Solved Problems

A composite beam is designed for full composite action. The concrete slab's maximum compressive strength force (0.85fcAc0.85 f'_c A_c) is 600 kips. The steel beam's yield force (AsFyA_s F_y) is 450 kips. Each 3/4-inch shear stud anchor has a nominal strength (QnQ_n) of 21.5 kips.
Calculate the total number of shear studs required between the point of maximum positive moment and the support.

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Case Studies

Case Study 1: Shored vs. Unshored Construction

A contractor is planning the construction sequence for a multi-story office building with composite steel-concrete floors.
Scenario: The engineer's drawings allow for either "shored" or "unshored" construction. The contractor must decide which method is more cost-effective.
Solution: In unshored construction, the steel beams must support their own weight, the wet concrete, and construction loads entirely by themselves. This often requires heavier steel beams.
In shored construction, temporary props (shoring) support the steel beams at midspan until the concrete cures. This allows the engineer to design lighter steel beams because the wet concrete load is supported by the shores, and the full composite action is available to resist all subsequent loads.
However, installing and removing shoring is labor-intensive and slows down the construction schedule on lower floors. The contractor ultimately chooses unshored construction, accepting the slightly higher steel material cost to achieve a significantly faster erection speed.

Case Study 2: Partial Composite Action

During the detailing phase of a composite floor system, the structural engineer realizes there isn't enough physical space on the steel beam flange to fit the required number of shear studs for "full composite action."
Scenario: The maximum number of studs that can fit is 30, but the calculations for full composite action require 45 studs.
Solution: The engineer does not have to upsize the steel beam immediately. AISC allows for partial composite action.
By providing 30 studs, the beam will transfer less horizontal shear than the full capacity of the steel or concrete (V=ΣQnV' = \Sigma Q_n). The engineer re-calculates the plastic moment capacity (MnM_n) based on this reduced shear transfer force. If this reduced composite capacity is still greater than the required factored moment (MuM_u), the design with 30 studs is acceptable. It is often more economical to design for partial composite action than to maximize stud counts.

Additional Solved Problems

Determine the Plastic Neutral Axis (PNA) location and the nominal plastic moment capacity (MnM_n) for a fully composite W18x35 steel beam (As=10.3 in2A_s = 10.3 \text{ in}^2, Fy=50 ksiF_y = 50 \text{ ksi}, depth d=17.7 ind = 17.7 \text{ in}) and a concrete slab (fc=4 ksif'_c = 4 \text{ ksi}, effective width be=90 inb_e = 90 \text{ in}, thickness tc=5 int_c = 5 \text{ in}). Assume the compressive strength of the concrete governs.

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Determine the nominal axial compressive strength (PnP_n) of a Concrete-Filled Tube (CFT) composite column. The steel section is an HSS 10×10×1/210\times10\times1/2 (As=17.2 in2A_s = 17.2 \text{ in}^2, Fy=46 ksiF_y = 46 \text{ ksi}). It is filled with normal weight concrete (fc=5 ksif'_c = 5 \text{ ksi}, Ac=81.0 in2A_c = 81.0 \text{ in}^2). Assume the column is short (KL/r0KL/r \approx 0) so that buckling does not govern (i.e., we are finding the cross-section crushing strength PnoP_{no}).

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