Abridgeis36.5mlongandweighs2.56x105 N. Atruckweighing 5.25x104Nis10.2 m from one end of the bridge. Calculate the upward force that must be exerted by each pier to support thisweight

Explanation:

Bridge length A B = 36.5 m

weight W = 2.56 x 10⁵ N acting at middle point that is at 18.25 m from either end.

weight of truck W₁ = 5.25 x 10⁴ N  standing at 10.2 m from A .

Let force at A be F₁ and at B be F₂ .

Balancing total upward and downward force

F₁ + F₂ = ( 2.56 + .525 ) x 10⁵ = 3.085 x 10⁵ N

Taking torque of all the forces , for rotational balancing

2.56 x 10⁵ x 18.25 + .525 x 10⁵ x 10.2 = F₂ x 36.5

(46.72 + 5.355 )x 10⁵ = F₂ x 36.5

F₂ = 1.42 x 10⁵ N

F₁ = 1.665 x 10⁵ N