TABLE OF CONTENTS Figure 7.1a shows a diving board bending under the weight of the diver at the end of the board. The diving board must have adequate flexibility to provide the spring force that the divers can use to launch themselves into a dive. The bridge in Figure 7.1b shows beams that must provide enough stiffness to resist large deflections due to the weight of the traffic. Adequate flexibility or stiffness can be incorporated into beam design if we can find the beam deflection, which is the topic of this chapter.
As shall be seen, the deflection of a beam can be obtained by integrating either a second-order or a fourth-order differential equation. A differential equation, together with all the conditions necessary to solve for the integration constants is called a boundary-value problem. The solution of the boundary-value problem gives the deflection of the beam at any location x along the length of the beam.
The learning objective in this chapter is how to formulate and solve the boundary-value problem for the deflection of a beam at any point.
In Chapter 6 on the symmetric bending of beams, we established that if we can find the deflection in the y direction of one point on the cross section, then we know the deflection of all points on the cross section. In other words, the deflection at a cross section is independent of the y and z
