) chemical pipes in industrial environments, (f) hazardous and chemical waste pipelines, and (g) in some instances, sewage pipelines. While these items are normally carried from one part of the building to the other at the same level, but in some instances, the NSEs are continued from a certain level (in height) of one part of the building to a different level in the adjacent part.
3-6
Differential movement occurs at ends of lineal NSEs that span across to adjoining parts of the building. Design of these NSEs and their connections to SEs needs to accommodate these relative deformations that occur between the two portions of the building during earthquake ground shaking (Figure 3.6), and thereby prevent failure of NSE and other secondary effects.
3.3 Design against Pulling and Shearing Hazards Over the last two decades, countries faced with high earthquake hazard have recognized the importance of seismic safety of NSEs along with that of the buildings and their SEs. 3.3.1 Design Relative Lateral Displacement for SEs When buildings shake during earthquakes, they move laterally by different amounts at different levels. Under the design lateral force V B, buildings are required not to deform laterally by more than 0.4% of the height. This is applicable to the overall lateral displacement of the building as well as to the inter-storey displacement. But, these displacement values under the design lateral forces are only a fraction of the actual displacements that normal buildings are likely to deform by during strong shaking. This is attributed to the fact that normal buildings are not designed to remain elastic during earthquake shaking, and hence are designed only for a fraction of the lateral force that the building is likely to experience, if it were to remain elastic. The main reason for this is that earthquake shaking imposes displacement loading on the structure and not force (Figure 2.1). 3.3.2 Design Relative Lateral Displacement for NSEs The seismic relative displacement D p for which NSEs must be designed to accommodate, shall be determined as per Clauses 7.13.4.1, 7.13.4.2 and 7.13.4.3 of Draft IS:1893. These values are helpful to architects and engineers to select and design NSEs that are connected to the building at multiple levels of the same building or of adjacent buildings. These expressions provided in this section provide a rational basis for assessing the flexibility or clearances required by NSEs and their connections to accommodate the expected building movements during earthquake shaking. Clause 7.13.4.1 of Draft IS:1893 provides an estimate of the seismic relative displacement D p between two levels on the same building, one at height h x and other at height h y from the base of the building across which the NSE spans, as: (3.3) D p xA yA , but the value of Dp should not be greater than
max R hx h y
h
aA
,
(3.4)
sx
where xA and xB are the seismic deflections at building levels x and y of the building under the application of the design seismic lateral force determined by elastic analysis of the building, and multiplied by Response Reduction factor R of the building (Table 3.1), h x and hy the heights of building at levels x and y at which the top and bottom ends of the NSE are attached, aA the allowable storey drift of building A at level x calculated as per Clause 7.12.1 of the Draft IS:1893, and h sx height of storey below level x of the building A. In the calculation of D p , the multiplication with R is a critical step. Figure 3.7 clarifies this. If
is the displacement from Linear Analysis at point x in building A subjected to Design Lateral Force, then the actual displacement xA of the building that undergoes nonlinear actions is estimated by an excellent approximation that was proposed (Newmark and Hall, 1973), as (3.5) xA R . This entire c hapter on safety of NSEs governed by displacement actions is controlled by this simple procedure. Eq.(3.5) gives an estimate of the actual displacements of the SEs as determined by elastic analysis based on design lateral forces on the building. Eq.(3.6) provides an estimate of the actual maximum displacement that is expected between the ends of the NSE considering the Response Modification Factor R of the building.
3-7 Support
Lat eral movement of support of NSE
Lineal NSE
(a) Multi-linear NSE
Lat eral movement of support of NSE
(b) Figure 3.6: Relative Displacement between two items shaking independently on ground – Lineal NSEs need to sustain lateral and vertical displacements without failure: (a) connected to the same level on both parts of a building, and (b) connected to different levels on the two parts of a building
Clause 7.13.4.2 of Draft IS:1893 gives an estimate of the seismic relative displacement Dp between two points on two adjoining buildings, one on the first building at height h x from its base and other on the second building at height hy from its base, across which the NSE spans, as: (3.6) D p xA yB , but the value of Dp should not be greater than max R h x aA hy aB , hsx hsy
(3.7)
where R is the Response Reduction factor of the buildings (Table 3.1), h x and hy the heights of buildings at levels x and y at which the top and bottom ends of the NSE are attached, aA and aB the allowable storey drifts of buildings A and B calculated as per Clause 7.12.1 of the Draft IS:1893, and h sx and h sy heights of storeys below levels x and y of the buildings. Clause 7.13.4.3 of Draft IS:1893 requires that the seismic relative displacements mentioned above be combined with displacements caused by other loads, like thermal and static loads.
