Mechanics of Materials – MAE 243 (Section 002) Spring 2008 Dr. Konstantinos A. Sierros

Problem A cantilever beam AB is loaded by a couple M 0 at its free end (see figure). The length of the beam is L = 1.5 m and the longitudinal normal strain at the top surface is The distance from the top surface of the beam to the neutral surface is 75 = mm. Calculate the radius of curvature, the curvature, and the vertical deflection at the end of the beam.

Problem A thin, high-strength steel rule (E = 30 x (10^6) psi) having thickness t = 0.15 in. and length L = 40 in. is bent by couples M 0 into a circular arc subtending a central angle θ = 45° (see figure). (a) What is the maximum bending stress in the rule? (b) Does the stress increase or decrease if the central angle is increased?

5.6: Design of beams for bending stresses When designing beams many factors must be considered. Some of them are: - Type of structure (airplane, automobile, bridge, buildings…) - Materials to be used - Loads to be supported - Environmental conditions - Cost

5.6: Design of beams for bending stresses When designing beams to resist bending stresses, which are very important, we should begin by calculating the required section modulus The allowable stress is based on the properties of the material and the desired factor of safety

5.6:Beams of standardized shapes and sizes Structural steel sections The standardized steel sections are manufactured by a process called rolling Aluminum structural sections Aluminum structural sections are manufactured by a process called extrusion Wood beams They are surfaced in order to be smoother

5.6:Relative efficiency of various beam shapes It can be shown that a beam of a very narrow rectangular section will fail due to lateral buckling A beam of a square cross-section is more efficient in resisting bending than is a circular beam of the same area. Why? Because a circle has a relatively larger amount of material located near the neutral axis

5.6: Nonprismatic beams Nonprismatic beams have varying section modulus S We use nonprismatic beams for weight reduction and aesthetic reasons

Friday: QUIZ on Chapter 4 Duration 20 minutes 1 question to answer