Question

GROUP PROBLEM SOLVING I 2-3ft Given: Two couples act on the beam with the geometry shown and d 4 ft. Find: The resultant couple Sa lb 80 1b Plan: 3 1 80 tb 1) Resolve the forces in x and y-directions so they can be treated as couples. 2) Add these two couples to find the resultant couple

Find the resultant couple

Answer 1

let us first determine the horizontal and vertical forces

so from the diagram we have

Fx=4/5*80=64lb and Fy=50*cos30=43.3lb

now taking the sum of the moments

$\sum$M=64*4 -43.3*3=126.1ft.lb

now taking the sum of the moment about A

$\sum$Ma=-64*3+64*7+43.3*2-43.3*5=126.1ft.lb

now taking the sum of the moment about B

$\sum$Mb=43.3*2-43.3*5-64*1+64*5=126.1ft.lb

so the resultant couple=126.1ft.lb+126.1ftlb=252.2ft.lb

so the answer is 252 ft.lb