truss type shear connectors used in segmental

TRUSS TYPE SHEAR CONNECTORS USED IN SEGMENTAL COMPOSITE SKEW SLABS Project report submitted to

MANIPAL UNIVERSITY For Partial Fulfillment of the Requirement for the Award of the Degree of

MASTER OF TECHNOLOGY in

STRUCTURAL ENGINEERING by

DHANUSH. S Under the Guidance of

Dr. K. BALAKRISHNA RAO Professor, Department of Civil Engineering, Manipal Institute of Technology

DEPARTMENT OF CIVIL ENGINEERING

MANIPAL INSTITUTE OF TECHNOLOGY (A constituent Institute of MANIPAL UNIVERSITY)

MANIPAL - 576 104, KARNATAKA, INDIA

2015

ABSTRACT

Keywords: Truss shear connector, composite slab, ATENA, slab flexure test, interface shear capacity, skew slabs. In the recent times, use of concrete-concrete composite slabs as bridge decks has become a common practice, mainly due to the ease of construction and considerable reduction in use of form work and labour. Most of the recent designs for bridge decks are often skew, skew shape of the slab facilitates a large variety of options for an engineer in terms of alignment opportunities in case of obstructions. Composite action of two concrete members is achieved by the interface shear transfer between the two members, this mechanism is of great significance. The interface shear carrying capacity is dependent on the surface properties and shear connectors provided. In the current research ATENA is used, it is a FEM based software in which the interface properties between materials can be modelled to a great level of detail. In the present study the effect of angle of inclination, size and the depth of embedment of truss connector on the load carrying behaviour is studied with the help of a beam model. Based on the results of the beam study shear connectors are then used in a one way slab of size 1m X 1m in varying patterns and the flexural load carrying capacity is compared with that of a solid slab and a non-composite slab. The angles of inclination varied are 30o, 45o, 60o and 75o with varying bar diameters of 8mm, 10mm and 12mm. Angles between 60o to 75o are found most efficient with no significant changes when

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diameters are varied. The ultimate load for a given connector is found to be independent of the depth of embedment. In the present study we also try to determine the effect of truss shaped shear connectors on the flexural load carrying capacity of slabs having various degrees of skew-ness. Four series of slabs are modelled, each corresponding to a certain degree of skew-ness, each series in turn is sub-classified into sub-series based on the number of shear connectors, and their layout. 8mm truss connector with 60o inclination and 70mm depth of embedment is used as shear connectors in skew one way slabs in varying configurations and analysed for pure bending. Results show that the load carrying capacity of the slab decreases as the angle of skew-ness increases, and the load carrying capacity of all slabs increases as the number of shear connectors in the longitudinal direction increases. Shear connectors when provided in transverse direction does not seem the influence the behaviour of the slab. However, when transverse shear connectors are provided along with longitudinal connectors the behaviour improves slightly.

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CHAPTER-1 INTRODUCTION 1.1 General The use of precast, pre-stressed concrete deck is typical in bridge and building construction.

The precast slabs are cast in controlled environment and can be

prevented from external hazards. It reduces the construction time by casting simultaneously large number of precast elements. The precast beams are fabricated at a pre-stressing plant and then shipped to the job site and set in place. Once in place, a field cast concrete slab is poured over the precast beams in order to provide integrity and stability to the structural system. In order for the composite beams to behave as purely monolithic, the composite interface bond must remain intact. If the bond is strong, the composite member will deform as a single beam when loaded as shown in Fig. 1.1. The fully bonded interface will allow the horizontal shear forces to be transferred across the interface. The fully composite action is reflected in strains remaining essentially linear across the panel thickness as shown in Fig.1.2. However, when a composite beam with a weaker bond is loaded, there is a greater chance for the interface to fail, resulting in relative slip between the two composite elements. If slip occurs, then slab and flange will independently resist a portion of the load as two separate members having two neutral axes as shown in Fig.1.3 and 1.4. It is important that horizontal shear forces being carried in both the deck and beam should readily cross the interface zone between these two members. The transfer of these shearing forces is commonly known as interface shear transfer or shear friction. 1

The shear transfer plays an important role in determining the composite action of the section.

Fig 1.1. Fully composite Section

Fig 1.2. Shear Transfer of Composite Section

Fig 1.3. Horizontal Slip

Fig 1.4. Non Composite Section 2

The interface shear transfer is governed by the shear connectors, which provide monolithic action between two composite members. It transfers the horizontal shear effectively and forms a fully bonded composite member. The strength of the shear connector between the two composite members should be high enough to prevent any progressive slip from taking place. The presence of a shear connection prevents the slip between the two components and achieves a much stiffer and stronger composite section. The resulting degree of composite action is affected by the number and property of the shear connector resulting in a wide range of possible behavior of the section from non-composite to fully composite. 1.2 Elastic Behaviour of Composite Precast Slabs The behaviour of composite slabs under transverse loading is best illustrated by using two identical slabs, each having a same cross section and spanning a distance of λ, one placed at the top of the other. The precast slabs support a uniformly distributed load of w/unit length as shown. For theoretical explanation, two extreme cases of no interaction and 100% (full) interaction are given below:

(a) Fig 1.5. Elevation and section showing dimensions of the beam model

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(b)

(c)

Fig 1.5. (b) Flexural, (c) Shear Behaviour of solid and non-composite members

1.2.1 No Interaction Case It is first assumed that there is no shear connection between the beams, so that they are just seated on one another but act independently. The moment of inertia (I) of each 3

beam is given by bh /12. The load carried by each beam is w/2 per unit length, with 2

mid span moment of wλ /16 and vertical compressive stress of w/2b at the interface. From elementary beam theory, the maximum bending stress in each beam is given by, 𝑓=

𝑀𝑦𝑚𝑎𝑥 𝐼

=

3𝑤λ2

(1.1)

8𝑏ℎ2

Where, M is the maximum bending moment and ymax is the distance to the extreme fiber equal to h/2. The maximum shear stress (qmax) that occurs at the neutral axis of each member near support is given by 3 𝑤λ 1

3𝑤λ

4

8𝑏ℎ

𝑞𝑚𝑎𝑥 = 2

= 𝑏ℎ

(1.2)

4

and the maximum deflection is given by 𝛿=

5(𝑤⁄2)λ4 384𝐸𝐼

5𝑤λ4

= 64𝐸𝑏ℎ3

(1.3)

The bending moment in each beam at a distance x from mid span is, 𝑀𝑥 =

𝑤(λ2 −4𝑥2 )

(1.4)

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So, the tensile strain at the bottom fiber of the upper beam and the compression stress at the top fiber of the lower beam is, 𝜀𝑥 =

𝑀𝑦𝑚𝑎𝑥 𝐸𝐼

=

3𝑤(λ2 −4𝑥2 )

(1.5)

8𝐸𝑏ℎ2

Hence the top fiber of the bottom beam undergoes slip relative to the bottom fiber of the top beam. The slip strain i.e. the relative displacement between adjacent fibers is therefore 2εx. Denoting slip by S, we get, 𝑑𝑆 𝑑𝑥

= 2𝜀𝑥 =

3𝑤(λ2 −4𝑥 2 )

(1.6)

4𝐸𝑏ℎ2

Integrating and applying the symmetry boundary condition S = 0 at x = 0 we get the equation 𝑆=

𝑤(3λ2 𝑥−4𝑥 3 )

(1.7)

4𝐸𝑏ℎ2

The Eqn. (1.6) and Eqn. (1.7) show that at x = 0, slip strain is maximum whereas the slip is zero, and at x=λ/2, slip is maximum whereas slip strain is zero. The maximum slip (i.e. Smax = wλ3/4Ebh2) works out to be 3.2h/λ times the maximum deflection of each beam derived earlier. If λ /(2h) of beams is 20, the slip value obtained is 0.08 times the maximum deflection. This shows that slip is a very small in comparison to deflection of beam. In order to prevent slip between the two beams at the interface and ensure bending strain compatibility shear connectors are frequently used. Since the slip at the interface is small these shear connections, for full composite action, have to be very stiff.

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1.2.2 Full (100%) interaction case Let us now assume that the beams are joined together by infinitely stiff shear connection along the face AB in Fig. 1. As slip and slip strain are now zero everywhere, this case is called “full interaction”. In this case the depth of the composite beam is 2h with a breadth b, so that I = 2bh3/3. The mid-span moment is wλ2/8. The maximum bending stress is given by 𝑓𝑚𝑎𝑥 =

𝑀𝑦𝑚𝑎𝑥 𝐼

=

𝑤λ2 8

3

3𝑤λ2

ℎ = 16𝑏ℎ2 2𝑏ℎ3

(1.8)

This value is half of the bending stress given by Eqn. (1.1) for “no interaction case”. The maximum shear stress qmax remains unaltered but occurs at mid depth. The mid span deflection is 5𝑤λ4

𝛿 = 256𝐸𝑏ℎ3

(1.9)

This value of deflection is one fourth of that of the value obtained from Eqn. (1.3) Thus by providing full shear connection between slab and beam, the strength and stiffness of the system can be significantly increased, even though the material consumption is essentially the same. The shear stress at the interface is 𝑉𝑥 = 𝑞𝑥 𝑏 =

3𝑤𝑥

(1.10)

4ℎ

where x is measured from the centre of the span. The design of the connectors has to be adequate to sustain the shear stress. In elastic design, connections are provided at varying spacing normally known as “triangular spacing”. In this case the spacing works out to be 4𝑃ℎ

𝑠 = 3𝑤𝑥

(1.11)

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where, P is the design shear resistance of a connector. The total shear force in a half of the span is λ⁄ 3𝑤𝑥 2 𝑑𝑥 4ℎ

𝑉 = ∫0

=

3𝑤λ2

(1.12)

32ℎ

With a value of λ/(2h)≈ 20, the total shear in the whole span works out to be 2𝑉 = 2 ×

3λ 32ℎ

𝑤λ ≈ 8wλ

(1.13)

i.e. eight times the total load carried by the beam

1.3 Types of Shear Connectors: The design of shear connectors is a vital aspect in the design of composite beams. Shear connectors are of many types, and according to the distribution of shear forces and functional dependency between strength and deformation, they are often categorized as rigid or flexible. For rigid shear connectors, shear forces are resisted through the front side by shearing, and in the proximity of ultimate strength its deformation is insignificant. Stronger concentrated stress in the surrounding concrete is produced by this type of connector, which results in either failure of the concrete or failure of the connector. For flexible shear connectors, shear forces are resisted by bending, tension or shearing at the root, at the connection point of the steel beam, a point where upon reaching the ultimate strength values, such connectors are subjected to plastic deformation. Flexible shear connectors are more ductile and are not as prompt in terms of the manner of failure. Apart from depending on the strength of the shear connector itself, the shear strength and stiffness of the connection is also dependent on the resistance of the concrete slab against longitudinal cracking caused by high concentration of the shear force at each

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connector. Concrete resistance is a function of its splitting strength, which is directly related to the nature of concrete construction around the connector. In order to ascertain the behaviour of different types of shear connectors, experimental tests have been done extensively. Fig 1.6. to Fig 1.13. is an attempt that has been made to review the different types of shear connector that can be found in composite structures.

Fig 1.6. Head Stud Shear Connector.

Fig 1.7. Perfobond Ribs Shear Connector.

Fig 1.8. Oscillating-Perfobondstrip Shear Connector. 8

Fig 1.9. Waveform-Strip Shear Connector.

Fig 1.10. T Shear Connector.

Fig 1.11. Channel Shear Connector.

Fig 1.12 Pyramidal Shear Connector.

