guide to the design of diaphragms

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Guide to the Design of Diaphragms, Chords and Collectors Based on the 2006 IBC and ASCE/SEI 7-05

Part No.

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Timothy W. Mays, Ph.D., P.E.

Associate Professor

The Citadel

•Design Guide Overview•Introduction to Four-Story Concrete Building Example•Diaphragm Demand – SDC B•Diaphragm Design – SDC B•Diaphragm Design (with Opening) – SDC B•Collector Design – SDC B•Discussion of SDCs C, D, E, and F

Diaphragms, Chords, and Collectors

Structural Engineering and Education Solutions, LLC

Design Guide Overview

Topics covered:

• General Overview

• Concrete Diaphragms

• Wood Diaphragms

• Metal Deck Diaphragms

• Concrete Slab on Metal Deck Diaphragms

• Chord and Collector Detailing

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Introduction to Four-Story Concrete Building Example

• Concrete framed (beams, girders, and columns) building

• 12 in thick reinforced concrete shear walls resist lateral loads

• 6 ½ in. normal weight reinforced concrete slab (all floors and roof)

Interior beams 21 x 24Perimeter beams 21 x 24Interior girders 24 x 28Exterior columns 21 x 21Interior columns 24 x 24




3D Model and Section:

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Typical Floor Plan:




Second Floor Plan with Opening:

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Given Information:

• The example building has Occupancy Category II in accordance with Table 1-1 of ASCE/SEI 7-05. (I=1.0)

• Seismic weights:

• Material properties:

• Base shear:




Other Information:

• The redundancy factor, ρ, is equal to 1.0 in accordance with ASCE/SEI 7-05 Section 12.3.4.1 for Seismic Design Category B or C.

• Note that in this example the COM and COR are concurrent due to the symmetrical nature of the structure.

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Diaphragm Demand – SDC B

Floor Demand – All Floors:

• The diaphragm design forces must be calculated at each level, as follows:

• The diaphragm design force at each level need not exceed:

• The diaphragm design force at each level shall not be less than:





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fpx = γfx

fx




Third Floor Demand:

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Third Floor Demand:

• Based on ASCE/SEI 7-05 Section 12.3.1.2, a rigid diaphragm must have a span-to-depth ratio of less than 3 and no horizontal irregularities should exist.

• The diaphragm is rigid for this example.

• Rigid diaphragm analysis - assumes that there are no relative horizontal displacements within the diaphragm; no internal strains, and therefore no internal stresses.

• The distribution of forces within the diaphragm can not be captured in a rigid diaphragm analysis performed by a computer program.

• Can use plate elements to model diaphragm.

• An approximate and simple analytical model is proposed in this example.




Third Floor Demand:

Gridline B – Shear wall forces Gridline F – Shear wall forces

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Third Floor Demand:




Third Floor Demand:

fx

fpx = γfx

fpx = 1.49fx

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Third Floor Demand:

Shear diagram (k)

Moment diagram (k-ft)




Third Floor Demand – Maximum Shear Force in Diaphragm:

• The maximum shear occurs at gridline F. With a collector in place of length LdF, the maximum shear is:

Shear diagram (k)

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Third Floor Demand – Maximum Chord Force in Diaphragm:

• The maximum chord force is obtained from the moment diagram. Assuming an approximate center-to-center distance between chord elements of 95 percent of the total diaphragm depth, the maximum chord force is:




Diaphragm Demand (with Opening) – SDC B

Second Floor Demand:

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• Based on ASCE/SEI 7-05 Section 12.3.1.2, a rigid diaphragm must have a span-to-depth ratio of less than 3 and no horizontal irregularities should exist.

• The diaphragm is rigid for this example since the opening does not create an irregularity (doesn’t apply for SDC B anyway).





Gridline B – Shear wall forces Gridline F – Shear wall forces

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fpx = γfx

fpx = 2.49fx

fx

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Shear diagram (k)




Second Floor Demand – Maximum Shear Force in Diaphragm:

• The maximum shear is the larger shear occurring at gridline F and gridline E.

Shear diagram (k)

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Second Floor Demand – Maximum Chord Force in Diaphragm:

• The primary chord force is obtained from the moment diagram. Assuming an approximate center-to-center distance between chord elements of 95 percent of the total diaphragm depth, the primary chord force is:






• The secondary chord forces are calculated based on the internal moment in the diaphragm segment adjacent to the opening.

• Idealizing the segment above the opening as a beam with fixed ends, the applied loading is approximated based on the relative mass of each segment.

• Since the building is symmetric and the opening is located directly in its center, the applied loading on each segment will be equal to half of the overall applied trapezoidal load over this portion of the diaphragm

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w1 = 0.916 klfw2 = 1.14 klf





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• The secondary chord forces are obtained from the moment diagram. Assuming an approximate center-to-center distance between chord elements of 95 percent of the total diaphragm depth, the secondary chord force at the center of the segment span is:






• The secondary chord forces are obtained from the moment diagram. Assuming an approximate center-to-center distance between chord elements of 95 percent of the total diaphragm depth, the secondary chord force at the end of the segment span is:


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Diaphragm Design – SDC B

Third Floor Diaphragm Shear Check at Gridline F:

• The design shear strength of the 6 ½ inch-thick concrete floor slab is calculated as follows:

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Third Floor Diaphragm Chord Design:

• The design tension strength of the reinforcement is calculated as:

• Provide one #6 bar at the slab edge (As = 0.44 in2)




Third Floor Diaphragm Chord Design:

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Diaphragm Design (with Opening) – SDC B

Second Floor Diaphragm Shear Check at Gridline F:

• The design shear strength of the 6 ½ inch-thick concrete floor slab is calculated as follows:




Second Floor Diaphragm Chord Design:

• The design tension strength of the reinforcement is calculated as:


• Secondary chord reinforcement required for negative moment adjacent to opening:


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Second Floor Diaphragm Chord Design:



Collector Design – SDC B

Third Floor Diaphragm Collector Design:

• The collector should be designed for:

• The load combination used in the collector design for Seismic Design Category B is in accordance with ASCE/SEI 7-05 Section 12.4.2.3:

• Collector beam must be designed as a beam-column

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Collector Design – SDC B

Third Floor Diaphragm Collector Design:

• Determine axial force (k) distribution in collector:



Discussion of SDCs C, D, E, and F

• Irregularities may apply in higher SDCs.

• ASCE/SEI Section 12.11.2.2.1 addresses the requirements of continuous ties or struts between diaphragm chords for Seismic Design Categories C through F. This is not required in the example for Seismic Design Category B. It should be noted that in the case of a concrete diaphragm with beams, as in this example, the above requirement is satisfied automatically as these elements act integrally.

• An additional requirement, which applies for Seismic Design Categories C through F, is the application of load combinations with the overstrength factor (Ω0) in accordance with ASCE/SEI Section 12.10.2.1 for the design of collector elements, splices, and connections.

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Discussion of SDCs C, D, E, and F

SEAOC Seismology Committee’s Draft Recommendations (2008):

guide to the design of diaphragms

Documents

secondary chord force

primary chord force

design tension strength

secondary chord forces

seismic design category

seismic design categories

shear wall forces

maximum chord force