Chapter 9, Problem 20P

To determine

The vertical support force at each end.

Answer to Problem 20P

Solution:

The force on the left end support is 8100 N.

The vertical support force for the right end beam is 5800 N.

Explanation of Solution

Given:

Mass of the steel beam, $m=940\text{kg}$

Formula Used:

For equilibrium:

  ${\displaystyle \sum \tau }=r_i\times F_i=0$

Here, $F_i$ is the applied force and $r_i$ represents its corresponding distance from the rotational axis.

Calculations:

The force on the left end use the torque around the right end point. There are three forces acting.

The weight of the bottom beam and it is acting at the center of the beam.

The weight of the top beam and it is also acting at its center.

Consider rotational about the left support:

  $\begin{array}{l}\left|F_R\right|\times l+Mg\times \frac{l}{2}+\frac{Mg}{2}\times \frac{l}{4}=0\\ \left|F_R\right|=Mg\left(\frac{1}{2}+\frac{1}{8}\right)\\ \left|F_R\right|=940\times 9.8\times 0.625\\ \left|F_R\right|=5800\text{N}\end{array}$

Consider rotational equilibrium about the right support:

  $\begin{array}{l}\left|F_L\right|\times l+Mg\times \frac{l}{2}+\frac{Mg}{2}\times \frac{3l}{4}=0\\ \left|F_L\right|=Mg\left(\frac{1}{2}+\frac{3}{8}\right)\\ \left|F_L\right|=940\times 9.8\times 0.875\\ \left|F_L\right|=8100\text{N}\end{array}$

Conclusion:

Hence, the force on the left end support is 80605N and the vertical support force for the right end beam is 5757.5 N.