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Fig 1.13. Non-Welded Shear Connector. The interface shear transfer is governed by the shear connectors, which provide monolithic action between two composite members. It transfers the horizontal shear effectively and forms a fully bonded composite member. The strength of the shear connector between the two composite members should be high enough to prevent any progressive slip from taking place. The presence of a shear connection prevents the slip between the two components and achieves a much stiffer and stronger composite section. The resulting degree of composite action is affected by the number and property of the shear connector resulting in a wide range of possible behavior of the section from non-composite to fully composite. During the period, literature review was done on influence of shear connectors on concrete – concrete composite specimens. 1.4 Objective of study The following are the main objectives of the present study:  To study the effect of bar diameter on the interface shear carrying capacity of the shear connector in a composite member.  To study the effect of angle of inclination of the bar on the interface shear carrying capacity of truss type shear connector in a composite member.  To study the effect of depth of embedment of the shear connector on the interface shear carrying capacity of a composite member. 10

 To study the effect of position and direction of shear connectors on the interface shear carrying capacity in slabs subjected to flexure loading  To study the effect of position and direction of shear connectors on the interface shear carrying capacity in slabs subjected to push off test  To study the effect of spacing of shear connector on flexural and push off behaviour of slabs  To study the effect of value of cohesion on the interface shear carrying capacity in the interface modeling of concrete  To study the effect of co-efficient of friction on the interface shear carrying capacity in the interface modeling of concrete 1.5 Summary This chapter briefs about behavior of composite members and its difference from solid members, their elastic behaviour and the different types of shear connectors available to make a member composite.

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CHAPTER-2 LITERATURE REVIEW Overview This chapter deals with the backgrounds which lead to the present work. The chapter also lists various research works which have been previously conducted by various authors pertaining to the topic. It also summarizes the general outcome of the literature study. 2.1 Literature Review Benoyane et al (2008) studied the flexural behaviour of pre-cast concrete sandwich composite panel having truss type shear connector as shown in Fig. 2.1. The truss type shear connector used had a diameter of 6mm, zigzagged at an included angle of 90°. The distance for each bent of truss was 90 mm. The structural behavior was determined by using flexure test experimentally as shown in Fig 2.2 and Fig 2.3. The variant of the experiment are the specimen size and number of shear connectors. The specimen size was chosen such that it represents one way and two way slab. The flexural test results showed that the precast specimens had a load deflection profile similar to that of one way and two way slab. The difference in load is less than 4 %, when finite element result is compared to experimental result of one way specimen. It was observed that increasing the number of shear connector increases the ultimate load of the specimen.

Fig 2.1. Truss type Shear Connector, Benoyane et al (2008) 12

Fig 2.2. Flexure Test: One way slab, Benoyane et al (2008)

Fig 2.3. Flexure Test: Two way slab, Benoyane et al (2008)

Truss type shear connectors were used in ferrocement brick layer by Thanoon et al (2010). The shear connector used had a diameter of 5mm and zigzagged at an angle of 45°. The distance for each bent was 66.4 mm and the height was 80 mm. The structural performance of the specimen was determined by flexure test as shown in Fig 2.6. The 13

variant of the test were the number of shear connectors (two and three) and the arrangement (continuous and discontinuous) of brick layers. Single truss, dual truss type and concrete ribs were used as shear connector. From the strain distribution across the depth of the slab, the two layers are acting initially in a fully composite manner, but during failure the two layer started to separate forming a long horizontal crack. The shear connection has to be modified for better structural performance. Increasing the number of shear connectors increases the compositeness of the specimen. The specimens having discontinuous arrangement and having three number of truss type shear connector showed better performance compared to other specimens in terms of ductility and ultimate load. In another experiment the truss type shear connector was compared with the concrete ribs provided between the shear connector. The variant of the experiment were the rib thickness and the number of shear connectors. Push off test was carried out for the specimens as shown in Fig 2.5. The push off test results showed that the specimen with two number of shear connector and ribbed specimen have similar load slip behavior. The specimen with single shear connector showed a very large slip for smaller load. The failure was sudden and brittle.

Fig 2.4. Shear Connector, Thanoon et al (2010)

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Fig 2.5. Push-Off Test, Thanoon et al (2010)

Fig 2.6. Flexure Test, Thanoon et al (2010)

Thanoon et al (2010) studied the structural behaviour of ferrocement-brick composite floor slab panel. The slab panel consists of two layers (precast ferrocement layer and brick mortar layer) joined together using shear connectors as shown in Fig 2.7. They studied the influence of brick pattern in the flexural behaviour of the slab. The slab was simply supported and two line loads were created by applying load through hydraulic jack. The majority of crack pattern were found to be on moment region. The ductility ratios were observed to be more than 2. The cracking load observed is about 30 percent of the ultimate load. The concrete rib enhances the ductility of the slab. The specimen with triple shear connector showed higher experimental load. The increase in the 15

number of shear connector increased the compositeness, thereby increased the load carrying capacity of the member.

Fig 2.7. Arrangement of Steel truss and Shear Connector, Thanoon et al (2010) Joseph (2006) conducted push off test as shown in Fig 2.8. and compared the shear transfer on welded stud shear connector and the reinforcing stirrups crossing the shear plane, to study the horizontal shear transfer for full depth precast concrete bridge deck panels. The test was conducted by varying the number of nelson studs welded to the plate and the reinforcement stirrups crossing the shear plane. Increasing the number of shear connectors increased the peak stress. This significant increase was not seen in the tests with reinforcing bar stirrups.

Fig 2.8. Push Off Test, Joseph (2006)

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This is likely due to the fact that there is significantly more steel crossing the interface in these tests. As the amount of steel crossing the interface is increased so is the shear resistance that the shear connectors can provide. Once the shear resistance of the shear connectors exceeded, the peak load can’t be carried by the shear connectors. The specimens performed very similarly to the test specimens that utilized the typical reinforcement bar stirrups. Headed shear studs had a lower yield stress, so an increased number of studs may be required. Gonert (2003) studied the horizontal shear transfer across a roughened surface. He studied the influence of shear transfer capacity of precast member with cast in-situ member by performing push off test. He varied the surface roughness of the precast layer and its influence in the shear transfer capacity. The push-off test specimen used was as shown in the Fig 2.9. The precast member was braced and the in situ concrete is pushed by applying a ramped load until shear failure. The roller support was placed on the specimen to prevent the instabilities inherent in the test.

Fig 2.9. Push Off Test, Gonert (2003) Banta (2005) studied the horizontal shear strength of ductile and light weight concrete and compared the horizontal design shear equation. The effects from various surface treatments, reinforcement ratios, and aspect ratios were determined. The shear equation

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in the codes was found to be conservative. Twenty Four push-off tests were conducted and the push off test specimen used is as shown in Fig 2.10. and Fig 2.11. By removing a very thin layer of concrete from the surface of the flange using jack hammer or hydraulic demolition, the reinforcing fibers in the matrix were exposed. This allowed for extra mechanical bond between the deck and beam concrete.

Fig 2.10. Push-Off Test Specimen, Banta (2005)

Fig 2.11. Push Off Test Frame, Banta (2005) Pong et al (2005) studied GFRP Connectors in Sandwich Panels. GFRP V-shaped with end hooks was used in precast concrete sandwich panel as Shown in Fig 2.12. The

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sandwich panels were tested for flexure and push off test as shown in Fig 2.13. and Fig 2.14. The push off test result showed that while increasing the area of GFRP, the ultimate load value also increases. The ultimate load of the specimen having welded wire shear connector was more compared to that of the ultimate strength of GFRP. The load deflection curve of GFRP specimen exhibited their ductile nature. The results of the test showed that ultimate load was about 75 % of the full composite strength.

Fig 2.12. V-Shaped Shear Connector, Pong et al (2005)

Fig 2.13. Push Off Test, Pong et al (2005)

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Fig 2.14. Flexure Test, Pong et al (2005) Swamy et al (1987) conducted push-off test to study the shear transfer in steel fiber reinforced concrete. The variations in the test were crack width, number of stirrups and stirrup yield stress. The specimen used had a size of 520×300×125 mm and a shear plane of 220×125mm. A specially fabricated sliding bearing was placed centrally between the top face of the specimen and the upper platten of the test machine to ensure that separation of the two halves of the test specimen was not restrained by the test machine. The shear stress was obtained by dividing the ultimate load by shear area. The test compared the shear capacity of pre cracked and un-cracked specimen. The test result showed that there is an increase in residual strength. Fibers and stirrups both influence the shear strength. All the Pre cracked specimen failed along the cracked plane. Scholz (2004) studied the mortars and surface preparation of horizontal shear connection between precast concrete panels and concrete girders. The horizontal shear strength was determined by performing push off test through L-shaped specimen. The specimen was supported on the rollers and load was applied through hydraulic ram as shown in Fig 2.15.

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Fig 2.15. Push Off Test Specimen, Scholz (2004) A Kabir et al (2002) studied the effect of reinforcement pattern on the load carrying capacity simply supported skew slabs and concluded that when reinforcement is provided parallel to the edges is widely adopted due to ease in fabrication and the ultimate load is not much lesser compared to other patterns.

Fig 2.16. Skew slabs with various reinforcement configurations, A Kabir et al (2002)

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Bush and Stine (1994) studied the flexural behaviour of precast concrete sandwich panel with continuous truss connectors in which two series were tested. First series of composite precast concrete sandwich panel system contained various connector reinforcement and construction details which is similar to certain commercially produced panels, while the second series panels contained modified details to better evaluate interface shear transfer behaviour. Precast concrete sandwich panels were constructed to achieve up to 100 percent composite action, depending on the ability of the embedded connectors to transfer the shear generated by longitudinal flexureTwo series of test panels were constructed and production series panels were fabricated in the same manner as commercial panels produced at a precast plant, while modified series panels were constructed as idealized panels by eliminating extraneous paths of shear transfer through modification of certain construction details. Each series tested push out specimen and three panels of various wythe connectors configuration. In addition, a specimen for cyclic loading was constructed with a modified series. All statically loaded panels were tested in a horizontal position with simple supports and a uniform pressure applied from beneath with an air bag. The intent was to fully force the truss girder to fully participate in order to obtain information on their contribution towards panel stiffness and shear transfer between the wythes.

Fig 2.17. Truss Type Shear Connector, Bush and Stine (1994) Mohamad et al (2014) studied the structural behaviour of Precast Lightweight Foam Concrete Sandwich Panel (PFLP) under flexure. For these experiments four specimens 22

with double shear connector of 6mm diameter and steel reinforcement of 9mm diameter were cast and flexure load test was also carried out. The structural behaviour of these specimens was studied in the context of ultimate flexure load, crack pattern, loaddeflection profile and also the efficiency of shear connectors. All the panel specimens were found to behave in a partially composite manner with the ultimate flexure test load values as compared with theoretical values of non-composite panel. PFLP consists of two wythe layers of lightweight foamed concrete with polystyrene and these layers are bonded by double shear connectors that are diagonally embedded as shown in Fig 2.18.

Fig 2.18. Double Steel Shear Connector, Mohamad et al (2014) The PLFP panels were tested in a UTM of 1000 kN capacity in horizontal position. The panel was simply supported and was subjected to 2 line flexural loads. The force introduced to the load cell was generated by hydraulic pump and the force was transferred through the I-beams to the panel. A total of 12 strain gauges of size 30 mm were used to measure the strain across the depth in each panel. The strain gauge was placed on the surface and across the thickness at mid-span of panel. The locations of the strain gauges are as illustrated in Linear Voltage Displacement Transducer (LVDT) was used to measure the deflection. The ultimate load increases with the increase of the thickness, split tensile strength and compressive strength of foamed concrete.

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Sanjay Kumar (2012) He studied the behaviour of the simply supported skew slab under centre point loading by finite element modelling with ATENA and compared with the experimental results. In his work skew slabs with ratio of short diagonal to span lesser than unity and greater than unity were both studied. In this the skewed slabs with edge supports have been modelled and compared with experimental results of the skew slab without edge beam. The skewed slab is modelled with an angle of 16.49o and the nonlinear load deflection and crack patterns are studied at different load steps. Element geometric modelling of concrete has been done using 3D solid brick element having three degree of freedom and the reinforcements are modelled as 3D bar elements. In this model skew slab specimen load have been applied at the centre of the slabs and gradually increased in the steps till failure. From the modeling it was observed that the increase in uplift increases the displacement. The author concluded that by introducing edge supports in the skew slabs, the load carrying capacity has significantly increased and the uplifts has been minimized to greater extent.

