The mobile crane is symmetrically supported by two outriggers at A and two at R

Question

The mobile crane is symmetrically supported by two outriggers at A and two at R in order to relieve the suspension of the truck upon which it rests and to provide greater stability. If the crane boom and truck have a mass of 18 Mg and center of mass at G1 and the boom has a mass of 1.8 Mg and a center of mass at G2, determine the vertical reactions at each of the four outriggers as a function of the boom angle ft when the boom is supporting a load having a mass of 1.2 Mg. Plot the results measured from theta = 0degreeto the critical angle where tipping starts to occur.

Explanation / Answer

Solution:

Sum moments to zero about B
assume CW moment is positive
Let Fa be the force at each of the outrigger legs A

M(A) + M(load) + M(G) - M(G) = 0

2Fa[4] + 1.2(10)g[12.25sin - 2] + 1.8(10)g[6sin - 2] - 18(10)g[1] = 0

8Fa + 1.2(10)g(12.25sin) - (2)1.2(10)g + 1.8(10)g(6sin) - (2)1.8(10)g - 18(10)g = 0

8Fa + 14.7(10)gsin - 2.4(10)g + 10.8(10)gsin - 3.6(10)g - 18(10)g = 0

8Fa + 25.5(10)gsin - 24(10)g = 0

8Fa = g[24(10) - 25.5(10)sin]

Fa = g[3 - 3.1875sin] MN
Fa = 9.81[3 - 3.1875sin] MN
Fa = 29.43 - 31.269sin MN

Now just plot for values of theta

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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