3-8
H
Assumed Linear Behaviour of Building
Elast ic Maxim um For ce
Divide by R
Actual Nonlinear Behaviour of Building
Design Lat er al For ce
0
Displacement from Linear Analysis under Design Lateral Force
~R
Actual Inelastic Displacement under strong Earthquake Shaking
Figure 3.7: Relating Design Displacements with Actual Displacements of a Building – Elastic displacements from linear analysis need to be amplified by R to estimate inelastic displacements that are experienced by building Table 3.1: Response Reduction Factor R for Building Systems from Table 7 of Draft IS:1893 S.No. Lateral Load Resisting System R Building Frame Systems 3.0 i Ordinary RC moment-resisting frame (OMRF) 4.0 ii Intermediate RC moment-resisting frame (IMRF) 5.0 iii Special RC moment-resisting frame (SMRF) iv Steel frame with 4.0 (a) Concentric Brace Frame 5.0 (b) Eccentric Braces 5.0 v Steel moment-resisting frame designed as per SP:6(6) Buildings with Shear Walls vi Load bearing masonry wall buildings 1.5 (a) Unreinforced masonry without special seismic strengthening (b) Unreinforced masonry strengthened with horizontal RC bands and 2.25 vertical bars at corners of rooms and jambs of openings 3.0 (c) Ordinary reinforced masonry shear wall 4.0 (d) Special reinforced masonry shear wall 3.0 vii Ordinary reinforced concrete shear walls 4.0 viii Ductile shear walls Buildings with Dual Systems 3.0 ix Ordinary shear wall with OMRF 4.0 x Ordinary shear wall with SMRF 4.5 xi Ductile shear wall with OMRF 5.0 xii Ductile shear wall with SMRF
3.4 Examples Calculation of Design Relative Lateral Displacement for NSEs
3-9
Limited cases of typical NSEs are considered in this section to demonstrate how to calculate the relative displacement required for preventing the NSEs from fouling with the shaking of the SEs. These relative displacements are calculated as per the provisions given in the Draft IS:1893 published by the Gujarat State Disaster Management Authority, Gandhinagar (Gujarat), and available on the website www.nicee.org of National Information Center of Earthquake Engineering (NICEE), IIT Kanpur. The examples considered are categorized into three groups, namely (i) NSEs having Relative Displacement with respect to Ground, (ii) NSEs having Inter-storey Relative Displacement, and (iii) NSEs having Relative Displacement between two items shaking independently. 3.4.1 NSEs having Relative Displacement with respect to Ground 3.4.1.1 Water Mains, Fire Hydrant Supply Pipes and Gas Pipes from outside the building
Consider earthquake safety of a continuous mild steel pipe carrying water or gas from a tank outside the 5-storey RC frame benchmark building (resting directly on ground at a distance away from the building) to services inside the building (resting on the slab over the first storey of the building) (Figure 3.8). The pipe is of 300mm diameter with 4mm wall thickness; the length of the pipe is 6m from the support on the building to that on ground. Thus, the pipe is rigidly connected to both the ground and the building, both of whic h are shaking back and forth during strong earthquake shaking of the ground. The pipe can be pulled and compressed during this action of its two supports owing to the relative deformation between them. To secure it against strong earthquake ground shaking effects, the water and gas pipes should be checked against the imposed relative displacements between their ends. 6,000 Support
Pipe
Support
First level RC Beams & Slab
4,500
Eart hquake Shaking of Building
Figure 3.8: Water Mains, Fire Hydrant Supply Pipes and Gas Pipes connected to the building from the outside – shaking of the two supports of the pipe imposes relative displacements at its end The pipe is attached at a height of (1500+3000mm=) 4,500mm from the top of the foundation. The design displacement is imposed between the ends of the pipe, when the design earthquake imposes on the floor slab above the first storey to move horizontally from its initial position the under the design lateral forces. This movement is independent of the other support of the pipe which is shaken directly by the vibrating ground. For the benchmark building considered, from Eqs.(3.5) and (3.6), the relative displacement between the first slab level at 4.5m (i.e., hx =4.5m) and the top of the foundation of the column (i.e., h y =0) is taken from linear structural analysis of the benchmark building-pipe system, this value is 8.8 mm. Here, the other support is expected to move the same amount at the top of the foundation of the columns. Therefore, the relative deformation
3-10
between the top of the foundation and that at the first floor level is taken as the relative deformation between the ends of the pipe. Hence, D p is given by R times . For the benc hmark building, R is 5.0, and therefore D p 5 8.8 0 43mm .
From Eq.(3.7), the maximum allowable relative displacement max is given by max 5 4500 0.004 0 90mm
corresponding to the upper limit of 0.4% drift under design lateral forces specified in Clause 7.12.1 of Draft IS:1893 (Part 1) – 2005. The pipe should be able to resist an axial tension and compression corresponding to the axial displacement of 43mm calculated above, if the pipe is fixed as assumed at its two ends. If not, mitigation measure is required. In general, it is not possible to accurately estimate the relative displacement between the ends of the pipe, because that actual hazard is not quantifiable precisely. Also, when the diameter of the pipe is large, even a small axial deformation can cause large stresses in the pipe, owing to higher stiffness of large pipes. Hence, it is prudent to not defy the earthquake shaking, but to comply with it. Thus, adequate slack is required to be provided at one end of the pipe corresponding to the expected relative deformation between the ends (Figure 3.10). A device that facilitates this is called a flexible coupler; it is like the bellows of an accordion. Pipe Coupl er Pipe
Support
First level RC Beams & Slab
Earthquake Shaking of Building
Figure 3.10: Water Mains, Fire Hydrant Supply Pipes and Gas Pipes connected to building from the outside – mitigation measure of using a pipe coupler to allow for flexibility along the length of the pipe 3.4.1.2 Sewage Mains from outside the building
Consider earthquake safety of the 6m long segmented ceramic pipe carrying sewage that run from outside the 5-storey RC frame benchmark building to servic es inside the building (resting on the slab over the first storey of the building) (Figure 3.11). The pipe segments are of 150mm diameter with 10mm wall thickness. The pipe is rigidly connected to both the ground and the building, both of which are shaking back and forth during strong earthquake shaking of the ground. The pipe can be pulled and compressed during this action of its two supports owing to the relative deformation between them. To secure it against strong earthquake ground shaking effects, the safety of this pipe system should be checked against the imposed relative displacements between their ends. The compression generated in the pipe should to crush the pipe not the tension should open the joints between the pipe segments. As in Section 3.4.1.1, D p is 43mm from Eq.(3.6) and max 90mm from Eq.(3.7). The segmented pipe system should be able to resist an axial tension and compression corresponding to the axial displacement of 43 mm with its ends restrained against this translation in the direction of the length of the pipe; if not, mitigation measure is required. Again, as in Section 3.4.1.1, it is prudent to provide adequate slack in the pipe system at the end corresponding to the expected relative deformation between the ends (Figure 3.13) using a flexible coupler at the end of the pipe.