Fig 2.19. Failure and Crack Patterns for Mid-Point Loading, Sanjay Kumar (2012)

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2.2 Summary In the review of literature on analytical and experimental studies, the authors studied the interface shear properties between concrete-concrete composite members, the types of shear connectors used, truss shear connectors importantly. Loading and experimental setups were also studied and adopted for the present study. Research gap was found in the field of truss shear connectors used as bridge decks in one way slabs, especially skew slabs, and this was adopted as one of the main objectives on the current study.

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CHAPTER-3 FINITE ELEMENT MODELLING

Overview In this chapter, the basic concept of finite element method, geometric and material modelling of concrete, steel, interface, and bond model are discussed. Modelling and validation of a typical composite slab is carried out so that same modelling can be adopted for further studies 3.1. Finite Element Method The finite element method (FEM) is a numerical technique for finding approximate solutions to boundary value problems for differential equations. It uses variation methods (the calculus of variations) to minimize an error function and produce a stable solution. Analogous to the idea that connecting many tiny straight lines can approximate a larger circle, FEM encompasses all the methods for connecting many simple element equations over many small sub domains, named finite elements, to approximate a more complex equation over a larger domain. The Finite Element Method is a good choice for solving partial differential equations over complex domains. To summarize in general terms how the finite element method works we will list these steps; the basics steps involved in any finite element analysis consist of the following: 1. Discretize the Continuum. The first step is to divide the member or solution region in to elements. A variety of element in regular shapes may be used, and different element shapes may be employed in the same solution region. Indeed, when analysing an elastic structure that has

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different types of components such as columns, slabs and beams, it is not only desirable but also necessary to use different elements in the same solution. 2. Select Interpolation Functions. The next step is to assign nodes to each element and then choose the interpolation function to represent the variation of the field variable over the element. The field variable may be a scalar, a vector, or a higher-order tensor. Often, polynomials are selected as interpolation functions for the field variable because they are easy to integrate and differentiate. The degree of the polynomial chosen depends on the number of nodes assigned to the element, the nature and number of unknowns at each node, and certain continuity requirements imposed at the nodes and along the element boundaries. The magnitude of the field variable as well as the magnitude of its derivatives may be the unknowns at the nodes. 3. Find the Element Properties. Once the finite element model has been established (that is, once the elements and their interpolation functions have been selected), we are ready to determine the matrix equations expressing the properties of the individual elements. For this task we may use one of the three approaches just mentioned: the direct approach, the variational approach, or the weighted residuals approach. 4. Assemble the Element Properties to Obtain the System Equations. To find the properties of the overall system modelled by the network of elements we must assemble all the element properties. In other words, we combine the matrix equations expressing the behaviour of the elements and form the matrix equations expressing the behaviour of the entire system. The matrix equations for the system have the same form as the equations for an individual element except that they contain many more terms because they include all nodes. The basis for the assembly procedure stems

27

from the fact that at a node, where elements are interconnected, the value of the field variable is the same for each element sharing that node. A unique feature of the finite element method is that the system equations are generated by assembly of the individual element equations. In contrast, in the finite difference method the system equations are generated by writing nodal equations. 5. Impose the Boundary Conditions. Before the system equations are ready for solution they must be modified to account for the boundary conditions of the problem. At this stage we impose known nodal values of the dependent variables or nodal loads. 6. Solve the System Equations. The assembly process gives a set of simultaneous equations that we solve to obtain the unknown nodal values of the problem. If the problem describes steady or equilibrium behaviour, then we must solve a set of linear or nonlinear algebraic equations. There are standard solution techniques for solving these equations. If the problem is unsteady, the nodal unknowns are a function of time, and we must solve a set of linear or nonlinear ordinary differential equations. 7. Make Additional Computations If Desired. Many times we use the solution of the system equations to calculate other important parameters. For example, in a structural problem the nodal unknowns are displacement components. From these displacements we calculate element strains and stresses. 3.1.2. Application of finite element method  FEM helps in solving complex elasticity and structural analysis problem in civil engineering.  FEM helps tremendously in producing stiffness and strength visualizations and also in minimizing weight, materials, and costs.

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 FEM allows detailed visualization of where structures bend or twist, and indicates the distribution of stresses and displacements.  FEM software provides a wide range of simulation options for controlling the complexity of both modeling and analysis of a system. Similarly, the desired level of accuracy required and associated computational time requirements can be managed simultaneously to address most engineering applications.  FEM allows entire designs to be constructed, refined, and optimized before the design is manufactured.  FEM is the most powerful design tool which significantly improved both the standard of engineering designs and the methodology of the design process in many civil engineering applications.  In summary, benefits of FEM include increased accuracy, enhanced design and better insight into critical design parameters, virtual prototyping, and fewer hardware prototypes, a faster and less Common FEA Applications.  FEM is used in different branches of science and engineering such as Mechanical, Aerospace, Civil, Automotive Heat Transfer Electromagnetic Fields Acoustics and Biomechanics. 3.2. Finite element modelling Hence, the basic concept of Finite element modelling is the subdivision of the mathematical model into disjoint (non-overlapping) components of simple geometry. The response of each element is expressed in terms of a finite number of degrees of freedom characterized as the value of an unknown function, or at a set of nodal points. The response of the mathematical model is then considered to be the discrete model obtained by assembling the collection of all elements. Within the framework of the finite element method, reinforced concrete can be represented either by superimposition

29

of the material models for the constituent parts (i.e., for concrete, for reinforcing steel), or by a constitutive law for the composite concrete, embedded steel. The finite element method is well suited for superimposition of the material models for the constituent parts of a composite material. Several constitutive models covering these effects are implemented in the computer code ATENA, which is a finite element package designed for computer simulation of concrete structures. The graphical user interface in ATENA provides an efficient and powerful environment for solving many anchoring problems. ATENA enables virtual testing of structures using computers, which is the present trend in the research and development world. Material models of this type can be employed for virtually all kinds of reinforced concrete structural members. Depending on the type of material modelling to be solved in ATENA, concrete can be represented by solid brick element, the reinforcement is modelled by bar elements (discrete representation).Geometry and shape of any mathematical element help in proper placement of the nodal points and materials properties helps in using proper modelling. Material modelling defines the various parameters of the materials involved in the specimen which then determine the behaviour of the structure. ATENA carries a finite element analysis based on the SBETA model. The most important material models in ATENA for RCC structure are concrete and reinforcement. These advanced models take into account all the important aspects of real material behaviour. 3.2.1. Modelling of concrete 3.2.1.1. Geometry of the Concrete Element geometric modelling of concrete has been done using 3D solid brick element with 8 nodes in ATENA, shown in Fig 23.

30

Fig 3.1. Geometry of Brick elements 3.2.1.2. Element Properties 3D solid brick element having three degree of freedom at each node: translations in the nodal x, y and z directions. This is an iso-parametric elements integrated by Gauss integration at integration points. This element is capable of plastic deformation, cracking in three orthogonal directions, and crushing. The most important aspect of this element is the treatment of non-linear material properties. 3.2.1.2. Element Interpolation function 3D solid brick element interpolation functions for all variants of the elements are given below: N1= (1/8) (1+r) (1+s) (1+t)

N2= (1/8) (1-r) (1+s) (1+t)

N3= (1/8) (1-r) (1-s) (1+t)

N4= (1/8) (1+r) (1-s) (1+t)

N5= (1/8) (1+r) (1+s) (1-t)

N6= (1/8) (1-r) (1+s) (1-t)

N7= (1/8) (1-r) (1-s) (1-t)

N8= (1/8) (1+r) (1-s) (1-t)

3.2.1.3. Compressive failure of Concrete The nonlinear Behavior of concrete in the biaxial stress state is described by means of effective stress σcef, and the equivalent uni-axial strain ϵeq. The effective stress in most cases is the principal stress. The equivalent uni-axial strain is introduced in order to

31

eliminate the Poisson’s effect in the plane stress state. Unloading is a linear function to the origin. The equivalent uniaxial stress strain diagram as shown in fig 3.2.

Fig 3.2. Equivalent uniaxial stress strain law 𝜀𝑒𝑞 =

𝜎𝑐𝑖

(3.1)

𝐸𝑐𝑖

The equivalent uniaxial strain can be considered as the strain, that would be produced by the stress 𝜎𝑐𝑖 in a uniaxial test with modulus 𝜎𝑐𝑖 associated with the direction i. The relation between stress σcef and strain ϵeq is not unique and depends on a load history. A change from loading to unloading occurs, when the increment of the effective strain changes the sign. If subsequent reloading occurs the linear unloading path is followed until the last loading point U is reached again. Then, the loading function is resumed. The peak values of stress in compression f’cef and in tension f’tef are calculated according to the biaxial stress state. The above defined stress-strain relation is used to calculate the elastic modulus for the material stiffness matrices. It is used in the constitutive equation to calculate stresses for the given strain state. 𝜎𝐶

ECS= ∈𝑒𝑞

(3.2)

32

Fig 3.3 Biaxial stress strain curve for concrete The behaviour of concrete in tension without cracks is assumed linear elastic. Ec is the initial elastic modulus of concrete, f’tef is the effective tensile strength derived from the biaxial failure function. A biaxial stress failure criterion according to KUPFER et al. (1969) 24 is used as shown in Fig 3.3. In the compression-compression stress state the failure function is 𝑒𝑓

𝑓′𝑐 =

1+3.65𝑎 (1+𝑎)2

𝜎

𝑓′𝑐 , 𝑎 = 𝜎𝑐1

(3.3)

𝑐2

Where 𝜎𝑐1 and 𝜎𝑐2 are the principal stresses in concrete and f’c is the uniaxial cylinder strength. In the biaxial stress state, the strength of concrete is predicted under the assumption of a proportional stress path. In the tension-compression state, the failure function continues linearly from the point σc1=0, σc2=fc’ into the tension-compression region with the linearly decreasing strength: 𝜎𝑐1

fc’ef= fc’rec; rec = (1+5.3278 𝑓′𝑐 )

(3.4)

Where rec is the reduction factor of the compressive strength in the principal direction 2 due to the tensile stress in the principal direction 1 and has a range from 0.9-1.

