Chapter 18, Problem 29A

Compression and tension stress occurs in a beam that supports a load (even when the load is its own weight). Show by means of a simple sketch an example where a horizontal load-carrying beam is in tension at the top and compression at the bottom. Then show a case where the opposite occurs: compression at the top and tension at the bottom.

To determine

To sketch: An example of load carrying beam with a tension at the top and compression at the bottom. Also, an example of load carrying beam with a compression at the top and tension at the bottom.

Answer to Problem 29A

An example of load carrying beam with a tension at the top and compression at the bottom is shown in Figure 1.

An example of load carrying beam with a compression at the top and tension at the bottom is shown in Figure 2.

Explanation of Solution

Introduction:

When the load is applied at the top of a beam, the beam bends based on the support conditions.When both ends are supported, the top of the beam experiences compression and bottom of the beam experiences tension.When one end is supported and the another end is free, the top of the beam experiences tension and bottom of the beam experiences compression.

Case 1:

For a cantilever structure when a beam is bent by placing a weight at the edge of the beam, top part of the beam expands and stretches producing concave shape upwards. While the bottom side of the beam experiences compression. Therefore tension occurs in top side and compression occurs in bottom side of the beam as shown below.

  

Figure 1

Case 2:

Consider a simple supported structure resting on the wall support. A load is placed on the structure, as a result it bends downward producing convexity. In this case the bottom side of the beam will experiences tension and stretches. While the top part of the beam experience compression due to the load (weight of the object placed) as shown below.

  

Figure 2