A simply supported beam is subjected to a uniform service dead load of 1.0 kips/

Question

A simply supported beam is subjected to a uniform service dead load of 1.0 kips/ft (including the weight of the beam), a uniform service service live load of 2.0 kips/ft, and a concentrated service dead load of 40 kips. The beam is 40 feet long, and the concentrated load is located 15 feet from the left end. The beam has continuous lateral support, and A572 Grade 50 steel is used. Is W30x108 adequate?
A. Use LRFD
DO NOT use ASD

FIGURE P5.5-2 A simply supported beam is subiected to a uniform service dead load of 1.0 kips/ft (including the weight of the beam). a unito 5.5-3 of the beam), a uniform service live load concentrated service dead load of 40 kips. The beam of 2.0 kips/ft, and a is 40 feet long, and the concentrated load is located 15 feet from the le end. The beam has continuous lateral support, and A572 Grade 50 steel is used. Is a W30 × 108 adequate? a. Use LRFD. b. Use ASD Po = 40 k 25' wp 1.0 k/ft "-= 2.0 k/ft W30 × 108 40 FIGURE P5.5-3

Explanation / Answer

Uniform dead load=1 kip/ft

Uniform live load=2 kip/ft

Concentrated dead load=40 kips

The governing load combination is 1.2D+1.6L

Factored uniform dead load=1.2*1=1.2 kips/ft

Factored uniform.live load=1.6*2=3.2 kips/ft

Factored concentrated live load=1.6*40=64 kips

Vertcal reaction at left support=(1.2*40/2)+(3.2*40/2)+(64*25/40)=128 kips

Maximum bending moment in beam will be where shear force is zero or changes sign

The shear force changes sign at point of application of concentrated force.therefore, maximum moment on beam is at that point.

Bending moment at that point=(128*15)-(4.4*15²/2)=1425 kip-ft

Moment capacity of continuously braced w30x108=1297 kip-ft

Beam is not adequate

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