33

In the tension-tension state, the tensile strength is constant and equal to the uniaxial tensile strength f’t. In the tension-compression state, the tensile strength is reduced by the relation: σc2

ft’ef = ft’ret; ret = (1- 0.9 fc’ )

(3.5)

Where ret is the reduction factor of the tensile strength in the direction 1 due to the compressive stress in the direction 2. 3.2.1.4. Cracking model for concrete Concrete without cracks is considered as in isotropic material and with cracks is taken to be orthotropic. The behaviour of concrete before cracking is assumed to be linear. The initial modulus of concrete in compression is taken to be the elastic modulus in tension for the linear portion. For the post cracking behaviour of concrete, an exponential law depicts cracking is used as shown in fig.3.4. the crack width is found from below equation (3.6)

Fig 3.4. Exponential crack opening law Wc= 5.14

𝐺𝑓

(3.6)

𝑒𝑓

𝑓′ 𝑡

Where w is the crack opening, Wc is the crack opening at the complete release of stress, Gf is the Fracture energy needed to create a unit area of stress-free crack, ft’ef is the effective tensile strength derived from the failure function. The crack opening displacement w is derived from strains according to the crack band theory. The area under the curve (Gf) depicts the fracture energy of concrete. It is the energy required to create a unit area of stress free crack. The function for crack opening was 34

derived experimentally by HORDIJK (1991). wc is the crack opening at the complete release of stress. ATENA uses the model developed recommended by the CEB FIP Model Code 90. The formula in equation (3.7) is used to form the ascending part of the curve. 𝑒𝑓

𝑒𝑓

𝜎𝑐 = 𝑓′ 𝑐

𝑘𝑥−𝑥 2

𝜀

𝐸

, 𝑥 = 𝜀 , 𝑘 = 𝐸0 1+(𝑘−2)𝑥 𝑐

(3.7)

𝑐

Fig 3.5. Compressive stress strain diagram 𝑒𝑓

𝜎𝑐 -

Concrete compressive stress

𝑒𝑓

𝑓′ 𝑐 - Concrete effective compressive strength x

- Normalized strain

𝜀

- Strain

𝜀𝑐

- Strain at peak stress 𝑓′ 𝑐

k

- Shape parameter

𝑒𝑓

E0

–

Initial elastic modulus

Ec

– Secant modulus at peak stress, 𝐸𝑐 =

𝑒𝑓

𝑓′𝑐

𝜀𝑐

The slope of softening law is defined by means of softening modulus Ed and it is defined by two strain limits i.e. strain corresponding to compressive strength of concrete (𝜀𝑐 ) and a limiting compressive strain(𝜀𝑑 ).The later part of strain is calculated from plastic displacement (wd ) and band size during failure in compression (Lc ). 35

3.2.1.5. Tension Stiffening In concrete element, cracks cannot fully develop through the concrete section in case reinforcement is present, and further concrete contributes to the steel stiffness. This behaviour called as tension stiffening is incorporated in concrete model “CC3DNonLinCementitious2” of ATENA by specifying tension stiffening factor. This factor cts represents the relative limiting value of tensile strength in the tension stiffening 𝑒𝑓

diagram. The tensile stress cannot drop below cts*𝑓′𝑡

and factor cts is recommended

to be a value of 0.4 as per CEB-FIP model code 90.

Fig 3.6. Tension stiffening 3.2.1.6. Fracture Energy The fracture energy of concrete 𝐺𝑓 is the energy required to propagate a tensile crack of unit area.There have been different proposals for the calculation of fracture energy of concrete. It is mainly dependent on cylinder compressive strength and maximum particle size. However, it is mentioned that actual value may differ by almost 30% from the value obtained using equation (3.4). The empirical value of fcm0 is considered to be 10MPa. 𝑓

0.7

𝐺𝑓 = 𝐺𝑓0 (𝑓 𝑐𝑚 )

(3.8)

𝑐𝑚0

36

Remmel (1994) presented another approach for calculating fracture energy according to equation (3.9), where compressive strength of concrete and particle size were the parameters. Here, the empirical factor was taken as 65 for particle size of 16 mm. 𝐺𝑓 = 65 ln(1 +

𝑓𝑐

)

(3.9)

10

Vos (1983) also proposed an equation for fracture energy based on the tensile strength of concrete, equation (3.10). The values obtained using this equation were smaller as compared to those obtained by Remmel and CEB-FIP code. 𝑒𝑓

𝐺𝑓 = 25𝑓′𝑡 (N/m)

(3.10)

Table 3.1 gives the formulae used by ATENA in the material modelling if input data isn’t altered, ATENA will automatically use these formulae to calculate dependent parameters and predict the behaviour under loading.

Table 3.1 ATENA default formulae Parameter

Formula

Cylinder strength

𝑓′𝑐 = −0.85𝑓′𝑐𝑢

Tensile strength

𝑓′𝑡 = 0.24𝑓′𝑐𝑢3

Initial elastic modulus

𝐸𝑐 = (6000 − 15.5 𝑓 ′ 𝑐𝑢 )√𝑓′𝑐𝑢

Poisson’s ratio

ν = 0.2

Softening compression

wd = -0.0005 mm

Compressive strength in cracked concrete

c = 0.8

Tension stiffening stress

σst = 0

Fracture energy

𝐺𝑓 = 0.000025 𝑓′𝑡 [MN/m]

2⁄

𝑒𝑓

37

3.2.2. Modelling of steel 3.2.2.1 Geometry of the reinforcement Reinforcement modelling could be discrete or smeared. In our work, a discrete modelling of reinforcement has been done. The reinforcement has been modelled using bar elements in ATENA. 3.2.2.2. Element Properties Reinforcement steel is a 3D bar element, which has three degrees of freedom at each node; translations in the nodal x, y and z direction. Bar element is a uniaxial tensioncompression element. The stress is assumed to be uniform over the entire element. Also plasticity, creep, swelling, large deflection and stress-stiffening capabilities are included in the element.

Fig 3.7. Two noded bar element 3.2.2.3. Element Shape Functions: The shape functions in natural co-ordinate system for the three dimensional bar element without rotational degrees of freedom. N1= (1/2) (1+s) N2= (1/2) (1-s) 3.2.2.4. Bilinear law of steel The reinforcement can be designed as discrete element. Depending on the stress strain curve for steel test it is designed as bilinear. The bilinear law for elastic-perfectly plastic steel is as shown in Fig. 3.8. The initial elastic part has the elastic modulus of steel Es. The second line represents the plasticity of the steel with hardening and its slope

38

is the hardening modulus Esh. In case of perfect plasticity Esh =0. Limit strain 𝜀𝑙𝑖𝑚 represents limited ductility of steel

Fig 3.8. Bilinear Steel 3.3. Reinforcement bond models The basic property of the reinforcement bond model is the bond-slip relationship. This Relationship defines the bond strength depending on the value of current slip between Reinforcement and surrounding concrete. In this paper reinforcement bond model is according to the CEB-FIB model code 1990 as shown in fig.3.9. In this models, the laws are generated based on the concrete compressive strength, reinforcement, and Diameter and reinforcement type.

Fig 3.9. Stress vs slip Curve of reinforcement bond model 39

Table.3.2.Parameters for defining mean bond strength-slip relationship for ribbed bars

3.4. Interface modelling The interface elements are used to model a contact between two surfaces. Currently, these element are modelled as zero interface gap element in 3D analysis, respectively. These elements use linear approximation of geometry. For the case of nonlinear geometry, and these element is modelled based on Mohr’s column friction theory as shown in fig 3.10.

Fig 3.10. Mohr coulomb friction theory

40

According to EHE-98 code Cohesion c =βfctd

(3.11)

Coefficient of friction µ=tgϕ

(3.12)

Average values of β and µ are0.3 and 0.7, Design value of tensile strength fctd=0.3fck2/3/1.5 (MPA), fck is compressive strength of concrete. As we are modelling zero thickness element, The Knn and Ktt denote the initial elastic normal and shear stiffness respectively. The value of these stiffness correspond to a high penalty number. It is recommended not to use extremely high values as this may result in numerical instabilities. It is recommended to estimate the stiffness value using the following formulas as equations (3.13), (3.14) E

Knn= t

(3.13)

G

Ktt= t

(3.14)

Where E and G is minimal elastic modulus and shear modulus respectively of the surrounding material and t is the width of the interface zone. 3.5. Methods for non-linear solution The best part of the ATENA is the simpler way of solving the non-linear structural behaviour through finite element method and its incremental loading criteria. Different methods are available in ATENA for solving non-linear equations such as, linear method, Newton-Raphson Method, Modified Newton-Raphson method, Arc Length methods are used in ATENA. Among these the Newton-Raphson Method and Modified Newton-Raphson Method are more commonly used methods. In our present study, Newton-Raphson method is used for solving the simultaneous equations. It is an iterative process of solving the nonlinear equations. One approach to non-linear solutions is to break the load into a series of load increments. The load increments can be applied either over several load steps 41

or over several sub steps within a load step. At the completion of each incremental solution, the program adjusts the stiffness matrix to reflect the nonlinear changes in structural stiffness before proceeding to the next load increment. The ATENA program overcomes this difficulty by using Full Newton-Raphson method, or Modified Newton-Raphson method, which drive the solution to equilibrium convergence (within some tolerance limit) at the end of each load increment. In Full Newton-Raphson method, it obtains the following set of non-linear equation (3.15): K (p) Δp = q − f(p)

(3.15)

Where: q Is the vector of total applied joint loads, f(p) is the vector of internal joint forces, Δp is the deformation increment due to loading increment, p are the deformations of structure prior to load increment, K(p) is the stiffness matrix, relating loading increments to deformation increments.

Fig 3.11. Full Newton-Raphson Method Fig 3.11. Illustrates the use of Newton-Raphson equilibrium iterations in nonlinear analysis. Before each solution, the Newton-Raphson method evaluates the out-of balance load vector, which is the difference between the restoring, forces (the loads corresponding to the element stresses) and the applied loads. The program then performs a linear solution, using the out-of -balance loads, and checks for convergence. 42

If convergence criteria are not satisfied, the out-of-balance load vector is re-evaluated, the stiffness matrix is updated, and a new solution is obtained. This iterative procedure continues until the problem converges. But sometimes, the most time consuming part of the Full Newton-Raphson method solution is the re-calculation of the stiffness matrix K (pi−1) at each iteration. In many cases this is not necessary and we can use matrix K (p0) from the first iteration of the step. This is the basic idea of the so-called Modified Newton-Raphson method. It produces very significant time saving, but on the other hand, it also exhibits worse convergence of the solution procedure. The simplification adopted in the Modified Newton-Raphson method can be mathematically expressed by equation (3.16): K (pi−1) = K (p0)

(3.16)

The modified Newton-Raphson method is shown in Fig 3.11. Comparing Fig 3.12. it is apparent that the Modified Newton-Raphson method converges more slowly than the original Full Newton-Raphson method. On the other hand a single iteration costs less computing time, because it is necessary to assemble and eliminate the stiffness matrix only once. In practice a careful balance of the two methods is usually adopted in order to produce the best performance for a particular case. Usually, it is recommended to start a solution with the original Newton-Raphson method and later, i.e. near extreme points, switch to the modified procedure to avoid divergence.

Fig 3.12. Modified Newton-Raphson method 43

CHAPTER-4 VALIDATION OF SOFTWARE Overview In this chapter research done by other authors is validated using ATENA. ATENA as explained in Chapter-3 is designed specifically for RCC models. In this chapter various models of beams and slabs are validated numerically and compared with the original results. This is done for various reasons such as, determine the reliability of the software on the results, since the present study is purely analytical and no experiments are performed. To understand various aspects of the software such as mesh size, type of boundary condition, etc. 4.1. Özgür Anil , Nalan Kaya, Onur Arslan (2013)

Fig 4.1. Dimensions and reinforcement details of specimen, Özgür Anil et al (2013) The authors performed a series of tests on slabs with various patterns of CFRP fibre strips to study their effect in increasing the load carrying capacity of the slab. For validation purpose a fully solid slab without any openings or strips was chosen. The details of the slab are as shown in Fig 4.1. The same slab was modelled on ATENA and

44

analysed under load controlled method with a load increment of 5kN per step. Fig 4.2 shows the modeling of the slab in ATENA.

Fig 4.2. ATENA model for validation

Fig 4.3. Load v/s Deflection graph comparison

45

Fig 4.3. gives the comparison between the original results and the results obtained using ATENA. It can be seen that the behaviour exhibited is almost the same in both the cases and the peak load is varying by 4.3%.

4.2. Dias-da-Costa .D, Alfaiate .J. Júlio (2012)

Fig 4.4. Dimensions and other details of specimens, Dias-da-Costa .D et al (2012) In their research the authors tested the interface shear capacity of a concrete-concrete interface using L-Beams as shown in the figure. The shear connectors used were bars of 8mm diameter. Three models were tested with 2, 4 and 6 bars acting as shear connectors respectively. Fig 4.4. gives the specimen details of the L-Beams. The same specimens were modelled on ATENA, the same values of parameters were given as inputs, and analysis was done using displacement control method. Fig 4.5. shows the ATENA model of the specimens. The results obtained for all the three cases were plotted and compared with the results from the original paper, Fig 4.7, 4.8, 4.9. This results match to a great level until the peak load value, beyond which the results follow different paths, this is due the absence of values of coefficient of friction and type of bond between reinforcement and concrete.

