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Textbook Question
Chapter 4, Problem 1RP

If the roller at B can sustain a maximum load of 3 kN, determine the largest magnitude of each of the three forces F that can be supported by the truss.

Chapter 4, Problem 1RP, If the roller at B can sustain a maximum load of 3 kN, determine the largest magnitude of each of

Prob. R4-1

Expert Solution & Answer
Check Mark
To determine

Find the largest magnitude of each of the three forces F that can be supported by the truss.

Answer to Problem 1RP

The largest magnitude of each of the three forces F that can be supported by the truss is 354N_.

Explanation of Solution

Given information:

  • The maximum load (P) of a roller support is 3 kN.
  • The length (L) between support A and B is 2 meters.
  • Intensity of load is F and the load is acting at a distance of 2 m, 4 m, and 6 m respectively from support A.

Calculation:

Show the free body diagram of the truss as in Figure 1.

Statics And Mechanics Of Materials, Student Value Edition Plus Mastering Engineering With Pearson Etext -- Access Card Package (5th Edition), Chapter 4, Problem 1RP

Use Figure 1.

Determine the largest magnitude of each of the three forces F that can be supported by the truss by taking the moment about support A.

MA=0F(l1)+F(l2)+F(l3)Pcosθ(L)=0 (1)

Here, the distance of force F acting on a truss at various points is l1,l2andl3 and the angle of roller support is θ.

Show the calculation of force as follows:

Conclusion:

Substitute 6.0 m for l1, 4.0 m for l2, and 2.0 m for l3, 3 kN for P, 45° for θ, and 2.0 m for L.

F(6.0)+F(4.0)+F(2)3.0cos45°(2.0)=012F=4.243F=4.24312kN×(1,000N1kN)F=353.55N

F354N

Thus, the largest magnitude of each of the three forces F that can be supported by the truss is 354N_.

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Chapter 4 Solutions

Statics And Mechanics Of Materials, Student Value Edition Plus Mastering Engineering With Pearson Etext -- Access Card Package (5th Edition)

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