3-11
6,000 Support
Sewage Pipe
Support
First level RC Beams & Slab
4,500
Earthquake Shaking of Building
Figure 3.11: Sewage Pipes connected to the building from the outside – shaking of the two end supports of the pipe imposes relative displacements at its end Pipe System in Compression
Pipe
Pipe System in Tension
Support
First level RC Beams & Slab
Pipe
Support
First level RC Beams & Slab
Earthquake Shaking of Building
Earthquake Shaking of Building
Figure 3.12: Sewage Pipe System connected to building from outside – relative deformation in pipe Flexible Pipe Coupl er Support
Pipe
First level RC Beams & Slab
Earthquake Shaking of Building
Figure 3.13: Sewage Pipe system connected to the building from the outside – mitigation measure of using a pipe coupler to allow for flexibility along the length of the pipe system
3-12
3.4.2 NSEs having Inter-storey Relative Displacement 3.4.2.1 Glass Windows & Partitions, and French windows
Consider earthquake safety of the single-piece window glass that spans the full space between the beam-column frame in the 5-storey RC frame benchmark building at the fifth storey (Figure 3.14). The glass panel is of size 3500mm×2600mm and of 6mm thickness. Thus, the glass panel is snugly held between beams and columns of the building, both of which are shaking back and forth during strong earthquake shaking of the ground. Hence, the glass panel is subjected to distortions imposed by the adjoining beams and columns. The only saving grace is when flexible packing is provided between the glass and the adjoining frame. To ensure that the glass is secured against strong earthquake ground shaking effects, the glass panel should be checked against the imposed relative displacements between its edges and for the sufficiency of the dimension of the flexible packing. In Eq.(3.3), design lateral displacements above and below the fifth storey are obtained as 20.58 mm and 19.63 mm from structural analysis of the benchmark building under the design lateral forces. Thus, from Eq.(3.5), Dp 5 20. 58 5 19.63 4. 75mm . In Eq.(3.4), R is 5, h x 16.5m, h y 13.5m, and aA / hsx 0.004. Hence, the maximum allowable relative displacement max is
max 516500 13500 0.004 60mm .
Since Dp 4.75mm is less than max 60mm , Dp will govern. Since the gap provided is 30mm between the frame columns and glass panel on each side, the laterally deforming frame columns will not touch the glass until a lateral deformation reaches 60mm. After this, the columns will foul with the glass panel (Figure 3.15); here, it is assumed that the glass panel cannot take any lateral deformation, even though it may be able to carry marginal relative deformation. Hence, the glass panel is safe in the fifth storey. It is important to perform similar checks to ensure the safety of such glass panels in all storeys, especially when the drift in the other storeys is larger.
Packing
30
Deformation of the building Glass
Small drift
Glass
2600
Large drift
g=30
Frame 3500
30 g=30
Figure 3.14: Single-piece Window Glass – flexible packing is provided all around between the building frame and glass panel
3-13
2g (=60mm)
Interference
Packing
Glass
Glass
Frame
Frame
(a) (b) Figure 3.15: Deformed Building Frame and un-deformed Window Glass – (a) limiting distortion governed by the packing width available between the two, i.e., 60mm, and (b) lateral deformation of frame more than 60mm play available 3.4.2.2 Water and Fire Hydrant Pipelines inside Building
Consider earthquake safety of a water main that runs vertically from the bottom to the top in the 5-storey RC frame benchmark building (Figure 3.16). In particular, the focus is on the pipe running between the fourth and fifth floor slabs. The pipe is 3000mm long and of 50mm diameter with 4mm wall thickness. The pipe is snugly held between slabs at two floor levels of the building, both of whic h are shaking back and forth during strong earthquake shaking of the ground. Hence, the pipe is subjected to relative lateral deformations between its ends. To ensure that the pipe is safe against strong earthquake ground shaking effects, its safety should be checked against the imposed relative displacements between its ends in the top storey. The relative lateral deformations between the two floor slabs in this case are the same as those in Section 3.4.2.1. Thus, D p is 4.75mm in the fifth storey and 27.5mm in the ground storey, and max 60mm. and, of the two, the former will govern. Structural analysis of the pipe is performed to demonstrate its safety under this level of the imposed deformations. Results show that the pipe in the ground storey develops a bending moment of 0.14 kNm, axial force of 2.06kN and shear force of 0.09kN. The pipe is safe under these forces, and hence under the expected earthquake shaking. Hence, there is no distress in to the water pipe. Here, the diameter of the pipe is 50mm. If larger diameter pipe are used in the building (e.g., fire hydrant pipes), the pipe may become unsafe for the same lateral deformation of the building. Flexible couplers may be used in each storey to ensure that the water pipes are not damaged. As in glass panels, it is important to perform similar c hecks to ensure safety of such glass panels in all storeys, especially when drift in other storeys is larger.
Deformation of the Water Pipe
Water Pipe
building Small drift
3000
Large drift
Frame
Figure 3.16: Water Pipe running vertically in a building – the floors at the top and bottom ends restrain the pipe from rotating at those locations
3-14
3.4.2.3 Electric Wires inside Building
Consider earthquake safety of an electric wire that runs vertically from the bottom to the top in the 5-storey RC frame benchmark building (Figure 3.17). In particular, the focus is on the wire running between the fourth and fifth floor slabs. The wire is 3000mm long and made of copper of 4mm diameter. The wire is snugly held between slabs at two floor levels of the building, both of which are shaking back and forth independently during strong earthquake shaking of the ground. Hence, the wire is subjected to relative lateral deformations between its ends, which results in elongation of the wire. To ensure that the wire is safe against strong earthquake ground shaking effects, its safety should be checked against the imposed relative displacements between its ends in the top storey.