46

(a)

(b)

(c)

Fig 4.5. ATENA model for validation with (a) 2 bars, (b) 4 bars, (c) 6 bars used as shear connectors.

Fig 4.6. 3D model of the specimen

47

Fig 4.7. Load v/s Deflection for model ‘a’

Fig 4.8. Load v/s Deflection for model ‘b’

Fig 4.9. Load v/s Deflection for model ‘c’ 48

4.3. A Kabir, S M Nizamud-Doulah, M Kamruzzaman (2002)

Fig 4.10. Dimensions and reinforcement details of specimens, A Kabir et al (2002) The authors studied the effect of reinforcement layout on the load carrying capacity of skew slabs by varying them in three different types as shown in Fig 4.10. They performed both numerical as well as experimental tests. The same models were recreated in ATENA as shown in Fig 4.11. all three slabs were analyzed under load controlled mode and results were plotted and compared as shown in Fig 4.12.

Type 1

Type 2

Type 3

Fig 4.11. ATENA model for validation The results are compared with the numerical and experimental results provided by the authors of the paper, it is found that the results from ATENA are much closer to the experimental results, even when compared to the numerical studies performed by the authors.

49

Fig 4.12. Load v/s Deflection for Type 1

Fig 4.13. Load v/s Deflection for Type 2

Fig 4.14. Load v/s Deflection for Type 3 50

4.4 Amer M. Ibrahim, nazar K. Ali , Wissam D. Salman (2013)

Fig 4.15. Test Configuration of Two-Way Slab, Amer M. Ibrahim (2013) The author’s performed a series of test on square two-way slabs, simply supported on all four sides by loading them in a 5-point load fashion as shown in Fig. 4.15. For validation purpose the control specimen of a solid slab was taken into consideration. The ATENA modeling of the specimen is shown in Fig 4.16.

(a)

(b) Fig 4.16. ATENA model for 2-way slab 51

The boundary conditions applied were done as per test set-up described in the paper and 5 point loads were applied over different points. Fig 4.17. gives the comparison between the experimental results from the paper and the results obtained using ATENA.


4.5 Madhu Sharma, Naveen Kwatra (2011)

Fig 4.18. Skew slab specimen details, Madhu Sharma et al (2011) The authors performed a mid-point loading test on skew slab of configuration as depicted in Fig 4.18. All details including the reinforcement details were modelled on

52

ATENA, analysis was done using both load controlled and displacement controlled modes to understand the difference between the two in terms of post-peak behaviour. Fig 4.19. shows the ATENA model of the specimen.

Fig 4.19. ATENA skew slab model


From the Fig 4.20. it’s clear that irrespective of the type of method used for analysis, i.e. load controlled or displacement controlled. The results are same upto the peak load value, after which they differ. In this case both the results match very closely to the values obtained from the experiment. 53

4.6 Summary In this chapter comparison between the results provided by the authors in their journals are compared with the results obtained from modeling the same problem in ATENA. The results match and are in correlation to a great extent. Hence, the software ATENA can be used for modeling of RCC structures and the interface properties between concrete and concrete layers. And the results obtained are fairly acceptable.

54

CHAPTER-5 MODELING AND DESIGN

Overview This chapter includes details of modeling, analysis and design of beams and slabs used for parameter study in the following chapters. It also discusses the truss type shear connector used.

5.1 Beam model To optimize the size, i.e. diameter, angle of inclination and depth of embedment of the shear connectors, a beam model of size 150mm x 150mm x 1000mm was used instead of a slab. This was done because modeling and analysis of a full slab for all the mentioned objectives in Chapter-1 would take up a lot of computational time and space. However, once the size of the shear connectors has been decided, it will be used in a square slab of size 1m x 1m simply supported on two edges and will be tested for two point bending. The beam size chosen for the study has cross section dimensions of 150 mm x 150 mm and an effective span of 1m. The beam is simply supported on either ends and loaded at 1/3rd spans to achieve pure flexure. It is reinforced with two bars of 8 mm at the bottom with an effective cover of 20mm and spacing of 110mm. For the composite section two beams of 75mm depth with an interface layer is modeled such that the overall dimensions of both models be same for comparison. The shear connector in the composite beams are provided at the centre with varying depths of embedments when necessary. The load increment is 1kN per step for all beam models.

55

(a)

(b) Fig 5.1. (a) Solid beam (b) Composite beam

Fig 5.2. Typical beam showing supports, loading, reinforcements and shear connector

The beam model was used for the following studies in the future chapters  To study the effect of cohesion on interface shear capacity of composite beams.  To study the effect of co-efficient of friction on interface shear capacity of composite beams.  To study the effect of angle of inclination of truss type shear connector on interface shear capacity of composite beams.  To study the effect of bar diameter of the truss type shear connector on interface shear capacity of composite beams.  To study the effect of depth of embedment of the truss type shear connector on the behaviour of composite beams. All beam results are compared and reported in comparison with a solid beam, i.e. a monolithic beam and a non-composite beam, i.e. two half beams without any composite-ness between them. 56

5.2 Slab Based on the results obtained from the beams studies, suitable shear connector was chosen and modeled in slabs to study the flexural and push off behavior of the same. There are three types of slabs used for study, they are as follows: 5.2.1 Square slab The dimensions of the slab are 1m x 1m and depth of 100 mm. The slab is simply supported on two opposite sides and is reinforced with 5 bars of 8mm at a spacing of 240 mm in both longitudinal and transverse directions, as seen in Fig 5.3 and 5.4. Same reinforcement is provided at the top as well. In both cases effective cover given is 15mm. In case of composite slab two slabs of 50mm depth are modeled one above the other with an interface layer. The depth of embedment of the shear connector is between the top and the bottom reinforcement i.e. 70mm. The slab is loaded with line loads of 4kN per step for all steps at the 1/3rd span of the slabs in the transverse direction.

(a)

(b) Fig 5.3. Square slab showing supports and loading

57

Fig 5.4. Typical slab showing supports, loading, reinforcements and shear connector. 5.2.2 Skew slabs In order the study the effect of degree of skew-ness of the slab on the flexural behaviour of composite slabs, skew slabs were modeled with varying degrees of skew-ness as shown in Fig 5.5 and 5.6, such as 30o, 45o, 60o and compared with a 0o i.e. a square slab as mentioned in 5.2.1. The dimensions of the slab are 1m width, 1m perpendicular span and depth of 100 mm. The slab is simply supported on two opposite sides and is reinforced with 5 bars of 8mm at a spacing of 240 mm in both longitudinal and transverse directions. Same reinforcement is provided at the top as well. In both cases effective cover given is 15mm. In case of composite slab two slabs of 50mm depth are modeled one above the other with an interface layer. The depth of embedment of the shear connector is between the top and the bottom reinforcement i.e. 70mm. The slab is loaded with line loads of 4kN per step for all steps at the 1/3rd span of the slabs in the transverse direction.

Fig 5.5. Typical slab showing supports (all dimension in mm) 58

(a)

(b)

©

(d)

Fig 5.6. Slabs with various angles of skew-ness, (a) 0 degrees, (b) 30 degrees, (c) 45 degrees and (d) 60 degrees

59

5.2.3 Rectangular slabs These slabs are used to study the effect of spacing on flexural load carrying capacity of composite slabs. The dimensions of the slab are 2m X 4m and depth of 150 mm, Fig 5.7. The slab is simply supported on two opposite sides and is reinforced with bars of 8mm at a spacing of 275 mm in the longitudinal direction with an effective cover of 15 mm and 350 mm in the transverse direction. In case of composite slab two slabs of 75 mm depth are modeled one above the other with an interface layer. The depth of embedment of the shear connector is between the top and the bottom reinforcement i.e. 120 mm. The slab is loaded with line loads of 5kN per step for all steps at the 1/3rd span of the slabs in the transverse direction. In order to ease the process of analysis, only half the slab was modeled and symmetric boundary conditions were applied to reduce computational space and time.

(a)

(b)

(c) Fig 5.7. ATENA model for rectangular half slab 60

5.3 Truss type shear connector Fig 5.8. represents a truss type shear connector, it has bar members inclined at a certain angle of inclination, a top bar and a bottom bar. The variation of the truss type shear connector used in the studies are trusses with different angles of inclination, with different bar diameters and with different depth of embedments. Shear connectors without top and bottom bars have also been used to compare to results with conventional shear connectors such as shown in the Fig 5.9. and 5.10.

Fig 5.8. Typical truss type shear connector

Figure 5.9. Typical beam showing supports, loading, reinforcements and shear connector

Figure 5.10. Typical slab showing supports, loading, reinforcements and shear connector

61

5.4 Design of slabs and connector. All slabs are designed as per IS 456-2000, all slabs including skew slabs were first modeled on STAAD.PRO V8i. The values of moments and shears are taken from the software and slabs as design as per codal provisions. The shear connectors were designed as per section 7.0 of IS 1395-1966. Fig 5.11 to 5.14. shows the varying of Mx in all the slabs.

Fig 5.11. STAAD output for 0o slab



Fig 5.14. STAAD output for 60o slab 62

5.5 Material modeling The input properties for the different materials are as described below: 5.5.1 Concrete Concrete is modeled as 3D-Nonlinear cemetitious material Table 5.1 Properties of Concrete Cube Strength (fcu) Elastic modulus (E) Poisson’s ratio(m) Tensile strength Compressive strength Specific weight (ρ) Coefficient of thermal expansion(α)

30 MPa 3.032 x 104 MPa 0.2 2.317 MPa -25.5 MPa 23 kN/m3 1.2 x 10-5 /K

5.5.2. Steel Steel plates are used as bearings under supports and loads only. It is modeled as a 3Delastic-isotropic material Table 5.2 Properties of steel Elastic modulus (E) 2 x 105 MPa 0.3 Poisson’s ratio(m) Specific weight (ρ) 78.5 kN/m3

5.5.3. Reinforcement Reinforcement bars are modeled as reinforcement elements with bilinear, elasto-plastic behaviour Table 5.3 Properties of Reinforcement Elastic modulus E Yield strength (fy) Specific weight (ρ) Coefficient of thermal expansion(α)

63

2.1 x 105 MPa 415 MPa 78.5 kN/m3 1.2 x 10-5 /K

5.5.4. Concrete-Concrete Interface The interface region between the two concrete elements is modeled using 3D-interface model Table 5.4 Properties of Concrete-Concrete Interface 2 x 105 kN/m3 Normal stiffness Tangential stiffness 2 x 105 kN/m3 0 Cohesion

In ATENA, steel plates are used as bearings where there is a need to apply loads and supports, this is to eliminate the effect of localization of stresses at immediate region under the point of application. The mesh size adopted is 50mm and brick elements are used for concrete modeling, whereas tetrahedral elements are used for steel plates. The type of solution adopted is modified Newton-Raphson method, to optimize the node numbers Sloan iterations are used. The stiffness used is the tangent stiffness and the values of the stiffness is updated after each iteration. The number of iterations under each load step is limited to 40. The models are analyzed under load controlled method, the post peak behaviour is not studied. Displacement controlled analysis is not performed.

64

CHAPTER-6 RESULTS AND DISCUSSIONS - PART 1 “FLEXURE STUDIES ON BEAM MODELS”

Overview This chapter deals with the results and discussion on all the studies done on beam models. They include the following, effect of cohesion, effect of friction coefficient, effect of bar diameter, effect of angle of inclination of truss and effect of depth of embedment on the interface shear capacity of a composite beam. All results obtained are compared with that of a solid beam and a non-composite beam. Fig 6.1 and 6.2 shows the difference in the behaviour of solid and non-composite beam. The ATENA simulation is identical to that presented in Chapter-1.

