Understanding the Complexities of Designing Diaphragms in ...

Understanding the Complexities of Designing Diaphragms in Buildings for Earthquakes Des K. Bull Holmes Consulting Group Ltd

Function of Diaphragms 1. Relatively thin but stiff horizontal structural systems which transmit inplane lateral forces to, or between, vertical lateral force resisting elements. 2. The diaphragms tie the whole structure together. 2

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Forces in diaphragms under earthquakes • ‘Inertia’ forces – Inertia at a particular floor • ‘Transfer’ forces – Forces develop between primary lateral force resisting structures – These forces are often very large. Force distribution in a floor diaphragm = Inertia + Transfer forces 4

Forces in diaphragm (cont.) • Inertia and “transfer” forces are COUPLED in the analysis. – through stiffness and deformation compatibility of the diaphragms and vertical structural systems. • CAN’T determine distribution of “transfer” forces or inertia in isolation. 5

Floor plan configuration issues

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• Plan configurations 7

• Plan configurations 8

Pretensioned, precast concrete floors with castin-place topping • Are these more of a concern than cast-in-place slabs ?

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Pretensioned, precast concrete floors with castin-place topping

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Structural Behaviour of Diaphragms

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Beam Analogy

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Openings in diaphragms and “Strut & Tie” methods • “Strut & Tie” – Advantages over the simple Beam or Tied Arch approach 13

Openings in diaphragms and “Strut & Tie” methods

Diagonal compression fields 14


Load paths in a section of floor: “micro strut & tie” solution 15


Diagonal tension fields 16

“Beam” or “Tied Arch” or “Strut & Tie” ?

– simple model – Provision of “tie” reinforcement

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“Drag Bars” or “Collectors”

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“Strut & Tie” with “drag” bars

A bit complex? 19

“Drag Bars” or “Collectors”

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Diaphragms: Force distribution and detailing Fi : floor, beams, columns and cladding

EQ

Floor plate 21


EQ

Inertia effects, distributed across the floor 22


EQ

Compression fan develops 23


EQ

C’ C

C

Sketch in the centres of compression: struts of a truss 24


EQ

C’ C

C

T

Note: the tie T is connected at the mid points of the beams •

more later

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EQ

C’ C

C

T

Part of the floor (mauve) wants to “fall out” of the building 26


EQ

C’ C

C

T

Must tie this part back in to the truss or arch (dotted red ties) 27


EQ

C’ C

C

T

Alternatively: use secondary beams as ties/chords and make smaller struts to collect on these ties 28


EQ

C’ C

C

T

Or, combine the secondary beams with the floor reinforcement acting as ties

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EQ

C’ C

C

More struts, closer to the fan compression field 30

Diaphragms: Forces Fi : floor, beams, columns and cladding

EQ

C’ C

C

Struts and ties T

T is smaller To get other ties, requires some cracking and yielding within the floor: “redistribution of actions”

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Issues for Diaphragms when resisting Earthquakes

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Beam elongation

Beam elongation

Loss of support possible over this region

Deformation modes with beam elongation

Mode 1

(a) Beam plastic hinge rotates to allow for beam elongation (10 – 50 mm) 34

Deformation modes with beam elongation

Beam elongation

Loss of support possible over this region

Beam elongation

Mode 2

(b) Entire beam rotates to allow for beam elongation (10 – 50 mm) 35

Delamination of topping from hollowcore units North

South

Plan View 36

Diaphragms: Connections or Nodes of the Struts and Ties Column-Beam Node: Traditional view • Higher compressive stress - smaller contact surface

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Diaphragms: Connections or Nodes of the Struts and Ties Column-Beam Node

• Potentially large plasticity demands in38Ties

Diaphragms: Connections or Nodes of the Struts and Ties

Node locations (where the struts and ties meet): • Mid-point of beams – these points are relatively undamaged by ductile frame action – Keep TIE steel away from primary beams because this steel can be included in the tension flange (negative moment, typ.)

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Diaphragms: Connections or Nodes of the Struts and Ties Floor-Beam Node • Distributed node - keeps compressive stresses down

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Diaphragms: Connections or Nodes of the Struts and Ties Floor-Beam Node • Distributed node - keeps compressive stresses down

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NZS 3101:1995 requires: Tension component

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Alternative layout of reinforcement for column tie

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Detailing for integrity

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Detailing for integrity

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Determining forces in Diaphragms resulting from Earthquakes

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Diaphragms: Forces ‘Inertia’ & ‘Transfer’ forces are COUPLED – These can not be treated in isolation.

Fi

• Some analysis methods: Equivalent Static Analysis (ESA) • You have equilibrium (magnitudes and directions of the applied forces at the boundary of the diaphragm). • If the TIES are connected correctly, this mitigates the coarseness of ESA. 47

Diaphragms: Forces Fi

Fi

Peak Ground Accn.

Equivalent Static Analysis (ESA)

Maxima Envelope of Floor Accelerations (DR 902 Parts)

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Diaphragms: Forces

‘Inertia’ & ‘Transfer’ forces Modal Analysis WON’T work • you DO NOT have equilibrium. – Or model the diaphragm in the analysis model ?

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Height

Diaphragms: Introduced Forces

F2

Vbase i Shear in Wall i

At each floor: • Using an ESA (?) : – Determine the shear force distribution for walls, frames and columns • Calculate the storey forces Fi for each structural subsystem – It is these Fi that make up the boundary conditions on each floor. 50

Diaphragms: Introduced Forces FD = 2000 kN

Fi : floor, beams, columns and cladding

250

250

250

Inertia = 165 kN

1500 kN 500 kN 250

250

250

Actions on the diaphragm: ESA 51

Diaphragms: Introduced Forces FD = 2000 kN

Fi : floor, beams, columns and cladding

250

250

250

1500 kN 500 kN 250 ≅ 1500 kN

250

250 ≅ 500 kN

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Diaphragms: Introduced Forces

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Conclusions: Issues • Strut and Tie method is more versatile than the Beam or Tied Arch approach. • Diaphragm will be damaged locally and may need some limited redistribution of internal forces. – Detailing of the floors to ensure integrity of the floor is essential: • Maintenance of load paths • Continued support of gravity

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Conclusions: Issues • Estimating magnitudes of the inter-related inertia and “transfer” forces requires further study: – A type of Equivalent Static Analysis that generates the deformations of the structure (induces “transfer” forces) while producing reasonable magnitudes of inertia is highly desirable for desk-top design.

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