Question

If the yield stress for steel is assumed to be 36ksi, what is the plastic moment limit (MP) for the beam #1 and will the current design of beam fail (reach plastic moment) under the loading 1kip/ft? In case the loading is increased, will the beam reach that strength limit or buckling will occur first? The guide for checking local buckling limit is provided by AISC specification and attached below. (E=31,200ksi) #1= W21x55 beam spans 40ft, and is simply supported at the ends and continuously laterally supported. It is loaded with 1kip/ft over the entire span.

Answer 1

fy = 36 ksi E= 31, 200 ks fon W 21x 5 5 3 zx= 126 b = 7.87 z te h = so tw 1) Plastic moment Me Mp= fy Zx 45 36 K-in = 36 * 126 s 378 k-ft. 2) moment due to given load Ik/ft m 40 Maximum moment @ Center 2 ME WL 8 1x402 200 K-ft 8

Mp = 378 koft Resistance M 200 Lond k-ft hence safe. Mp>M beam will not fail 3) check for local buckling fon W 214 SS 7.87 Aw=so from AISC 360 E E r = 0.38 fy 3.76 fy 31200 = 0 - 38 31200 = 3.76 36 36 11.186 = 110.69 claro inf. لي ( <low are compact hence both web & flange when the loading is increased since The section is compact, beam will limit first. reach the stregth