Fig 6.1. Deflection contour plot for Solid Beam

Fig 6.2. Deflection contour plot for Non-Composite Beam (only half beam shown) 65

6.1 Effect of cohesion Beam model mentioned in section 5.1 is used for the study. The value of cohesion is varied from 1 MPa to 5 MPa and models were analysed. The results obtained are plotted and compared with that of a solid beam and a non- composite beam. Fig 6.3. gives the comparison results.

Fig 6.3. Load v/s deflection graph for different values of cohesion From the results it can be seen that the non-composite beam i.e. the beam with cohesion value 0 MPa, has the least peak load and fails early when compared to the other beams. It’s also seen that the behaviour of the beams increase as the value of cohesion is increased to 1 MPa and 2MPa. But beyond 2 MPa, the behaviour of the beams is exactly identical to that of a solid beam. This shows that at a value of 2 MPa itself the behaviour has become monolithic. Since the present study is purely analytical there is no sure way of telling what exactly the value of cohesion between the two layers of concrete is. Hence, for all beam and slab models the value of cohesion will be considered as 0 MPa and all the results obtained will be worst case scenario, where the composite action completely depend on the shear connector used.

66

6.2 Effect of Co-efficient of friction Beam model is modelled with a cohesion value of 0 MPa and the co-efficient of friction varied from 0 to 1. The results are plotted and are compared with that of solid and noncomposite beam.

Fig 6.4. Load v/s deflection graph for different values of cohesion Fig 6.4. gives the results of comparison. It can be seen that as the value of friction coefficient increases the behaviour of the beams as improves. For a friction co-efficient for a maximum value of 1, the behaviour is nowhere close to that of a solid beam. This is because the behaviour of the interface between concrete-concrete doesn’t depend on co-efficient of friction alone, it may depend on other factors such as cohesion, surface texture etc. 6.3 Effect of angle of inclination of truss type shear connector Shear connectors with angles of inclination of 30o, 45o, 60o, 75o were modeled in beams and results were plotted and compared with that of solid and non-composite beams. Fig 6.5. shows the shear connectors with different angles of inclinations modeled in beams.

67

(a)

(b)

(c)

(d) Fig 6.5. Beam model with shear connector truss having (a) 30o, (b) 45o, (c) 60o, (d) 75o angle of inclination

Fig 6.6. Load v/s Deflection graph for 8 mm truss

68

Fig 6.7. Load v/s Deflection graph for 10 mm truss

Fig 6.8. Load v/s Deflection graph for 12 mm truss From Fig 6.6, 6.7 and 6.8. gives the behaviour of beams with different trusses having variation in angle of inclination for a given value of diameter. It is evident that, as the angle of inclination increases the load carrying capacity increases up to 60o. Beyond which there is no significant change. This is because, at 60o the angle of steel provided gives sufficient bondage for monolithic action and any increase in the percentage of steel beyond this, there is no significant change. And since 60o will require less steel than 75o without compromising on efficiency, 60o truss was used for slab models.

69

6.4 Effect of bar diameter of truss type shear connector

Fig 6.9. Load v/s Deflection graph for 30o truss




From Fig 6.9, 6.10, 6.11 and 6.12. it can be seen that all shear connectors have a peak load of around 50kN, however some are more ductile in their behaviour compared to the others, for example 30o connectors as seen in Fig 6.9. It can also be seen that for a given angle of inclination when the diameter is varied, there is no significant change in the load carrying behaviour. However, as the percentage of steel increases, there is a slight decrease in the deflection for all models. From section 6.3. 60o truss was already chosen to be modelled in slabs, for 60o the variation with respect to change in diameter is almost negligible and since 8mm diameter will give almost the same result as the other two, but at a much lesser percentage of steel. 60o truss having 8mm diameter will be used in modeling of slabs. 70

6.5 Effect of depth of embedment of truss type shear connector

(a)

(b)

(c)

(d)

(e) Fig 6.13. Beam model with 8mm, 60o truss having (a) 30mm, (b) 50mm, (c) 70mm, (d) 90mm and (e) 110mm depth of embedment Fig 6.13 shows the different beams with varying depths of embedments of shear connectors. Using 60o truss with 8mm diameter, beams were modelled with trusses having various depths of embedments and behaviour was observed. The results obtained are plotted in Fig 6.14. It is observed that, for a given angle of inclination, the 71

load carrying capacity is independent of the depth of embedment. This is because for a given angle of inclination and given span, the area of steel per unit length will remain the same irrespective of the depth of embedment. The table below gives the length of steel used in per meter run of shear connector of a given type of truss shear connector Table 6.1. Depth of embedment and corresponding steel per meter run. Depth of embedment Length of steel per meter run of shear connector 30 mm 2113 mm 50 mm 2078 mm 70 mm 2101 mm 90 mm 2078 mm 110 mm 2032 mm

Fig 6.14. Load v/s Deflection graph for 8mm, 60o truss with different depths of embedment

72

CHAPTER-7 RESULTS AND DISCUSSIONS - PART 2 “FLEXURE AND PUSH-OFF STUDIES ON SLAB MODELS”

Overview This chapter deals with the results and discussion on all the studies done on square and skew slab models. They include the following, effect of shear connectors in longitudinal direction, effect of shear connectors in transverse direction and effect of shear connectors in both directions. Table 7.1 Nomenclature for Slab Models Full depth solid slab Solid Non-Composite Two-half slabs, without any shear connector Two Connectors in longitudinal direction 2L Three Connectors in longitudinal direction 3L Two Connectors in transverse direction 2T Three Connectors in transverse direction 3T Two Connectors in both direction 2L-2T Three Connectors in both direction 3L-3T

Fig 7.1. Slab with 3 connectors in both longitudinal and transverse directions (3L-3T)

73

Fig 7.2. Typical deflection in a slab

Fig 7.3. Typical crack formation in a slab

Fig 7.4. Typical deflection contour in a slab

Fig 7.5. Typical interface zone stresses in a slab

74

7.1 Results for 0 Degree Slab

Fig 7.6. Load v/s Deflection graph for solid and non-composite slab

Fig 7.7. Load v/s Deflection graph for


slabs with shear connectors in transverse

slabs with shear connectors in

direction only

longitudinal direction only



slabs with shear connectors in both the

all the slabs

directions

75

Fig 7.6. shows the load v/s deflection behavior of the solid slab when compared with a non composite slab for a sqaure slab. It is seen that the load carrying capacity of noncomposite slab is much lower than solid slab. This is due to the absence of monolithic action between the two composite members in the non-composite slab. Fig 7.7. and Fig 7.8. show the load v/s deflection for 0 degree slab with shear connectors in transverse and longitudinal directions respectively. It is evident that shear connectors when provided in transverse directions does not improve the behaviour in anyway, whereas in longitudinal direction they increase the load carry capacity to a great extent, when two connectors are provided in longitudinal direction, it is as good as a solid slab, when three connectors are provided the load carrying capacity is much higher than the solid slab itself. Fig 7.9. shows the load v/s deflection comparison of composite slabs, when shear connectors are provided in both longitudinal and transverse directions. When compared to Fig 7.7. It can be seem that transverse connectors when provided independently do not affect the load carrying capacity, however when provide along with longitudinal connectors it does improve the behaviour slightly. It must be noted that although the ultimate load carrying capacity has increased, the monolithic action of none of the composite slabs is near solid slab. The increase in the load carrying capacity is due to the additional increase in the percentage of steel provided in the form of shear connectors. However, monolithic action also increases as the number of shear connectors in the longitudinal direction increases. The initial stiffness or the initial load v/s deflection curve for all composite slabs lies between that of non-composite slab and solid slab. This holds true for all of the suture slabs as well. 76







direction only





all the slabs

directions

77

Fig 7.12. and Fig 7.13. show the load v/s deflection for 30 degree slab with shear connectors in transverse and longitudinal directions respectively. When compared to the 0 degree slab, it can be seen that the load carrying capacity has decreased. However, the rest of the behaviour is similar. Transverse connectors have no much effect; longitudinal connectors improve the load carrying capacity. Transverse connectors when provided with longitudinal connectors improve the behaviour slightly, Fig 7.14. It must also be noted that the window between the solid and non-composite slab is reduced when compared to 0 degree slab as seen in Fig 7.11. Fig 7.5, Fig 7.10, Fig 7.15. and Fig 7.20. shows the load v/s deflection comparison of all the slabs for 0 degree, 30 degrees, 45 degrees and 60 degrees respectively. By compassion it can be seen that, irrespective of the degree of skew-ness of the slab, the general trend is the same. Solid slabs performs much well than a Non-Composite slabs. It has a much higher failure load. Transverse connectors do not alter the load carrying behaviour; longitudinal connectors improve the behaviour significantly. Transverse connectors when provided along with longitudinal connectors does improve the load carrying capacity, although not significantly 7.3 Results for 45 Degree Slab Fig 7.16. shows the load v/s deflection for solid and non-composite slab for 45 degrees slab. Fig 7.17, Fig 7.18, and Fig 7.19. shows the load v/s deflection comparison for 45 degree slab when connectors are provided in transverse direction, longitudinal direction and both transverse and longitudinal directions respectively. Here again, the behaviour is similar, as for 0 degree slab and 45 degree slab, however the load carrying capacity has further reduced. 78






direction only





all the slabs

directions

79







direction only





all the slabs

directions 80

Behaviour of 60 degree slab is very similar to that of all the other slabs, except the load carrying capacity has reduced to a great extent; the window between the solid and the non-composite slab has reduced. Fig 7.21. shows the load v/s deflection for solid and non-composite slab for 45 degrees slab. Fig 7.22, Fig 7.23, and Fig 7.24. shows the load v/s deflection comparison for 60 degree slab when connectors are provided in transverse direction, longitudinal direction and both transverse and longitudinal directions respectively.

Fig 7.26. Load v/s Deflection graph for all the solid slabs for different values of θ

Fig 7.27. Load v/s Deflection graph for all slabs with 2L connectors for different values of θ

81

Fig 7.28. Load v/s Deflection graph for all slabs with 3L connectors for different values of θ For better understanding and for comparison the load v/s deflection results for solid slab, slabs with 2 longitudinal shear connectors and 3 longitudinal shear connectors are plotted in Fig 7.26, Fig 7.27 and Fig 7.28 respectively. It can be seen that irrespective of the configuration or the presence of shear connectors for a given type of slab the load carrying capacity decreases as the angle of skew-ness of the slab increases. 7.5 Push-off tests on square slabs. Square slabs of sizes 1m X 1m is used for push-off analysis. The slab model consist of two half slabs of depth 50 mm, the test is performed such that the bottom half is restrained from moving and lateral load is applied over an entire face of the top slab. The entire setup is restrained from bending by applying suitable boundary conditions. Fig 7.29. shows the model for push-off test, Fig 7.30. shows the behaviour of the push off specimen after loading. The entire analysis is carried out in displacement controlled mode. The slabs used are same as those mentioned in section 7.1. Fig 7.31. shows the push-off behaviour of various slabs in terms of load v/s deflection plot. It can be clearly seen that transverse shear connectors do not have any effect in 82

imparting compositeness to the model. And the degree of monolithicity increases as the number of shear connectors n the longitudinal direction increases.

(a)

(b) Fig 7.29. Square slab model for push-off test

Fig 7.30. Displacement vector and stress distribution diagram after push-off

Fig 7.31. load v/s deflection graphs for push-off specimens

83

The results obtained from the push-off studies fully co-relate with those obtained from the flexure studies. It can therefore be concluded that shear connectors in transverse direction do not impart monolithicity to the members, only longitudinal connectors do. But when transverse connectors are provided with longitudinal connectors, the behaviour improves slightly. Here after, only longitudinal connectors will be modelled to study the behaviour of slabs.

