Question

10% A steel beam W18x76 spans 32 feet and is subjected to a Moment of 334 kips-ft. Find the load w on the beam. Determine the deflection at 14 span and mid span. What is the shear stress?

Answer 1

w = 10.437 kips

deflection at 1/4 span 20.83\E ft

at mid span = 1.23\E ft

shear stress 7.3629 psi

Step-by-step explanation:

area of cross section = 18*76

length of span = 32 ft

moment = 334 kips-ft

we know that

moment = load *eccentricity

334 = w * 32

w = 10.437 kips

deflection at 1/4 span

`\delta = (wa^2b^2)/(3EI)`

`= (10.4375*8^2 *24^2)/(3E (BD^3)/(12))`

`=(10.437 *8^2*24^2)/(3E (18*16^3)/(12))`

= 20.83\E ft

at mid span

`\delta = (wl^3)/(48EI)`

`= (10.43 *32^3)/(48 *E*(18*16^3)/(12))`

`\delta = 1.23\E ft`

shear stress

`\tau = (w)/(A) = (10.43 7*10^3)/(18*76) =7.3629 psi`