Deformation of the Electric wire
Electric wire
building Small drift
Frame
3000
Large drift
Figure 3.17: Electric wire running vertically in a building – the wire is held at the top and bottom ends
The relative lateral deformations between the two floor slabs in this case are the same as those in Section 3.4.2.1. Thus, D p is 4.75 mm and max 60mm. The former will govern. The wire will be stretched between slabs by an amount 2600 4.752 2600 0.0044 mm. The strain generated in the wire will be 0.0044/2600=0.000002. Normal electric wires are made of copper, which have a yield strain of 230 MPa and an elastic modulus of 120GPa; thus, the yield strain is 0.00192. This strain generated in the wire is small compared to this limiting strain of copper. Hence, the copper wire is safe. Similar check should be performed at the ground storey also. Notwithstanding that the strain induced in the wire is small, it is not desirable to strain an electric power wire. It is advisable to provide slack in each storey to accommodate the seismic deformations. 2
3.4.2.4 Sewage Lines inside Building
Consider earthquake safety of sewage pipeline that runs vertically from the bottom to the top in the 5-storey RC frame benc hmark building (Figure 3.18). In particular, the focus is on the sewage pipe segments made of ceramics put together between the ground and first floor slab. The pipe is 4500mm long and of 100mm diameter with 10mm wall thickness; each pipe segment is 600mm. The pipe is snugly held between the fourth and the fifth floor slabs of the building, the latter shakes back and forth during strong earthquake shaking of the ground. Hence, the pipe is subjected to relative lateral deformations between its ends. To ensure that the pipe is safe against strong earthquake ground shaking effects, the pipe should be checked for its adequacy to resist the imposed relative displacements between its ends in the top storey.
3-15
Sewage Pipe
Sewage Pipe
3000
Frame Figure 3.18: Sewage pipe running vertically in a building – the floor slabs at the ends restrain the pipe from rotating at those levels
The relative lateral deformations between the two floor slabs in this case are the same as those in Section 3.4.2.1. Thus, D p is 4.75 mm and max 60mm. and, of the two, the former will govern. Structural analysis of the pipe-system (with the pipe system running vertically between the fourth and the fifth floor slabs of the building) should performed to demonstrate its safety under this level of the imposed deformations (Figure 3.19). If found insufficient, adequate slack should be provided in the pipe system, using a flexible pipe coupler at one of the ends (Figure 3.20).
Frame Figure 3.19: Sewage Pipe System running between the floor slabs – relative deformation in pipe system
Flexible Pipe Coupl er
Frame Figure 3.20: Sewage Pipe system running between the floor slabs of the building – mitigation measure of using a pipe coupler to allow for flexibility at the top end of the pipe system
3-16
3.4.2.5 Exhaust Fume Pipe of Generator
Consider earthquake safety of the exhaust fume pipe of a generator (Figure 3.21) resting in the ground storey of the 5-storey RC frame benchmark building (discussed in Chapter 2 of this document) to carry the exhaust fumes from the generator to outside the building. The generator has base dimensions of 3m×4m and height 2.5m. The generator has a pipe of 0.3m diameter, with 6mm wall thickness. It has a length of 4m from the top of the generator to the masonry wall. Normally, this fume pipe is rigidly connected to the generator at the inside end, and is built into the masonry wall at its outside end. In as much as it is not the intent to fix the outer end to the masonry wall, many a time it is rigidly held at that end owing to lack of clear detailing practice on how that end should rest on the wall. Thus, the pipe is rigidly connected to both the massive generator and the wall of the buildings that is swinging back and forth during strong earthquake shaking of the ground. It can be pulled and compressed during this action of its supports. To secure it against strong earthquake ground shaking effects, the fume pipe should be checked against the imposed relative displacements between its ends.
First level RC Beams & Slab Fume Pipe
200
Fume Pipe 1500
2500 Masonry wall
Generator
1500
Flooring in ground floor
Earthquake Shaking of Building
Figure 3.21: Exhaust Fume Pipe of Generator connected to SEs – imposed displacements at its end The pipe is attached at a height of (1500+2500mm=) 4,000mm from the top of the foundation. The design displacement is imposed between the ends of the pipe, when the earthquake swings the building wall laterally from its initial position the under the design lateral forces. From Eq.(3.5), for the benc hmark building considered, the relative displacement between the top of wall at 4m (i.e., h x =4m) and the base of the column (i.e., hy =0) is taken from linear structural analysis, and this value is 0.67 mm. D p is given by R times . For the benchmark building, R is taken as 5.0, and therefore D p 5 0. 67 0 3 .35mm .
From Eq.(3.6), the maximum value of this relative displacement max is max 54000 1500 0.004 50mm
corresponding to the upper limit of 0.4% drift under design lateral forces specified in Clause 7.12.1 of Draft IS:1893 (Part 1) – 2005. Hence, the governing relative displacement is 3.35mm. Exhaust fume pipe should be able to resist an axial tension and compression corresponding to axial displacement of 3.35mm calculated above, if it is fixed to the wall at the outside end. Based on linear structural analysis of the pipe system, the maximum stress in the pipe is obtained as 0.49MPa. The pipe is safe under this stress. But, it needs to be seen if the masonry wall can withstand an out-of-plane lateral displacement of 3.35mm at the point of attachment of the pipe to the wall. If found insufficient, a mitigation measure is required to accommodate the above imposed relative displacement. One way is to ensure that the pipe slides on the masonry wall, by providing a “no-friction” surface underneath the pipe and adequate gap all around the pipe and the adjoining masonry wall (Figure 3.22).
