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Mechanics of Materials – MAE 243 (Section 002) Spring 2008

Mechanics of Materials – MAE 243 (Section 002) Spring 2008. Dr. Konstantinos A. Sierros. Problem 5.4-4

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Mechanics of Materials – MAE 243 (Section 002) Spring 2008

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

  2. Problem 5.4-4 A cantilever beam AB is loaded by a couple M0 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 0.001. 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.

  3. Problem 5.5-3 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 M0 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?

  4. 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. 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

  6. 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

  7. 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

  8. 5.6: Nonprismatic beams • Nonprismatic beams have varying section modulus S • We use nonprismatic beams for weight reduction and aesthetic reasons

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

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