84

CHAPTER-8 RESULTS AND DISCUSSIONS - PART 3 “EFFECT OF SPACING ON FLEXURE AND PUSH-OFF BEHAVIOUR”

Overview From Chapter-7 it can be seen that transverse shear connectors do not effect the composite action in a large way, all the compositeness imparted to the specimen is due to the longiotudinal shear connectors only. In this chapter we study the effect of spacing of shear connector on the push-off and flexural behavior of slabs. 8.1 Effect of spacing on flexural behavior of one way slab The slab specifications are as mention in section 5.2.3. three types of shear connectors are used with six different values of spacing to study the behavior of slabs. The three types of shear connectors are i.

Truss shear connectors with maximum depth of embedment and with top and bottom bars, Fig 8.1.

ii.

Truss shear connectors with maximum depth of embedment and without top and bottom bars, Fig 8.2.

iii.

Truss shear connectors with lesser depth of embedments and with top and bottom bars, Fig 8.3.

Fig 8.1. Type-1 Shear connector with maximum depth of embedment and with top and bottom bars 85

Fig 8.2. Type-2 Shear connector with maximum depth of embedment and without top and bottom bars

Fig 8.3. Type-3 Shear connector with lesser depth of embedment and without top and bottom bars Using the three types of shear connectors, six slabs with varying values of spacings of 1970 mm, 985 mm, 656 mm, 492 mm, 394 mm and 328 mm are modeled for each type. The results are plotted and compared with that of solid and non-composite slab. For example Fig 8.4. and 8.5. shown slab with 656 mm and 328 mm spacing of shear connectors respectively.

Fig 8.4. Slab with 656 mm spacing of shear connector

Fig 8.5. Slab with 328 mm spacing of shear connector

86

The load v/s deflection plot for the three types are given in Fig 8.6, 8.7, and 8.8 respectively. The results are plotted in comparison with solid and non-composite slab.

Fig 8.6. Load v/s deflection graphs for Type-1 shear connector

Fig 8.7. Load v/s deflection graphs for Type-2 shear connector

Fig 8.8. Load v/s deflection graphs for Type-2 shear connector 87

For better understanding of the results, the behaviour of different types of shear connectors are plotted for a given value of spacing and compared with that of solid and non-composite slab. Fig 8.9 to 8.14 shows the load v/s deflection behaviour of various slabs with different spacing of shear connectors having the three different types of shear connectors.

Fig 8.9. load v/s deflection graph for spacing of 1970 mm






88

From the results it’s clear that as the spacing reduces the load carrying capacity and the composite action increases. It can also be seen that type 1 and type 3 show almost same behaviour, which is in accordance with the results obtained in Chapter-6 which was that the depth of embedment of the shear connector does not affect the behaviour of the shear connector in a composite member. i.e. behaviour is independent of the depth of embedment. There are two aspects to a shear connector i.

To impart monolithicity to the composite member.

ii.

To improve the load carrying capacity, since by virtue it’s actually a percentage increase in the area of steel provided.

So to better understand the results it will be split in two halves, one to estimate the efficiency in terms compositeness imparted and the other in terms of peak load achieved before failure. Table 8.1 Effect of spacing of three types of shear connectors on flexural behaviour of slabs Spacing(mm)

1970

985

656

492

394

328

Type

Type-1 Type-2 Type-3 Type-1 Type-2 Type-3 Type-1 Type-2 Type-3 Type-1 Type-2 Type-3 Type-1 Type-2 Type-3 Type-1 Type-2 Type-3

Ps(kN)

96

Δs(mm)

Px(kN)

Δx(mm)

Efficiency (%)

Monolithicity (%)

7.08

112 104 112 120 112 120 136 112 136 144 112 144 160 120 152 168 120 160

10.00 10.63 9.91 8.74 9.14 8.28 8.05 8.40 7.60 7.66 8.07 7.35 7.37 7.82 7.08 7.16 7.65 6.92

116.67 108.33 116.67 125.00 116.67 125.00 141.67 116.67 141.67 150.00 116.67 150.00 166.67 125.00 158.33 175.00 125.00 166.67

58.76 49.86 60.03 76.55 70.97 83.05 86.30 81.37 92.66 91.81 85.99 96.19 95.90 89.59 100.00 98.87 91.89 102.26

89

Where, Ps Δs Px Δx Efficiency Monolithicity

Peak load of solid slab(kN) Displacement of solid slab at peak load(mm) Peak load of the slab (kN) Displacement at peak load corresponding to solid slab (mm) Peak load as a percentage of peak load of solid slab (%) Monolithicity as a percentage of displacement of solid slab (%)

The above results can be plotted in a graphical form, the results of spacing v/s efficiency and spacing v/s monolithicity is shown in Fig 8.15. and 8.16 respectively.

Fig 8.15. Spacing v/s efficiency for three types of shear connectors

Fig 8.16. Spacing v/s monolithicity for three types of shear connectors

90

From Fig 8.15. and 8.16. it can be seen that as the spacing decreases the value of efficiency and monolithicity increases. Although it must be noted that the decrease in efficiency is exponential, whereas the rate of decrease for monolithicity is more or less linear. 8.2 Effect of spacing on push-off behavior of sqaure slab Square slab of specification mentioned in section 5.2.1 is used to study the influence of spacing on the interface shear strength i.e. the push off strength of the specimen. Shear connectors are provided in longitudinal direction only. Nine slabs are modelled with spacing varying from 107 mm to 970 mm. For example Fig. 8.17 and 8.18 shows two slabs with spacing of 107 mm and 485 mm respectively.

Fig 8.17. Square slab with 107 mm spacing

Fig 8.18. Square slab with 485 mm spacing

91

The results thus obtained are plotted and compared with that of non-composite slab. Solid slab doesn’t show any slip when lateral load is applied on half the slab. Hence solid slab results are not used for comparison purpose. Fig 8.19. shows the load v/s deflection behaviour for all the push off specimens with varying values of spacing.

Fig 8.19. Load v/s deflection behaviour for push off slabs with varying values of spacing From the graphs it can be seen that as the number of shear connectors increases i,e as the spacing decreases the load carrying capacity as well as the monolithicity of the slabs increases. Non-composite slabs shows the least composite behaviour. To understand the effect of spacing in better way spacing v/s peak load values are plotted in Fig 8.20. it can be seen that there is an exponential decrease in the peak load value as spacing increases.

Fig 8.20. Spacing v/s peak load values for all push-off specimens 92

CHAPTER-9 CONCLUSION Overiew In the present study, effort was made to understand the interface shear behavior between two layers of concrete in beam and slab models. Beams studies were performed to understand the effect of cohesion and co-efficient of friction. It was also used to study the behaviour of composite members with shear connectors, and effect of various parameters associated with the shear connector. Studies were performed on slab to understand the optimal orientaion of shear connector as well as to study the effect of spacing with the help of flexure and push-off tests. 9.1 Concluding remarks 1. Monolithicity of composite beams increases as the value of cohesion increses upto 2 MPa, beyond which the behaviour is identical to that of a solid slab. This is beccause at 2 MPa, the value has reached a maximum, beyond which composite members will behave monolithically. 2. The coefficient of friction has negligible effect on the interface property of concrete. However it is never zero. 3. The load carrying capacity increases as the angle of inclination of the truss connectors increases up to 60o beyond which it remains same, this is because at 60o the area of steel provided is sufficient to ensure monolithic action, anything beyond this, does not make much of a difference. 4. For a given angle of inclination there is no significant change in the behaviour for a change in bar diameter. However as the percentage of reinforcement increases there is a reduction in the deflection. 93

5. For a given angle of inclination and bar diameter, the behaviour remains the same independent of depth of embedment of the connector. Since, for a given angle of inclination, the area of steel per unit length remains same, irrespective of the depth of embedment. 6. The load carrying capacity of the slabs decreases as the angle of skew-ness of the slab increases. 7. The load gap between the solid and the non-composite slab decreases as the angle of skew-ness of the slab increases. 8. In a slab, shear connectors provided in the transverse direction does not improve the behaviour in any significant way. 9. As the number of connectors in the longitudinal direction is increased, the load carrying capacity of the slab also increases. 10. Transverse connectors when provided with longitudinal connectors influence the load carrying behavior, increasing it slightly 11. Trasverse connectors have absolutely no influence on the push-off strength of composite slabs. 12. Push off strength increases as the number of shear connctors in longitudinal direction increases. 13. Incase of slabs, depth of embedment does not have any effect on the behavior of the composite member. This behaviour is identical as that in case of beams. 14. Providing top and bottom bars will ultimately add to the percentage of steel and hence increase the load carrying capacity of the composit memebr, even when compared to the solid member itself. 15. Providing shear connctors without top and bottom bars ensures monlithic action, without increasing the load carrying capacity. Hence shear connectors can be

94

provided between the top and bottom reinforcements of the member, instead of of providing separate top and bottom bars exclusively for the connector. 16. The effciency, i.e. peak load carrying capacity as a percentage of peak load of the solid slab shows an exponential decrease with an increase in the value of spacing. 17. The monolithicity, i.e. the peak displacement as a percentage of peak load of solid slab shows linear decrease with an increase in the value of spacing. 18. For push-off tests the peak loads of slabs show an exponentioal decrease with increase in the value of spacing.

9.2 Scope for Future Work  Experimental verification of all the results from the present study  Different types of shear connectors such as dual steel truss type and lattice grid type can be used instead of truss type shear connectors  The study can be extended to two way slabs

95

REFERENCES

[1]

A Benayoune., Aziz A. Samad. A, Trikha. D.N, Abdullah Abang Ali. D.N, Ashrabov A.A.; ‘Structural behaviour of eccentrically loaded precast sandwich panels’, Construction and Building Materials, 2006; (20): 713-724.

[2]

A Kabir, S M Nizamud-Doulah, M Kamruzzaman, “Effective Reinforcement Layout For Skew Slabs”, 27th Conference on our World in Concrete & Structures: 29 - 30 August 2002, Singapore, PP. 271-276

[3]

Ali R. Khaloo and Nakseok Kim; ‘Influence of Concrete and Fiber Characteristics on Behavior of Steel Fiber-Reinforced Concrete under Direct Shear’, American Concrete Institute Materials Journal, November-December 1997; pg no: 592-600.

[4]

Amer M. Ibrahim, nazar K. Ali , Wissam D. Salman, “Flexural Capacities Of Reinforced Concrete Two-way bubble-deck slabs of plastic spherical VOIDS”, Diyala Journal Of Engineering Sciences, vol. 06, no. 02, pp. 9-20, june 2013

[5]

ATENA Theory manual by Vladimír Červenka, Libor Jendele and Jan Červenka, Cervenka Ltd.

[6]

Barr, B; ‘Fracture Characteristics of FRC Materials in Shear’, Fiber Reinforced Concrete Properties and Applications, SP-105, American Concrete Institute Detroit, 1987; pg no: 27-53.

[7]

Benayoune.A, Abdul Samad. A.A., Trikha. D.N., Abang Ali. A.A., Ellinna. S.H.M.; ‘Flexural behaviour of pre-cast concrete sandwich composite panel – Experimental and theoretical investigations’, Construction and Building Materials, 2008; (22):580-592.

[8]

Boksun Kim, Howard D. Wright, Roy Cairns; ‘The behaviour of through-deck welded shear connectors: an experimental and numerical study’, Journal of Constructional Steel Research, 2001; (57):1359-1380.

[9]

Bryan Barragán, Ravindra Gettu, Luis Agulló, and Raúl Zerbino; ‘Shear Failure of Steel Fiber-Reinforced Concrete Based on Push-Off Tests’, American Concrete Institute Materials Journal, July-August 2006; Vol 103, pg no: 251-257.

