Manufacturing Engineering And Technology
Manufacturing Engineering And Technology
7th Edition
ISBN: 9789810694067
Author: Stephen R. Schmid (author) Serope Kalpakjian (author)
Publisher: Pearson Education Orphans
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Chapter 3, Problem 27QTP

The natural frequency, f, of a cantilever beam is given by

f = 0.56 E I g w L 4 ,

where E is the modulus of elasticity, I is the moment of inertia, g is the gravitational constant, w is the weight of the beam per unit length, and L is the length of the beam. How does the natural frequency of the beam change, if at all, as its temperature is increased? Assume that the material is steel.

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A 5.0m long steel wire has a cross-sectional area of 0.55cm^2. Its proportional limit has a value of 0.0018 times its Young's modulus. Its breaking stress has a value of 0.0065 times its Young's modulus. The wire is fastened at its upper end and hangs vertically. a. How great a weight can be hung from the wire without exceeding the proportional limit? b. How much will the wire stretch under this load? c. What is the maximum weight that the wire can support?
Why are the beams that are short and carry large loads, especially those made of wood, are first designed to resist shear?
2.) When a beam 6 m long with a cross-sectional area of 19.4 cm2 is subjected to a compression force of 16 x 104 N, its length is shortened by 4.5 mm. What is the Young’s Modulus for the beam?

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