Page of 10 1 A chain hoist is allowed to roll along beam AE

Page of 10 1. A chain hoist is allowed to roll along beam AE and has a rated capacity of 6 kips. Determine the maximum positive bending moment in the beam at point D, the maximum negative bending moment in the beam at point B, and the maximum force in the cable BC. For each case, indicate the load location for maximum effect 12 ft 3 ft

Solution

For maximum positive moment at D, the 6 kip load should be placed at D

in this case, the structure will act like a simply supported beam with span of 9 ft and point load at 4.5 ft

maximum positive moment=6*9/4=13.5 kip-ft

For maximum negative moment at D, the 6 kips load should be placed at E

this will act like a simply supported beam of 9 ft support to support distnace with 3 ft overhang

for this case,let us determine the vertical component of tension in cable considering moment equilibrium at support A

6*12-9*T_y=0

T_y= 8 kips

bending moment at D=6*7.5 - 8*4.5=9 kip-ft

Therefore,maximum negative moment at D=9 kip-ft

for maximum tension in cable, 6 kips load should be placed at E

Let tension in cable be T

angle the cable makes with horizontal = tan^-1(12/9)=53.13^o

9*T*sin53.13 - 6*12=0

T=10 kips

Therefore, maximum tension in cable is 10 kips