Solved Problems

Determine the LRFD design strength of an ASTM A36 (Fy=36F_y=36 ksi, Fu=58F_u=58 ksi) plate 1/2×61/2 \times 6 inches connected by two 3/4-inch bolts in a single line.

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Case Studies

Case Study 1: Retrofitting a Truss Bridge

An aging steel truss bridge is undergoing an evaluation. Several diagonal tension members were found to have significant section loss due to corrosion near the gusset plate connections.
Scenario: The capacity of the corroded tension members needs to be determined to see if they can still carry the current traffic loads safely, or if they need retrofitting.
Solution: The engineers measure the remaining thickness of the members. They must re-calculate both the gross section yielding limit state (using the reduced overall area) and the net section rupture limit state (accounting for both the corrosion and the bolt holes at the connection).
If the reduced capacity is insufficient, common retrofits involve bolting or welding new steel plates onto the existing member to increase its area (strengthening) or replacing the member entirely.

Case Study 2: Long-Span Roof Bracing

A large warehouse features a long-span roof supported by steel trusses. During construction, the roof bracing is installed using very slender rod members.
Scenario: During a mild wind event before the roofing is installed, the slender bracing members are observed vibrating significantly, causing concern among the construction crew.
Solution: While the rods are strong enough in pure tension to resist the wind forces, their slenderness ratio (L/rL/r) is extremely high.
The AISC specification recommends a maximum slenderness ratio of 300300 for tension members (excluding rods in tension) to prevent excessive vibration and sagging. To resolve the issue, the engineers added intermediate supports to reduce the unbraced length (LL) of the rods, effectively decreasing their slenderness ratio and mitigating the vibrations.

Additional Solved Problems

Determine the block shear strength of the 1/2×61/2 \times 6 inch plate from the previous example. The plate is connected by two 3/4-inch bolts in a single line parallel to the applied load. The edge distance is 1.51.5 inches, and the bolt spacing is 3.03.0 inches. Steel is A36 (Fy=36 ksiF_y=36 \text{ ksi}, Fu=58 ksiF_u=58 \text{ ksi}). Hole diameter dh=7/8 ind_h = 7/8 \text{ in}.

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Check the slenderness ratio of a single angle L4x4x1/4 tension member with an unbraced length of 15 feet. Is it acceptable according to AISC recommendations?

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