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Ebook Mechanics of materials (Second Edition): Part 2

(BQ) Part 2 book "Mechanics of materials" has contents: Deflection of symmetric beams, design and failure, stress transformation, design and failure, stability of columns. Invite you to reference. | M. Vable Mechanics of Materials: Deflection of Symmetric Beams 7 325 CHAPTER SEVEN DEFLECTION OF SYMMETRIC BEAMS Learning Objective 1. Learn to formulate and solve the boundary-value problem for the deflection of a beam at any point. _ Greg Louganis, the American often considered the greatest diver of all time, has won four Olympic gold medals, one silver medal, and five world championship gold medals. He won both the springboard and platform diving competitions in the 1984 and 1988 Olympic games. In his incredible execution, Louganis and all divers (Figure 7.1a) makes use of the behavior of the diving board. The flexibility of the springboard, for example, depends on its thin aluminum design, with the roller support adjusted to give just the right unsupported length. In contrast, a bridge (Figure 7.1b) must be stiff enough so that it does not vibrate too much as the traffic goes over it. The stiffness in a bridge is obtained by using steel girders with a high area moment of inertias and by adjusting the distance between the supports. In each case, to account for the right amount of flexibility or stiffness in beam design, we need to determine the beam deflection, which is the topic of this chapter (a) Figure 7.1 (b) Examples of beam: (a) flexibility of diving board; and (b) stiffness of steel girders. We can obtain the deflection of a beam by integrating either a second-order or a fourth-order differential equation. The differential equation, together with all the conditions necessary to solve for the integration constants, is called a boundaryvalue problem. The solution of the boundary-value problem gives the deflection at any location x along the length of the beam. Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm 7.1 SECOND-ORDER BOUNDARY-VALUE PROBLEM Chapter 6 considered the symmetric bending of beams. We found that if we can find the deflection in the y direction of one point on the cross .