2011.11.08 - Diaphragm Considerations for Structural Engineers

Diaphragm Considerations for

Structural EngineersStructural Engineers

By Allen Adams, P.E., S.E.

Bentley Systems, Inc.

SE University, November, 2011 www.LearnWithSEU.com

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Types of Diaphragms

� Rigid

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Rigid Diaphragm

� Infinitely Rigid in the plane of the floor.

� Computationally Efficient.

� Frames are rigidly connected.� Frames are rigidly connected.

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Rigid Diaphragm

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Types of Diaphragms

� Rigid

� Flexible

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Flexible Diaphragm

� No diaphragm stiffness.

� No interaction between frames.

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Types of Diaphragms

� Rigid

� Flexible

� Semi-rigid� Semi-rigid

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Semi-rigid Diaphragm

� Some diaphragm stiffness.

� Interaction between frames.

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Distribution of Loads to Frames

� RigidFunction of relative stiffnesses of frames and of distance from

center of rigidity.

� Flexible� FlexibleDependent on drags, horizontal braces and ability of deck to

transfer shear.

� Semi-rigidFunction of relative stiffnesses of frames and of stiffness of

diaphragm.

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Code Requirements

� ASCE 7-10 Minimum Design Loads for

Buildings and Other Structures

� International Building Code 2009� International Building Code 2009

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12.3.1 Diaphragm Flexibility

The structural analysis shall consider the relative stiffnesses of diaphragms and the vertical elements of the seismic force-resisting system. Unless a diaphragm can be idealized as system. Unless a diaphragm can be idealized as either flexible or rigid in accordance with Sections 12.3.1.1, 12.3.1.2, or 12.3.1.3, the structural analysis shall explicitly include consideration of the stiffness of the diaphragm (i.e., semirigid modeling assumption).

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12.3.1.1 Flexible Diaphragm

Condition

Untopped steel decking or wood structural

panels:

a. Steel or concrete braced frames or concrete, a. Steel or concrete braced frames or concrete,

masonry, or steel shear walls.

b. One- and two-family dwellings

c. Light-frame construction (see code for

conditions, note that ASCE 7 is modified by

IBC 2009 Section 1613.6.1).

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12.3.1.2 Rigid Diaphragm

Condition

Diaphragms of concrete slab or concrete

filled metal deck with span-to-depth ratios

of 3 or less in structures that have no of 3 or less in structures that have no

horizontal irregularities are permitted to be

idealized as rigid.

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Span-to-depth ratios of 3 or less

� Span is measured between adjacent

frames.

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12.3.2.1 Horizontal Irregularity

Structures having one or more of the

irregularity types listed in Table 12.3-1

shall be designated as having a horizontal

structural irregularity.structural irregularity.

1. Torsional Irregularity

2. Reentrant Corner

3. Diaphragm Discontinuity

4. Out-of-Plane Offset

5. Nonparallel System25

1a. Torsional Irregularity

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2. Reentrant Corner

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� Abrupt discontinuity or variation in

stiffness.

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Abrupt discontinuity or variation in stiffness.

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stiffness.

� Cutout or open area greater than 50% of � Cutout or open area greater than 50% of

the gross enclosed diaphragm area.

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Cutout or open area greater than 50% of the

gross enclosed diaphragm area.

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stiffness.

� Cutout or open area greater than 50% of � Cutout or open area greater than 50% of

the gross enclosed diaphragm area.

� Change in effective diaphragm stiffness of

more than 50% from one story to the next.

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Change in effective diaphragm stiffness of

more than 50% from one story to the next.

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4. Out-of-plane Offset

� Transfer Slab

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5. Nonparallel System

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12.3.2.1 Horizontal Irregularity

Structures having one or more of the

irregularity types listed in Table 12.3-1

shall be designated as having a horizontal

structural irregularity.structural irregularity.

1. Torsional Irregularity

2. Reentrant Corner


4. Out-of-Plane Offset

5. Nonparallel System36

12.3.1.2 Rigid Diaphragm

Condition

Diaphragms of concrete slab or concrete

filled metal deck with span-to-depth ratios

of 3 or less in structures that have no of 3 or less in structures that have no

horizontal irregularities are permitted to be

idealized as rigid.

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12.3.1.3 Calculated Flexible

Diaphragm Condition

Diaphragms not satisfying the condition of

Sections 12.3.1.1 [flexible] or 12.3.1.2

[rigid] are permitted to be idealized as [rigid] are permitted to be idealized as

flexible where the … in-plane deflection of

the diaphragm … is more than two times

the average story drift of adjoining vertical

elements of the seismic force-resisting

system….