96

[10] Bush

TD, Stine GL; ‘Flexural Behavior of composite precast concrete sandwich panels

with continuous truss connectors’, Precast/prestressed Concrete Institute Journal, 1994; (39): 112–121. [11] Bush

TD, Zhiqi Wu; ‘Flexural analysis of prestressed concrete sandwich panels with

truss connectors’, Precast/prestressed Concrete Institute Journal, 1998; pg no: 76-86. [12] Buyukozturk,

O; Bakhoum, M. M.; and Beattie, S.M; ‘Shear Behavior of Joints in

Precast Concrete Segmental Bridges’, Journal of Structural Engineering, ASCE, Vol No: 116, No. 12, Dec. 1990; pg no: 3380-3401. [13] CEB-FIP Model [14] CEB-FIP

Code 1990, Comite Euro International Du Beton.

Model Code, First Draft, Committee Euro-International du Beton, Bulletin

d'information, 1990; No. 195,196, Mars. [15] Cervenka

V; ‘Constitutive Model for Cracked Reinforced Concrete’, Journal American

Concrete Institute, Proceedings Vol no 82, November-December 1985; No.6, pg no: 877882. [16] Chris

P. Pantelides, Rajeev Surapaneni, Lawrence D. Reaveley, ‘Structural

Performance of Hybrid GFRP/Steel Concrete Sandwich Panels’, Journal of Composite Construction, 2008; (12): 570-576. [17] Constantinescu

Horia And Măgureanu Cornelia; ‘STUDY OF SHEAR BEHAVIOUR

OF HIGH PERFORMANCE CONCRETE USING PUSH-OFF TESTS’, JAES(14)22011; Pg No:77-82. [18] Crisfield,

M.A; ‘An Arc-Length Method Including Line Search and Accelerations’,

International Journal for Numerical Methods in Engineering, 1983; Vol no 19,pg no: 1269-1289. [19] Darwin,

D., Pecknold, D.A.W.; ‘Inelastic Model for Cyclic Biaxial Loading of

Reinforced Concrete’, Civil Engineering Studies, University of Illinois, July 1974. [20] Dias-da-Costa

.D. Alfaiate .J. Júlio; ‘FE modeling of the interfacial behaviour of

composite concrete members’, Construction and Building Materials, 2012, (26): 233– 243. [21] Dong-Uk

Choi, James O. Jirsa, and David W. Fowler; ‘Shear Transfer across Interface

between New and Existing Concretes Using Large Powder-Driven Nails’, American Concrete Institute Structural Journal, March-April 1999; Vol No 96; pg no: 183-192. 97

R. John; ‘Full-Depth Precast Concrete Bridge Deck Construction’, Annual

[22] Fowler.

Conference of the Transportation Association of Canada, Toronto, Ontario. [23] Frénay,

J. W; ‘Shear transfer across a single crack in reinforced concrete under sustained

loading’, Stevin Laboratory, Report 5-85-5, Delft University of Technology, June 1985. Taplin and Mario Attard; ‘Three-Point Loading Tests on Composite Slabs With

[24] Geoff

Interface Slip’, University Of New South Wales. [25] Giovanni

Metelli , Nicola Bettini and Giovanni Plizzari; ‘Experimental and numerical

studies on the behaviour of concrete sandwich panels’, European Journal of Environmental and Civil Engineering, 2011; Vol No 15, pg no: 1465 to 1481. [26] Holomek.

J, Bajer .M And Barnat .J; ‘Effect Of Prestressed Embossments Under

Various Types Of Loading Using Fem Analysis’, Admos 2013;

Vi International

Conference On Adaptive Modeling And Simulation. Standard 11384, “Code of Practice for Composite Construction in Structural

[27] Indian

Steel and Concrete”, (1985). [28] IS

456:2000 Part 1: Indian Standard Plain and Reinforced Concrete.

[29] Jayaprakash.J;

‘Experimental Investigation on Shear Capacity of Reinforced Concrete

Pre cracked Push-off Specimens with Externally Bonded Bi-Directional Carbon Fibre Reinforced Polymer Fabrics’, Modern Applied Science, July 2009; Vol No 3, pg no: 8698. [30] Johnson

R.P, ‘Composite Structures Of Steel And Concrete’; Second Edition, University

Of Warwick, 1982; Vol 1. [31] Joseph

A. Wallenfelsz, ‘Horizontal shear transfer for full-depth precast concrete bridge

deck panels’ MS Thesis, Blacksburg, Virginia, 2006. [32] Júlio

E.N.B.S., Dias-da-Costa D., Branco F.A.B and Alfaiate J.M.V; ‘Accuracy of

design code expressions for estimating longitudinal shear strength of strengthening concrete overlays’, Engineering Structures, 2010; (32): 2387-2393. [33] Kabir

M.Z.; ‘Structural Performance of 3D Sandwich panels under shear and flexural

loading’, Scientia Iranica, 2005; Vol No 12, pg no: 402-408. [34] Kahn

L.F., Slapkus; ‘Interface Shear in High Strength Composite T-Beams’,

Precast/prestressed Concrete Institute Journal, July-August 2004; pg no. 102-110.

98

[35] Lawrence

F. Kahn and Andrew D. Mitchell; ‘Shear Friction Tests with High-Strength

Concrete’, American Concrete Institute Structural Journal, January- February 2002; Vol No 99; pg no: 99-103. [36] Mansur.

M. A., Vinayagam.T and Kiang-Hwee Tan; ‘Shear Transfer across a Crack in

Reinforced High-Strength Concrete’, JOURNAL OF MATERIALS IN CIVIL ENGINEERING, ASCE, April-2008; pg no: 294-302. [37] Mattock,

A. H, and Hawkins, N. M; ‘Shear Transfer in Reinforced Concrete: Recent

Research’, Precast/prestressed Concrete Institute Journal, Vol No: 17, No. 2, 1972, pg no: 55-75. [38] Mattock,

A. H; ‘Shear Friction and High-Strength Concrete’, American Concrete

Institute Structural Journal, 2001; pg no: 50-59. [39] Mattock,

A. H; ‘Shear transfer in concrete having reinforcement at an angle to the shear

plane’, Shear in reinforced concrete, American Concrete Institute, 1974; Vol. 1, SP-42, 17–42. [40] Mitchell

Gohnert; ‘Horizontal shear transfer across a roughened surface’, Cement &

Concrete Composites Journal, 2003; 25: 379–385. [41] Mitchell

Gohnert; ‘Proposed theory to determine the horizontal shear between

composite precast and in situ concrete’, Cement & Concrete Composites Journal, 2000; 22: 469-476. [42] Mohan

Ganesh.G, Akhil Upadhyay and Surendra K. Kaushik; ‘simplified Design of

Composite slabs using Slip Block Test’, Journal of Advanced Concrete Technology, October 2005; Vol 3, pg no: 403-412. [43] Noridah

Mohamad, Khalil A.L., Abdul Samad A.A., Goh W.L.; ‘Structural Behavior

Of Precast Lightweight Foam Concrete Sandwich Panel With Double Shear Truss Connectors Under Flexural Load’, ISRN, 2014. [44] Oliva

.M.G., Bank . L.C and Russell R.S.; ‘Full Depth Precast Concrete Highway

Bridge Decks’, Report to the Wisconsin Department of Transportation, University of Wisconsin, October 2007. [45] Özgür

Anil , Nalan Kaya, Onur Arslan, “Strengthening of one way RC slab with

opening using CFRP strips”, Construction and Building Materials, 2013, (48): 883–893

99

[46] Pong.

W.A, Morgan Girgis A.F., Tadros M.K.; ‘Proposed GFRP Connectors in

Sandwich Panels’, ACI Special Publication, 2005; (230):21-38. [47] Rahele

Naserian, Abdollah Hosseini and Mohammad Sadegh Marefat; ‘Assessment

of shear transfer capacity of non-cracked concrete strengthened with external GFRP strips’, Construction and Building Materials, 2013; (45): 224–232. [48] Rahman.

M. H. A., Jaini. Z.M.; ‘The Combined Finite-Discrete Element Analysis of

Precast Lightweight Foamed Concrete Sandwich Panel (PLFP) Under Axial Load’, Proceedings of the International Conference on Advances in Structural, Civil and Environmental Engineering, SCEE 2013; ISBN: 978-981-07-6261-2 doi:10.3850/ 978981-07-6261-2_79. [49] Scholz,

D. P; ‘Performance Criteria Recommendations for Mortars Used In Full Depth

Precast Concrete Bridge Deck Panel Systems’, MS Thesis, Virginia Tech, Blacksburg, December 2004. [50] Sean

Sullivan, ‘Construction and Behavior of Precast Bridge Deck Panel Systems’, PhD

Thesis, Blacksburg, Virginia, 2007 [51] Shyh-Jiann

Hwang, Hsin-Wan Yu, and Hung-Jen Lee; ‘Theory of interface shear

capacity of reinforced concrete’, Journal of Structural Engineering, 2000; (126):700-706. [52] Swamy,

R.N.; Jones, R.; and Chiaro, T; ‘Shear Transfer in Steel Fiber Reinforced

Concrete’, Fiber Reinforced Concrete Properties and Applications, SP-105, American Concrete Institute, Detroit, 1987; pg no: 565-592. [53] Tan,

K. H., and Mansur, M. A; ‘Shear Transfer in Reinforced Fiber Concrete’, Journal

of Materials in Civil Engineering, Vol No 2, No. 4, Nov. 1990; pg no: 202-214. [54] Thanoon

WA, Yardim Yavuz, Jaafar MS, Noorzaei J; Development of interlocking

mechanism for shear transfer in composite floor; Construction Building Materials Journal, 2010; 24(11): 2604–2611. [55] Thanoon

WA, Yardim Yavuz, Jaafar MS, Noorzaei J; Ferrocement-brick composite

panel – an alternate system for floor slab, Construction Building Materials Journal, 2010; 24(11):2224–30. [56] Van

Mier J.G.M.; ‘Multi-axial Strain-softening of Concrete, Part I: Fracture, Materials

and Structures’, RILEM, 1986, 19(111).

100

PUBLICATIONS 1.

International conference: 

S. Dhanush , K. Balakrishna Rao, “Truss Type Shear Connectors Used in Segmental Composite Slab”, Proceedings of The International Conference on Advances in Civil Engineering Materials and Processes, Coimbatore Institute of Technology, Coimbatore, Jan-2015

2.

Notional conference: 

S. Dhanush , K. Balakrishna Rao, “Behaviour of Segmental Composite Skew Slabs Subjected to Flexure Loading”, Proceedings of The National Conference on Technological Innovations for Sustainable Infrastructure, National Institute of Technology, Calicut, March-2015

3.

Journals papers: 

S. Dhanush , K. Balakrishna Rao, “Study of Behaviour of Composite Beams With Truss Type Shear Connector”, IJRET: International Journal of Research in Engineering and Technology, Volume 04, Issue 03, Mar-2015, 289-295



S. Dhanush , K. Balakrishna Rao, “Flexural Behaviour of Segmental Composite Skew Slabs with Truss Shear Connector”, International Journal of Scientific Research Engineering & Technology (IJSRET), Volume 4, Issue 3, March 2015, 239-246

101

PROJECT DETAILS

Student Details

Student Name Contact Address

Dhanush S #1243, Visvesvaraya Layout, Ullala post, near Chikka Basthi Bangalore 560056 Karnataka, India.

Register Number

130918007

Section

Email address

[email protected]

Phone No.

Project title

STUDY OF BEHAVIOUR OF SEGMENTAL COMPOSITE SKEW SLABS USED AS BRIDGE DECKS

Guide Details Faculty Name

Dr. K. Balakrishna Rao

Contact address

Department of Civil Engineering, Manipal Institute of Technology, Manipal – 576 104, Karnataka , India.

Email address

[email protected]

102

M. Tech. - Structural Engineering 91 8147492091

truss type shear connectors used in segmental

truss type shear connectors used in segmental

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