Engineering Mechanics: Statics
Engineering Mechanics: Statics
13th Edition
ISBN: 9780132915540
Author: Russell C. Hibbeler
Publisher: Prentice Hall
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Chapter 4.9, Problem 37FP

Determine the resultant force and specify where it acts on the beam measured from A.

Chapter 4.9, Problem 37FP, Determine the resultant force and specify where it acts on the beam measured from A.

Expert Solution & Answer
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To determine
The resultant force and the distance of resultant force that acts on the beam measured from A.

Answer to Problem 37FP

The resultant force FR is 40.5kN()_ and the distance (d) of resultant force that acts on the beam measured from A is 1.25m_.

Explanation of Solution

Given information:

  • The intensity of uniformly varying load w1 is 6.0kN/m.
  • The intensity of uniformly varying load w1 is 9.0kN/m.
  • The intensity of uniformly varying load w1 is 3.0kN/m.

Explanation:

Assumption: Upward is positive.

Determine the resultant force using the equation of equilibrium.

FR=FyFR=(w1×l1)(w2×l2)(w3×l3) (I)

Here, the length of w1 is l1, the length of w2 is l2, and the length of w3 is l3.

Assumption: Anticlockwise is positive.

Determine the distance of resultant force which acts on the beam measured from A by taking the moment about A.

(MR)A=MAFR(d)=(w1×l1×l12)(w2×l2×l22)(w3×l3×(l32+3.0)) (II)

Show the calculation of resultant force and the distance as follows:

Conclusion:

Substitute 6.0kN/m for w1, 1.5 m for l1, 9.0kN/m for w1, 3.0 m for l2, 3.0kN/m for w1, and 1.5 m for l3 in Equation (I).

FR=(6.0×1.5)(9.0×3.0)(3.0×1.5)FR=40.5kN()

Thus, the resultant force FR is 40.5kN()_.

Substitute 40.5 kN for FR, 6.0kN/m for w1, 1.5 m for l1, 9.0kN/m for w1, 3.0 m for l2, 3.0kN/m for w1, and 1.5 m for l3 in Equation (II).

40.5(d)=(6.0×1.5×1.52)(9.0×3.0×3.02)(3.0×1.5×(1.52+3.0))d=50.62540.5d=1.25m

Thus, the distance of resultant force which acts on the beam measured from A is 1.25m_.

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Chapter 4 Solutions

Engineering Mechanics: Statics

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