3-17
max
Fume Pipe
Friction-free surfaces Masonry wall
Generator
Flooring in ground floor
Figure 3.22: Friction-free detailing at the end of the exhaust fume pipe resting over the masonry wall – sliding bearing or sliding joint between the masonry wall and the exhaust fume pipe
3.4.3 NSEs having Relative Displacement between two items shaking independently 3.4.3.1 Electric Cables from Pole to Building
In many instances, electric power lines are brought to a building directly form an electric power supply pole adjoining building (Figure 3.23). The electric cable is supported at one end on the pole and at the other on the building; it is possible that the power line is received at any elevation of the building, depending on the field conditions of safety. During strong earthquakes, both the building as well as the electric pole shakes. Hence, the electric wire can get loose and sag more, or get taut and straighten out, depending on whether the building is shaking towards the electrical pole or away from it. In the latter case, if the movement of the building away from the pole is large (Figure 3.24b), it is possible that the electric wire is stretched in tension to the extent of even snapping. This can result in loss of electricity supply to the building, and if the cable drops down to the ground, it may lead to electrocution of people on ground. Relevant calculations are presented to ensure that cables do not stretch in tension and break during the expected earthquake shaking at the location of the building.
Δb Δp
(a)
(b)
Figure 3.23: Cable wire connected between building and cable: (a) Initial position, and (b) Extreme position of building and pole causing maximum tension in cable
3-18
The relative lateral displacement between the pole and the building will determine whether or not the electric wire will break. Conversely, the electric wire should be designed to accommodate the relative displacement D p suffered between its supports during strong earthquake shaking, as calculated by Eq.(3.8). Dp shall be obtained by (3.9b) L b p , where b R b and p p , in which b and p are design lateral displacements of the building and the pole obtained as below. Before earthquake shaking, let the two supports (i.e., the building and the pole) holding the electric cable be at a horizontal distance L, the sag in the cable y 0 , and the tension in the cable T (Figure 3.24). During earthquake shaking, let the supports suffer a maximum relative lateral displacement ΔL when the two supports move away from each other. Let the maximum tension be Tmax generated in the cable in the stretched position during the expected design earthquake shaking. The exercise is to design the cable (i.e., determine the area A of cross-section and initial sag y0 or tension T0 ) such that the cable does not break in physical tension created by the pull during the expected design earthquake shaking.
V
T H
y0
L Figure 3.24:
T Before Shaking
Tmax Maximum position during shaking
ΔL
Tension, sag and extreme positions of cable before and during earthquake
The lateral displacement Δb of the benchmark building is estimated as per Eq.(3.8) using R=5 and the design lateral displacement obtained from structural analysis of the building under the action of the design floor lateral loads; this displacement is measured at the point on the building where cable is connected from the electric pole. Hence, (3.10) b 5 . The electric pole can be simplified as a mass attached to a cantilever having c ross-section properties L and I and material property E. When the pole is made of non-prismatic sections (Figure 3.25), say in three steps, then the cross-section properties L1 , L2 , L3 , I 1 , I2 and I3 are used. The lateral displacement A at point A of the non-prismatic cantilever pole under lateral force H applied at the top of the pole, is given by A B B L 3
where B C C L 2 B C
HL33 , 3EI 3
HL32 H L 3 L 22 , and 3EI 2 3EI 2
HL22 H L 3 L 2 , 2EI 2 EI 2
in which C C
HL31 H L 2 L 3 L21 , and 3EI 1 2EI 1
HL21 HL 2 L 3 L 1 . 2EI 1 EI 1
(3.11)
3-19
A
H
L3 B L2 C L1
(a)
(b)
Figure 3.25: Schematic of (a) electric pole, and (b) its idealisation with deformed shape under lateral earthuake shaking
Hence, the lateral stiffness k of the pole subjected to concentrated lateral force H at the tip of the pole is given by H 1 , (3.12) k
A
X B RB L3
3
L3 3EI 3
where X B X C RC L 2
L 32 L L2 L2 LL 3 2 , and RB RC 2 3 2 , 3EI 2 2 EI 2 2EI 2 EI 2
in which XC
L L3 L21 , and L L3 L1 . L 31 L2 2 RC 1 2 3EI 1 2EI 1 2EI 1 EI 1
The equivalent static Design Lateral Force VB applied at the tip of the pole is a modified version of Eq.(2.4), namely
VB
ZI Sa 2 g
W ,
(3.13)
In Eq.(3.13), the Response Reduction Factor R is dropped in comparison to Eq.(2.4), because the pole does not have any redundancy and is expected to remain elastic at the end of the earthquake. In Eq.(3.13) for calculation of S a g , Natural Period T of the pole is calculated in the direction of shaking using basic principles of mechanics, the natural period of the pole is given by
T 2
m , k
(3.20)
where m is the effective mass at the top of the pole and k is lateral stiffness of the pole given by Eq.(3.12). Hence, the displacement p at the tip of the pole due to force VB is given by
p
VB . k
(3.21)
3-20
Let the initial arc length of the cable be Lc. Let the weight per unit length be w of the cable of area of cross section A. Consider an infinitesimally small differential element of arc length ds of the cable at a horizontal distance of x from the left support and an arc length s away (Figure 3.26). Let H be the horizontal pull in the cable at the supports (it is the same at the two supports). Taking moment about point B,
H y ws x w s Dividing by Δx,
x . 2
(3.22)
y ws w s . x H 2H Since
w ws s is small compared to , it can be neglected considering small deformations. Hence, 2H H
the equilibrium equation becomes
dy ws . dx H
(3.22)
d 2 y w ds . dx 2 H dx
(3.23)
ds2 dx 2 dy 2 .
(3.24)
Taking the derivative again with respect to x,
Also, from geometry in Figure 2.27, Hence, 2
ds dy 1 . dx dx
(3.25)
Combining Eqs.(3.23)and (3.25), 2
d2 y w dy 1 . 2 dx H dx
(3.26)
The boundary conditions for this differential equation are
y 0 0 and
dy 0 0 . dx
(3.27)
Integration Eq.(3.26) gives
X s Y
dy
ds x
dx
H
w(s+Δs)
A
T ws
Figure 3.26: An infinitesimally small element of cable
B
T+ΔT H
3-21
dy wx Sinh c1 . dx H
(3.28)
Using Eq.(26) in Eq.(3.28), c1 0 . Therefore,
dy wx Sinh . dx H
(3.29)
Integrating Eq.(3.29),
y
x H Cosh c 2 . W h
(3.30)
Using Eq.(3.27) in Eq.(3.30),
c2
H . W
Hence, the solution is
y
H W
x Cosh h 1 .
