Solved Problems
Determine the design flexural strength () of a continuously braced W16x31 beam of A992 steel ( ksi). The plastic section modulus is .
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Case Studies
Case Study 1: Temporary Bracing during Construction
A 40-foot span steel beam is designed to support a composite concrete floor slab.
Scenario: During the concrete pouring phase, before the concrete cures and bonds to the shear studs, the steel beam must support the entire wet weight of the concrete by itself.
Solution: Once the concrete cures, it provides continuous lateral bracing to the top flange of the beam (). However, during construction, the unbraced length () is the full 40-foot span.
Because , the bare steel beam would fail via elastic lateral-torsional buckling (LTB) under the wet concrete load. To solve this, the contractor must install temporary lateral bracing (such as bridging or strut members) at 10-foot intervals. This reduces to 10 feet, keeping it within Zone 2 (inelastic LTB) and ensuring the beam has sufficient temporary strength until the concrete hardens.
Case Study 2: Retrofitting a Non-Compact Section
An existing older building is being evaluated for a change in use that will significantly increase floor loads.
Scenario: The existing floor beams are older rolled shapes where the flanges are classified as "non-compact" according to modern AISC specifications.
Solution: Because the flanges are non-compact, they are susceptible to local buckling before the entire cross-section can reach its full plastic moment capacity (). The nominal moment capacity () is governed by Flange Local Buckling (FLB) rather than yielding.
To increase the flexural capacity without replacing the beams, the engineers design a retrofit. They specify welding continuous steel cover plates to the top and bottom flanges. This not only increases the section modulus but also effectively thickens the flanges, changing their classification from non-compact to compact and allowing the modified section to reach its full plastic capacity.
Additional Solved Problems
Determine the nominal flexural strength () of a W18x50 beam () if it is braced at its ends and at midspan. The total span is 30 ft.
Given properties: , , , and for , the inelastic buckling capacity at is calculated as . The actual moment gradient modifier for this segment is .
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A built-up I-shaped beam has a non-compact flange but a compact web. The yield stress is . The plastic moment capacity is . The flange width-to-thickness ratio is . The limits are and . The yield moment accounting for residual stresses () is . Determine the nominal moment capacity assuming continuous bracing ().
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