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.

Prob. R4-1

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 $\underset{\_}{354\text{N}}$.

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.

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.

$\begin{array}{l}{\displaystyle \sum M_A=0}\\ F\left(l_1\right)+F\left(l_2\right)+F\left(l_3\right)-P\cos \theta \left(L\right)=0\end{array}$ (1)

Here, the distance of force F acting on a truss at various points is $l_1,l_2\text{and}{l}_3$ and the angle of roller support is $\theta$.

Show the calculation of force as follows:

Conclusion:

Substitute 6.0 m for $l_1$, 4.0 m for $l_2$, and 2.0 m for $l_3$, 3 kN for P, $45°$ for $\theta$, and 2.0 m for L.

$\begin{array}{l}F\left(6.0\right)+F\left(4.0\right)+F\left(2\right)-3.0\cos 45°\left(2.0\right)=0\\ 12F=4.243\\ F=\frac{4.243}{12}\text{kN}\times \left(\frac{\text{1,000}\text{N}}{\text{1}\text{kN}}\right)\\ F=353.55\text{N}\end{array}$

$F\approx 354\text{N}$

Thus, the largest magnitude of each of the three forces F that can be supported by the truss is $\underset{\_}{354\text{N}}$.