Question

A grade 50 W21 x 62 section is used for a simple span of 20 feet. The only dead load is the weight of the beam. The beam is fully laterally braced.

a) what is the largest service concentrated load that can be placed at the center of the beam?
b) what is the maximum unbraced length?

Answer 1

Step 1:

Fy=50 ksi

L=20 ft

D.L=62/1000=0.062 kips/ft

Consider the L.L as X

Wdl=1.2(D.L)

Wdl=0.0744

Moment due to dead load=WdlL2/8=3.72 ft-kips

Moment due to Live load=1.6X/4

Step 2:

Now the capacity of W21X62 section

Mp=FyZx

Mp=50x144

Mp=7200 in-kips

Mn=540 ft-kips

Step 3:

Mn=Mu (for maximum capacity)

540=3.72+32X/4

X=67 kips is the maximum Load that can be carried at center

(b)

For a W21X62 section

Lp=6.25 ft, Lr=18.1 ft

Lb=?

Mn=Cb[Mp-(Mp-0.7FySx)(Lb-Lp)(Lr-Lp)]

6480=1.14[7200-(7200-0.7x50x127)(Lb-6.25)/(18.1-6.25)]

5684=[7200-(2755)(Lb-6.25)/11.85]

-1516= -2755(Lb-6.25)/11.85

Lb=12.77 ft