(3.31)
Using Eq.(3.29), the arch length of the cable is 2
2
L L L wx H ds wx dy wL . dx Cosh Lc dx 1 dx 1 Sinh dx Sinh 0 dx 0 0 0 w H H H dx L
The vertical force equilibrium from Figure 3.27 suggests that vertical force V at the support is
(3.32)
wLc . 2
(3.33)
T H2 V2 ,
(3.34)
H T2 V2 .
(3.35)
V
At the support (Figure 6), the inclined tension force T is given by: or
The following step-wise procedure may be followed to arrive at the design initial sag y 0 in the cable: (a) Step 1: In stretched state, assume the length of cable to be L+ΔL = L*, say. Using Eq.(3.33), estimate the vertical component of force at support, as
V*
wL* . 2
Tension in cable in its stretched state should be less than Tmax to ensure no rupture in the cable. Hence, from Eq.(34), 2
2 H Tmax V * .
(b) Step 2: Calculate actual arc length of cable Lc using Eq.(3.32) as
Lc
H wL L Sinh . w H
(c) Step 3: If assumed length L* is within tolerance of calculated length Lc, i.e., Lc L* , then go to Step 4, else assume L* Lc and go to Step 1.
(d) Step 4: Calculate sag in stretched state from Eq.(30), as
3-22
L L w 2 Tmax Cosh y0 1 . w T max This gives a feel of the state of the cable during earthquake. (e) Step 5: Lc is known from Step 3 and L is given. Hence, solve the nonlinear Eq.(3.32) and calculate H. (f) Step 6: Calculate V using Lc from Eq.(3.33). Calculate T, using H and V from Eq.(3.34). (g) Step 7: Calculate the original sag y 0 required in cable using Eq.(3.31). This is helpful while installing the cable. Consider power supply to the third storey of the benchmark building from a pole 10 m away from building through an electric cable (Figure 3.27). The direction of the arrival of the cable to the building is along the direction in whic h the building has three bays. The electic pole height is 7m above the ground. It carries two copper core conductors (each of area of 35 mm 2) with PVC insulation to the building at the slab above the third storey. The initial length of the electric cable and its sag needs to be designed, so that it does not break in tension under lateral shaking of building and pole during the expected strong earthquake at the building site. The specifications and assumptions of the electric pole and the cable are given below: (i) Pole: A hollow mild steel tube (named 410 TP-16) is chosen as the electric pole to get an effective pole height of 7m. As per Table 1 associated with Clause 5.1 of IS:2713-1980, this pole is a threestep pole is of 8.5m height with step heights of L1 =4.5m, L2=2m and L3 =2m, and a planting depth of 1.5m. The outside diameters are 114.3, 88.9 and 76.1 mm, with a wall thickness of 3.65mm. Hence, the effective free height above ground is 7m. The outer diameters of the pole at the three steps are, φ1 =114.3 mm, φ2=88.9mm and φ3 =76.1mm; the thickness of hollow tube is 3.63mm all through the height irrespective of the outer diameter. The mass of the pole is 73 kg. The mass of the supplements on top of tower is assumed to be 10 kg. (ii) Electric Cable: As per Clause 9.2 and 9.3 of IS:1554 (Part 1)-1988, the material (i.e., copper) of the cable with conductor area of 35 mm2 has a mass density of 8,920 kg/m3 , yield strength of 230 MPa and modulus of elasticity of 120GPa. The thickness of the PVC insulation of the conductor is chosen as 1.5 mm; the mass density of the insulation material is 1,400 kg/m 3 . In the calculation of the mass of the cable effective at the top of the pole, 5m is taken out of the total 10m length of the cable between the pole and the building. The design lateral displacements are listed in Table 3.2 at different storeys as obtained from structural analysis. Since the electric cable is connected to roof slab of the third storey, the building displacement ∆b to be used in Eq.(3.9b) is taken from Table 3.2 as 32mm.
