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

Timothy W. Mays, Ph.D., P.E. Associate Professor Professor The Citadel

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

Diaphragms, Chords, and Collectors Design Guide Overview Topics covered: • Gener General al Over Overvie view w • Concret Concrete e Diaphra Diaphragms gms • Wood Wood Diaph Diaphra ragms gms • Metal Metal Deck Deck Diaph Diaphragm ragms s • Concrete Concrete Slab on Metal Metal Deck Deck Diaphragms Diaphragms • Chord Chord and Collec Collector tor Detail Detailing ing

Structural Engineering and Education Solutions, LLC

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Diaphragms, Chords, and Collectors Introduction to Four-Story Concrete Building Example • Concrete Concrete framed (beams, (beams, girders, girders, and columns) columns) building building • 12 in thick reinforc reinforced ed concrete concrete shear walls walls resist lateral lateral loads loads • 6 ½ in. normal normal weight weight reinforced reinforced concrete slab slab (all floors floors and roof) roof) Interior beams Perimeter beams Interior girders Exterior columns Interior columns

21 x 24 21 x 24 24 x 28 21 x 21 24 x 24


Diaphragms, Chords, and Collectors Introduction to Four-Story Concrete Building Example 3D Model and Section:


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Diaphragms, Chords, and Collectors Introduction to Four-Story Concrete Building Example Typical Floor Plan:


Diaphragms, Chords, and Collectors Introduction to Four-Story Concrete Building Example Second Floor Plan with Opening:


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Diaphragms, Chords, and Collectors Introduction to Four-Story Concrete Building Example 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: Structural Engineering and Education Solutions, LLC

Diaphragms, Chords, and Collectors Introduction to Four-Story Concrete Building Example 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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Diaphragms, Chords, and Collectors 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:


Diaphragms, Chords, and Collectors Diaphragm Demand – SDC B Floor Demand – All Floors:


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Diaphragms, Chords, and Collectors Diaphragm Demand – SDC B Floor Demand – All Floors:

f x f px = γf x Structural Engineering and Education Solutions, LLC

Diaphragms, Chords, and Collectors Diaphragm Demand – SDC B Third Floor Demand:


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Diaphragms, Chords, and Collectors Diaphragm Demand – SDC B 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.



Gridline B – Shear wall forces

Gridline F – Shear wall forces


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f x

f px = γf x f px = 1.49f x


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Shear diagram (k)

Moment diagram (k-ft)


Diaphragms, Chords, and Collectors Diaphragm Demand – SDC B 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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Diaphragms, Chords, and Collectors Diaphragm Demand – SDC B 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:

Moment diagram (k-ft) Structural Engineering and Education Solutions, LLC

Diaphragms, Chords, and Collectors Diaphragm Demand (with Opening) – SDC B Second Floor Demand:


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Diaphragms, Chords, and Collectors Diaphragm Demand (with Opening) – SDC B Second 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 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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f x

f px = γf x f px = 2.49f x


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Shear diagram (k)

Moment diagram (k-ft)


Diaphragms, Chords, and Collectors Diaphragm Demand (with Opening) – SDC B 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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Diaphragms, Chords, and Collectors Diaphragm Demand (with Opening) – SDC B 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:


Diaphragms, Chords, and Collectors Diaphragm Demand (with Opening) – SDC B Second Floor Demand – Maximum Chord Force in Diaphragm: • 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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Diaphragms, Chords, and Collectors Diaphragm Demand (with Opening) – SDC B Second Floor Demand – Maximum Chord Force in Diaphragm:

= 0.916 klf w2 = 1.14 klf w1




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Diaphragms, Chords, and Collectors Diaphragm Demand (with Opening) – SDC B Second Floor Demand – Maximum Chord Force in Diaphragm: • 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:


Diaphragms, Chords, and Collectors Diaphragm Demand (with Opening) – SDC B Second Floor Demand – Maximum Chord Force in Diaphragm: • 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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Diaphragms, Chords, and Collectors 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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Diaphragms, Chords, and Collectors Diaphragm Design – SDC B 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)


Diaphragms, Chords, and Collectors Diaphragm Design – SDC B Third Floor Diaphragm Chord Design:


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Diaphragms, Chords, and Collectors 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:


Diaphragms, Chords, and Collectors Diaphragm Design (with Opening) – SDC B Second 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) • Secondary chord reinforcement required for negative moment adjacent to opening:

• Provide one #5 bar at the slab edge (As = 0.31 in2) Structural Engineering and Education Solutions, LLC

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Diaphragms, Chords, and Collectors Diaphragm Design (with Opening) – SDC B Second Floor Diaphragm Chord Design:


Diaphragms, Chords, and Collectors 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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Diaphragms, Chords, and Collectors Collector Design – SDC B Third Floor Diaphragm Collector Design: • Determine axial force (k) distribution in collector:


Diaphragms, Chords, and Collectors 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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Diaphragms, Chords, and Collectors Discussion of SDCs C, D, E, and F SEAOC Seismology Committee’s Draft Recommendations (2008):


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Guide to the Design of Diaphragms

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