A force and a couple are applied to a beam Replace this syst

A force and a couple are applied to a beam. Replace this system with a single force, F applied at point G, and determine the distance d.

Solution

>> External Forces acting on a beam are :-

1). F1 = 220 lb, at point C, 4.5 ft from A (downward direction)

2). F2 = 160 lb, at point D, 6 ft from A(upward direction)

3). F3 = 160 lb, at point E, 12 ft from A (downward direction)

>> Let rsultant force = F and acts atatG, \'\'d\'\' distance from A

>> Now, as Net Force, F = F1 + F2 + F3

=> F = 220 - 160 + 160 = 220 lb

>> Now, considering moment about point A

=> 4.5*220 - 6*160 + 12*160 = d*220

=> d = 8.86 ft

>> S, net forcee, F = 220 lb at point G, 8.86 ft fom A....