Table 3.2: Design displacements along the considered direction from structural analysis Storey Deflection Δy (mm) 4 38 3 32 2 23 1 12
3-23
3000 3000 3000 3000
7000
4500
Figure 3.27: Cable wire connected between building and cable: Geometry of building and pole
The design lateral displacement ∆p of the pole is calculated only for shaking along the considered direction in whic h the cable is oriented. The mass of half length of the cable is assumed to act with the pole during earthquake shaking. Hence, Mass of cable = 0.367kg/m × 5m = 1.8 kg Total Mass at top of pole = (0.5×73)+10+1.8 = 48.3 kg The geometric properties of the three steps of the cantilever pole are shown in Table 4. Considering the modulus of elasticity E of the material of the pole to be 200GPa and geometric properties as listed in Table 4 of IS:2713, the lateral stiffness k of the pole is obtained using Eqs.(3.113.12), as
Xc 0.1865
Rc 7.4 10 5 XB 0.1857 RC 1.07 10 4 R A 0.2403 , and X A 0.6125 ,
and hence, lateral stiffness k of the pole from Eq.(3.12) is
k
1 1.633N / mm . XA
Using the mass and the lateral stiffness of the pole, the Natural Period T of the pole is obtained using Eq.(3.20) as
T 2
48.3 1.08s . 1.633
As per Eq.(2.3),
Sa 1.36 g
Hence, the design lateral force VBp on the pole from Eq.(3.13) is
VBp
0.36 1.0 1.36 0.423 0.35 kN 2
Therefore, the design lateral displacement of the pole is given by Eq.(3.21) as
p
348.4 213.4 220mm 1.633
Hence, the design relative displacement between the ends of the pole are calculated using Eq.(3.9b) as
p p 220mm
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B R p 5 32 160 mm Hence, using Eq.(3.9b)
L 220 160 380mm 400mm
Therefore, L = 10m, and L+ΔL =L+D= 10.4m
To estimate the weight per unit length of the cable, the area of the insulation needs to be 2 estimated. Therefore, area of insulation is Dout D in2 4 9.68 2 6.68 2 4 38.54 mm2 . Thus, weight w per unit length of wire is given by
w Acore core g Ainsulation insulation g 35 8.92 9.8 38.54 1.4 9.8 3.76N / m Assuming a factor of safety of 2 for against yielding in tension of copper cable, the design maximum tension Tmax of the cable is
Tmax
230 35 4025N . 2
Repeating step 1-7 mentioned in above procedure will lead to final result. Step 1 L* =10.4 m
V*
*
wL 19.084N 2
Step 2 2
2 H Tmax V * 40252 19.084 2 4024.95N
Lc
wL L 4024.95 3.6710 0.4 H Sinh Sinh 10.40015587m w H 3.67 4024.95
Step 3 Since Lc L* , Lc = 10.4m Step 4
10 0.4 L L w 3.67 Tmax 2 4025 2 1 12.3 Cosh y0 Cosh mm 1 w 3 . 67 4025 T max Step 5
Lc
wL L H H 3.67 10.4 Sinh Sinh 10.4 w H 3.67 H
Solving, H = 75.4 N Step 6
3.67 10.4 19.084 N 2 T H 2 V 2 75.4 2 19.084 2 77.78N V
3-25
Step 7
y0
T wL 77.78 3.67 10 Cosh Cosh 1 1 0.6 m w 2T 3.67 2 77.78
So, the length of the cable to be provided is 10.41m and the initial sag to be provided is 0.6m. During strong ground shaking, the electric cable may get taught and sustain large relative displacement between its ends. But, if the cable sag is as per the above design, it is should not undergo any tension. 3.4.3.2 Water Pipes across Seismic Joint in a Building
Consider earthquake safety of water pipes that runs horizontally between two parts across the seismic joint of the 5-storey RC frame benchmark building (Figure 3.28). In particular, the focus is on the pipe running at the roof level, because the relative movement between the two parts of the building is the largest. The pipe is 3000mm long and of 50mm diameter with 4mm wall thickness. The pipe is snugly held between its supports anchored to the two adjoining parts of the building, both of which are shaking back and forth independently during strong earthquake shaking of the ground. Hence, the pipe is subjected to relative lateral deformations between its ends. To ensure that the pipe is safe against strong earthquake ground shaking effects, its safety should be checked against the imposed relative displacements between its ends in the top storey.
b1 b2
(a)
(b)
Figure 3.28: Water Pipe across Seismic Joint of a building: (a) Initial position, and (b) Extreme position of building parts during earthquake shaking
The relative lateral displacement between the two parts of the building will determine whether or not the pipe will be damaged. From Eq.(3.5), for the benchmark building considered, the horizontal displacement 1 atop one part of the building (i.e., h x =16.5m) and is taken from linear structural analysis of the building under design seismic lateral force acting on it, and this value is 20.58 mm. Hence, the expected displacement D p1 of one part of the building under actual seismic shaking is R times 1 . For the benchmark building, R is 5.0, and therefore Dp 1 5 20. 58 0 102.4 mm. Similarly, the expected displacement Dp2 of the other part of the building under actual seismic shaking is 102.4 mm. Hence, from Eq.(3.8), the estimated relative displacement between the two parts of the building is Dp Dp1 Dp2 102.4 102.4 204.8 mm. From Eq.(3.9), the maximum relative displacement max is aB 5 16500 0.004 16500 0. 004 5 66 66 660mm aA h R h max y h x h sy sx
corresponding to the upper limit of 0.4% drift under design lateral forces specified in Clause 7.12.1 of Draft IS:1893 (Part 1) – 2005. Hence, the governing relative displacement is the smaller of the two, i.e., 205 mm.
3-26
Clearly, the 3m long water pipe is subjected to a strain of 205/3000=0.069, because it is anchored at its two ends resting on the two parts of the benchmark building. This strain is c lose to the fracture strain of mild steel. Thus, the mitigation measure should ensure that such large strain is not generated in the pipe. The best way of achieving this is by providing a flexible pipe coupler with 660mm of relative movement. 3.4.3.3 Electric Wires across Seismic Joint in a Building
Consider earthquake safety of electric that runs horizontally between two parts across the seismic joint of the 5-storey RC frame benchmark building (Figure 3.29). In particular, the focus is on the wire running at the roof level, because the relative movement between the two parts of the building is the largest. The wire is 3000mm long and made of copper of 4mm diameter. The wire is snugly held between its supports anchored to the two adjoining parts of the building, both of which are shaking back and forth independently during strong earthquake shaking of the ground. Hence, the wire is subjected to relative lateral deformations between its ends. To ensure that the wire is safe against strong earthquake ground shaking effects, its safety should be checked against the imposed relative displacements between its ends in the top storey. As in Section 3.4.3.2, the governing relative displacement is 205 mm. Clearly, the 3m long wire is subjected to a strain of 205/3000=0.069, because it is anchored at its two ends resting on the two parts of the benchmark building. This strain is well beyond the fracture strain of copper, i.e., 0.00192. Thus, the mitigation measure should ensure that such large strain is not generated in the pipe. The best way of achieving this is by providing large slack of 660mm in the electric wire to accommodate the relative movement.
