A W 30 times 116 simply supported beam shown below is subjected to a uniform ser

Question

A W 30 times 116 simply supported beam shown below is subjected to a uniform service dead load of 1.0 k/ft (including the weight of the beam), a uniform service live load of 2.5 k/ft, and a concentrated service dead load of 45 kips. The beam is 40 ft 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 used. is the beam adequate to support the load? If not design the most economical section to support the load.

Explanation / Answer

factered load

UDL= 1.2*1+1.6*2.5 =5.2 k/ft

point load= 1.6*45 =72 k

taking moment balance about pin joint

5.2*40*40/2 +72*15= RB*40

RB = 131 k

RA = 149 k

moment diagram

maximum moment will be under point load and will be equal to 149*15- 5.2*152/2 =1845 k-ft

for given section

W 30X116

Zx= 329 in3

Mn=Mp= fy*Zx= 50*329 = 16450 kip-in=1370.8 kip-ft which is less then 1845 kip-ft hence section is not adequate

for LFRD

b =0.9

design moment

1845/0.9=2050 kip-ft= 24600 kip-in

minimum ZX required = 24600/50=492 in3

hence most adequate section in this category is W30X173 With Zx= 539 in3

thanks

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