Solved Problems

Determine if a W18x50 (Fy=50F_y = 50 ksi) beam is adequate for shear and deflection. It spans 24 feet and carries a service uniform dead load of 0.8 kips/ft and a service uniform live load of 1.2 kips/ft. The allowable live load deflection is L/360L/360.
Section properties for W18x50:
  • d=18.0d = 18.0 in
  • tw=0.355t_w = 0.355 in
  • Ix=800I_x = 800 in4^4
  • h/tw=46.6h/t_w = 46.6

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Case Studies

Case Study 1: Resolving Floor Vibration Issues

A newly constructed open-plan office features long-span steel composite beams supporting a concrete floor deck.
Scenario: Shortly after occupancy, employees complain that the floor feels "bouncy," and their monitors shake when someone walks briskly down the main aisle.
Solution: The engineers confirm that the floor meets all code requirements for strength and static deflection. However, the floor system's natural frequency is too close to the human walking pacing rate (approx. 1.5 to 2.5 Hz).
Because serviceability (vibration) governed over strength, the engineers had to stiffen the floor system to increase its natural frequency. Since the beams were already installed, the retrofit involved welding steel plates to the bottom flanges of the existing beams, significantly increasing their moment of inertia (IxI_x) without altering the architectural floor-to-ceiling height, thereby stiffening the floor and reducing the vibrations to acceptable levels.

Case Study 2: Bridge Girder Web Crippling

During the launch (installation) of a massive continuous steel bridge girder over a highway, the girder is temporarily supported on a central pier by a small hydraulic jack.
Scenario: A loud "pop" is heard, and the girder sags slightly. Inspection reveals that the web of the girder has buckled directly above the hydraulic jack.
Solution: The failure was caused by a highly concentrated reaction force applied over a very small bearing area. The failure mode was web crippling (local buckling of the web under concentrated load).
The engineers had checked the global shear capacity, but they failed to check the local limit states of web yielding and web crippling at the temporary jacking location. The solution required installing transverse bearing stiffeners (steel plates welded vertically to both sides of the web directly above the jack) to transfer the concentrated force safely from the bottom flange up into the full depth of the web.

Additional Solved Problems

A W24x68 beam (Fy=50 ksiF_y = 50 \text{ ksi}) is subjected to a concentrated point load from a column resting on its top flange. The load is applied at the midspan. The bearing length of the load is N=6 inN = 6 \text{ in}. Determine the nominal strength for Web Yielding (RnR_n). Properties for W24x68: d=23.7 ind = 23.7 \text{ in}, tw=0.415 int_w = 0.415 \text{ in}, kdes=1.18 ink_{des} = 1.18 \text{ in}.

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Calculate the midspan serviceability deflection of a simply supported W16x31 steel beam (Ix=375 in4I_x = 375 \text{ in}^4, E=29,000 ksiE = 29,000 \text{ ksi}) spanning 20 ft. It is subjected to a single concentrated live load of 15 kips applied exactly at the midspan. Compare this to an allowable limit of L/240L/240.

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