b1 b2
(a)
(b)
Figure 3.29: Water Pipe across Seismic Joint of a building: (a) Initial position, and (b) Extreme position of building parts during earthquake shaking
3.5 Earthquake performance of code designed connections of NSEs As mentioned in Section 2.5, the displacement design at connections of NSEs with the SEs is based on lateral displacements of ends of NSE estimated as per Eqs.(3.3) and (3.6), which also involves many simplifications. Also, there are many uncertainties in arriving at the displacements used therein. Actual earthquake shaking may induce higher level of displacements than those estimated using Eqs.(3.3) and (3.6), especially when the building is located near major active earthquake faults or when the shaking is stronger than that shaking expected in design. When the displacement demand on the connections between NSEs and SEs exceeds the code specified forces, the design of connections of NSEs as per the discussion in the previous sections may not suffice. …
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Arnold,C., & Reitherman,R., (1982), Building Configuration and Seismic Design , John Wiley, USA Ambrose,J., and Vergun ,D., (1999), Design for Earthquakes, John Wiley & Sons, Inc., USA CSI, (2010), Structural Analysis Program (SAP) 2000, Version 14, Computers and Structures Inc., USA Eurocode 8, (2003), Design Provisions for Earthquake Resistance of Structures, Part 1- General Rules, Seismic Action and Rules for Buildings, prEN 1998-1, European Committee for Standardization, Brussels FEMA 356, (2000), Pre-standard and Commentary for the Seismic Rehabilitation of Buildings, Federal Emergency Management Authority, Washington DC, USA: This Pre-standard serves as a tool for design professionals, code officials, and building owners undertaking the seismic rehabilitation of existing buildings. The publication contains two parts. The Provisi ons include te chnical requirements for seismic rehabilitation. The Commentary explains the Provisions FEMA 368, (2001), NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures: Part 1-Provisions, Building Seismic Safety Council, National Institute of Building Sciences, Washington, DC, March 2001 FEMA 369, (2001), NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures: Part 2-Commentary, Building Seismic Safety Council, National Institute of Building Sciences, Washington, DC, March 2001 GHI-GHS-SR (2009), Reducing Earthquake Risk in Hospitals from Equipment, Contents, Architectural Elements and Building Utility Systems, GHI, GHS and Swiss Re Gillengerten,J.D., (2003), “Design of Nonstructural Systems and Components,” The Seismic Design Handbook (Naeim, F., Editor), Kluwer Academic Publishers, Second Edition IBC 2003, International Building Code, International Code Council, USA IITK-GDMA, (2005), IITK-GSDMA Guidelines for Seismic Evaluation and Strengthening of Buildings: Provisions with Commentary and Explanatory Examples, IITK-GSDMA-EQ06-V4.0, August 2005, Indian Institute of Technology Kanpur and Gujarat State Disaster Mitigation Authority, Gandhinagar, India IITK-GDMA, (2005), IITK-GSDMA Guidelines for Proposed Draft Code and Commentary on Indian Seismic Code IS:1893 (Part 1), IITK-GSDMA-EQ05-V4.0, August 2005, Indian Institute of Technology Kanpur and Gujarat State Disaster Mitigation Authority, Gandhinagar, India IS:1554 (Part 1), (1988), Speci ficati on for PVC Insulated (Heavy Duty) Electric Cables, Bureau of Indian Standards, New Delhi IS:1893 (Part 1), (2002), Criteria for Ear thquake Resistant Design of Structures, Bureau of Indian Standards, New Delhi IS:2713 (Parts 1-3), (2003), Specification for Tubular Steel Poles for Overhear Power Lines, Bureau of Indian Standards, New Delhi IS:____ (2007), Draft Indian Standard Code for Seismic Retrofitting of Reinforced Concrete Frame Buildings, under discussi on in the Earthquake Engineering Sectional Committee (CED 39), Bureau of Indian Standards, New Delhi Murty,C.V.R., (2010), IITK-BMTPC Earthquake Tips - Learning Earthquake Design and Construction, National Information Center of Earthquake Engineering, IIT Kanpur, India Newmark,N.M. and Hall,W.J., (1973), Procedures and Criteria for Earthquake Resist and Design, Building Practices for Disaster Mitigation, Building Science Series 46, US Department of Commerce, National Bureau of Standards, Washington DC, pp. 209–236 Paulay,T., & Priestley,M.J.N., (1992), Seismic Design of Reinforced Concrete and Masonry Buildings”, John Wiley, USA Stratta,J.L., (2003), Manual of Seismic Design , Pearson Education, First Indian Reprint, 2003 Villaverde,R., (2004), “Seismic Analysis and Design of Nonstructural Elements,” Earth Engineering: from Engineering Seismology to Performance-Based Engineering (Bozorgnia, Y., and Bereto, V.V., Editors), CRS Press, USA Makris,N., and Roussos,Y., (1998), Rocking Response and Overturning of Equipment Under Horizontal Pulse-Type Base Motion , Pacific Earthquake Engineering Research Center Report, No. PEER 1998/05 , University of California, Berkeley, USA
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Acknowledgements
3-28
The authors are extremely grateful to the Gujarat State Disaster Management Authority (GSDMA), Government of Gujarat, Gandhinagar (Gujarat, India), for readily agreeing to support the preparation of this book; the generous financial grant provided by GSDMA towards this effort is gratefully acknowledged. CSI India, New Delhi, provided the nonlinear structural analysis tools, e.g., SAP2000, to undertake numerical work for the preparation of this manuscript; this contribution is sincerely acknowledged. Professors Devdas Menon and A. Meher Prasad at IIT Madras provided resources during the early days of the work and offered continued encouragement during the entire course of this work; the authors are indebted to them for this affection and support. The authors acknowledge with thanks the support offered by various sections of IIT Madras in administering this book writing project. In particular, the support offered by Mrs. C. Sankari and Mr. Anand Raj of the Structural Engineering Laboratory of the Institute, is specially acknowledged. …
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