A particular bridge, with a length L , consists of a horizontal slab with a weig

Question

A particular bridge, with a length L, consists of a horizontal slab with a weight of 40.0 kN, with the weight uniformly distributed. The slab is held up by one support 20% of the way across the bridge, and a second support 80% of the way across the bridge. As shown in the picture, a truck with a weight of mg = 21.0 kN is driving from left to right across the bridge.

(a) Once the truck is completely off the bridge, how much force will the left support exert on the horizontal slab? We're looking for an answer in kilonewtons (kN), which is what values are given in above.

(b) When the truck is at the position shown, where its full weight can be taken to act at a point 40% of the way across the bridge, calculate the force that each support exerts on the horizontal slab. We're looking for two answers—the value of each of the support forces.

The force exerted by the left support is _______ kN. The force exerted by the right support is ________ kN.

(c) At the instant the truck's weight is directly above the right support, what is the magnitude of the force the right support exerts on the horizontal slab?

Explanation / Answer

net torque about the left support = 0

Fr *0.6L = W1*0.3L

Fr = 40*0.3/0.6 = 20 kN

along vertical

Fnet = 0

Fl + Fr - W1 = 0

Fl + 20 k - 40 K = 0

Fl = 20 kN <<<<----------answer

(b)

net torque about the right end = 0

Fl*0.6L = w1*0.3L + w2*0.4L

Fl = ((40*0.3)+(21*0.4))/0.6

fL = 34 KN

along vertical

Fnet = 0

Fl + Fr - w1 - w2 = 0

Fr = 40 + 21 - 34 = 27 kN

(c)

torque about left = 0

Fr*0.6 = w1*0.3L + w2*0.6

Fr*0.6 = 40*0.3 + 21*0.6

Fr = 41 kN <<<------------answer

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.