understanding the complexities of designing diaphragms · pdf file ·...

Understanding the Complexities of Designing Diaphragms in Buildings for Earthquakes

Des K. BullHolmes Consulting Group Ltd

2

Function of Diaphragms

1. Relatively thin but stiff horizontal structural systems which transmit in-plane lateral forces to, or between, vertical lateral force resisting elements.

2. The diaphragms tie the whole structure together.

4

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

5

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.

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Floor plan configuration issues

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• Plan configurations

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• Plan configurations

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Pretensioned, precast concrete floors with cast-in-place topping

• Are these more of a concern than cast-in-place slabs ?

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Pretensioned, precast concrete floors with cast-in-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

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Diagonal compression fields

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

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Diagonal tension fields

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“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?

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“Drag Bars” or “Collectors”

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Diaphragms: Force distribution and detailing

EQF i : floor, beams, columns and cladding

Floor plate

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Inertia effects, distributed across the floor


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Compression fan develops


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C C

C’

Sketch in the centres of compression: struts of a truss


25

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

• more later


C C

C’

T


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C C

C’

T

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


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C C

C’

T

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


28

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


C C

C’

T


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


C C

C’

T


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C C

C’

More struts, closer to the fan compression field


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Diaphragms: Forces


C C

C’

T

Struts and ties

T is smallerTo 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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Deformation modes with beam elongation

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

Bea

m e

long

atio

n

Beam elongation

Loss

of

sup

por

t pos

sible

ove

r thi

s re

gio

n

Mode 1

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Deformation modes with beam elongation

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

Beam elongation

Bea

m e

long

atio

n

Loss

o

f sup

po

rt p

oss

ible

ove

r thi

s re

gio

n

Mode 2

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Delamination of topping from hollowcore units

South

North

Plan View

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Diaphragms: Connections or Nodes of the Struts and Ties

Column-Beam Node: Traditional view• Higher compressive stress - smaller contact surface

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Column-Beam Node

• Potentially large plasticity demands in Ties

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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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Floor-Beam Node• Distributed node - keeps compressive stresses down

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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.

• 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.

Fi

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Diaphragms: Forces

Fi

Equivalent Static Analysis (ESA)

Maxima Envelope of Floor Accelerations

(DR 902 Parts)

Fi

Peak Ground Accn.

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Diaphragms: Forces

‘Inertia’ & ‘Transfer’ forcesModal Analysis

WON’T work

• you DO NOT have equilibrium.

– Or model the diaphragm in the analysis model ?

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Diaphragms: Introduced Forces

At each floor:• Using an ESA (?) :

– Determine the shear force distribution for walls, frames and columnsF2

Vbase i

He

ight

Shear in Wall i

• Calculate the storey forces Fi for each structural sub-system– It is these Fi that make

up the boundary conditions on each floor.

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Actions on the diaphragm: ESA

1500 kN

FD = 2000 kN

500 kN

F i : floor, beams, columns and cladding

250 250 250

250 250 250Inertia = 165 kN

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1500 kN

FD = 2000 kN

500 kN

F i : floor, beams, columns and cladding

250 250 250

250 250 250

≅ 500 kN≅ 1500 kN

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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.

understanding the complexities of designing diaphragms · pdf file ·...

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