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12.3.1.3 Calculated Flexible

Diaphragm Condition

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12.3.1 Diaphragm Flexibility

The structural analysis shall consider the relative stiffnesses of diaphragms and the vertical elements of the seismic force-resisting system. Unless a diaphragm can be idealized as system. Unless a diaphragm can be idealized as either flexible or rigid in accordance with Sections 12.3.1.1, 12.3.1.2, or 12.3.1.3, the structural analysis shall explicitly include consideration of the stiffness of the diaphragm (i.e., semirigid modeling assumption).

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12.7.3 Structural Modeling

A mathematical model of the structure shall

be constructed for the purpose of

determining member forces and structure determining member forces and structure

displacements…. Where the diaphragms

have not been classified as rigid or flexible

in accordance with Section 12.3.1, the

model shall include representation of the

diaphragm’s stiffness characteristics….

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12.7.3 Structural Modeling

� Steel Deck Institute, Diaphragm Design

Manual

� Deck Manufacturer� Deck Manufacturer

Technical Data

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Structural Engineers

Questions???

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Wind and Seismic Loads on

Diaphragms

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Wind Loads on Diaphragm

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Seismic Loads on Diaphragm

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Application of

Seismic and Wind Loads on

Rigid Diaphragm

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Application of

Seismic and Wind Loads on

Flexible Diaphragm

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Application of

Seismic Loads on


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Application of

Seismic Loads on


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12.8.4 Horizontal Distribution of

Forces

The seismic design story shear … shall be

distributed to the various vertical elements

of the seismic force-resisting system… of the seismic force-resisting system…

based on the relative lateral stiffness of

the vertical resisting elements and the

diaphragm.

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12.8.4.1 Inherent Torsion

“For diaphragms that are not flexible, the

distribution of lateral forces at each level

shall consider the effect of the inherent

torsion moment, M , resulting from torsion moment, Mt, resulting from

eccentricity between the location of the

center of mass and the center of rigidity.”

Note: this is automatically accounted for in a

3D analysis.

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12.8.4.1 Inherent Torsion

“For flexible diaphragms, the distribution of

forces to the vertical elements shall

account for the position and distribution of

the masses supported.”the masses supported.”

Note: this needs to be considered when

determining the nodal loads applied to the

frames.

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12.8.4.2 Accidental Torsion

“Where diaphragms are not flexible, the

design shall include … the accidental

torsional moments caused by assumed

displacement of the center of mass each displacement of the center of mass each

way from its actual location by a distance

equal to 5% of the dimension of the

structure perpendicular to the direction of

the applied forces.”

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12.8.4.2 Accidental Torsion –

Rigid Diaphragm

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Rigid Diaphragm

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12.10 Diaphragms, Chords and

Collectors

“Diaphragms shall be designed for both the

shear and bending stresses resulting from

the design forces.”the design forces.”

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12.10.1.1 Diaphragm Design Forces

� “Floor and roof diaphragms shall be designed to

resist design seismic forces from the structural

analysis, but shall not be less than that

determined in accordance with Eq. 12.10-1…”

“The force determined from Eq. 12.10-1 shall not � “The force determined from Eq. 12.10-1 shall not

be less than

Fpx = 0.2SDSIewpx (12.10-2)”

� “The force determined from Eq. 12.10-1 need

not exceed

Fpx = 0.4SDSIewpx (12.10-3)”

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� “Where the diaphragm is required to transfer

design seismic force from the vertical resisting

elements above the diaphragm to other vertical

resisting elements below the diaphragm due to

offsets in the placement of the elements or to offsets in the placement of the elements or to

changes in relative lateral stiffness in the vertical

elements, these forces shall be added to those

determined from Eq. 12.10-1.”

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“The redundancy factor, ρ, applies to the design of

diaphragms in structures assigned to Seismic

Design Categories D, E, or F.”

� “For inertial forces calculated in accordance with Eq. � “For inertial forces calculated in accordance with Eq.

12.10-1, the redundancy factor shall equal 1.0.”

� “For transfer forces the redundancy factor shall be the

same as that used for the structure [1.0 or 1.3].”

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“For structures having horizontal or vertical

structural irregularities of the types indicated in

Section 12.3.3.4, the requirements of that

section shall also apply.”

� 12.3.3.4 Increase in Forces Due to Irregularities

for Seismic Design Categories D through F.25% increase in design forces for some elements in some

cases

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Drags

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Chords

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Wind

ASCE 7 Chapters 26-31

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Structural Engineers

Questions???

[email protected]

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Structural EngineersStructural Engineers

By Allen Adams, P.E., S.E.

Bentley Systems, Inc.

SE University, November, 2011 www.LearnWithSEU.com

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2011.11.08 - Diaphragm Considerations for Structural Engineers