Diaphragm Flexibility and Torsion in a Long Narrow Retail Building
A 300-ft by 60-ft single-story retail building has a wood structural panel roof diaphragm and masonry shear walls at the two short ends. An expansion joint divides the building into two 150-ft segments. The lateral system is two lines of masonry walls at each end of each segment. A preliminary analysis using a rigid diaphragm assumption gives a maximum wall shear of 40 kips. The diaphragm has a length-to-depth ratio of 2.5 and the roof sheathing is 15/32-in. rated sheathing with 8d nails at 6 in. on center at the perimeter. The architect wants to remove one interior wall line to open the space.
1. Evaluate whether the rigid diaphragm assumption is appropriate and how it affects the wall shear distribution.
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The rigid diaphragm assumption is not appropriate here. A 150-ft by 60-ft wood diaphragm has a length-to-depth ratio of 2.5, which is within code limits, but wood diaphragms are flexible relative to masonry shear walls. Rigid analysis concentrates shear in the stiffer wall lines and can underestimate forces in flexible elements.
For a flexible diaphragm, shear is distributed to wall lines by tributary area, not by stiffness. This matters because:
- The end walls carry roughly half the segment shear each under flexible assumptions, but the actual distribution depends on diaphragm deflection compatibility.
- Torsion from any eccentricity (e.g., openings, mezzanines) is amplified because the diaphragm cannot redistribute as a rigid body.
- The 40-kip rigid-analysis value should be checked against a flexible-diaphragm analysis; the governing wall shear may be higher.
The design should use the envelope of rigid and flexible analyses, and the diaphragm chord and collector forces must be checked for the flexible case.
2. The architect removes one interior wall line. Explain the consequences for diaphragm demand and torsion, and what mitigation is required.
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Removing an interior wall line changes both the load path and the torsional response.
- Diaphragm demand: The remaining walls must carry the same total shear, so the unit shear in the diaphragm increases. The diaphragm sheathing and nailing must be rechecked; 8d at 6 in. on center may be inadequate for the higher demand, and the chord forces increase with the longer span between wall lines.
- Torsion: Removing an interior line shifts the center of rigidity, creating an eccentricity between the center of mass and the center of rigidity. With a flexible wood diaphragm, torsional effects are not reliably redistributed, so the perimeter walls see amplified shear.
- Mitigation: Either retain a partial wall line or add a new lateral element (e.g., a steel moment frame or braced frame) to restore stiffness symmetry. The diaphragm should be re-analyzed with the new configuration, and the connections at the remaining walls must be checked for the increased collector forces. A 3D model with flexible diaphragm properties is appropriate.