OVERVIEW

In Chapter 7 we saw that an axial load applied to a member produces a uniform direct stress across the cross section of the member (Fig. 7.2). A different situation arises when the applied loads cause a beam to bend which, if the loads are vertical, will take up a sagging or hogging shape (Section 3.2). This means that for loads which cause a beam to sag the upper surface of the beam must be shorter than the lower surface as the upper surface becomes concave and the lower one convex; the reverse is true for loads which cause hogging. The strains in the upper regions of the beam will, therefore, be different to those in the lower regions and since we have established that stress is directly proportional to strain (Eq. (7.7)) it follows that the stress will vary through the depth of the beam.

The truth of this can be demonstrated by a simple experiment. Take a reasonably long rectangular rubber eraser and draw three or four lines on its longer faces as shown in Fig. 9.1(a); the reason for this will become clear a little later. Now hold the eraser between the thumb and forefinger at each end and apply pressure as shown by the direction of the arrows in Fig. 9.1(b). The eraser bends into the shape shown and the lines on the side of the eraser remain straight but are now further apart at the top than at the bottom. Reference to Section...