05-01ChapGere.0003

05-01ChapGere.0003 - e 5 y r 5 t / 2 r 5 0.1 in. 200 in. 5...

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SECTION 5.4 Longitudinal Strains in Beams 287 Problem 5.4-5 A thin strip of steel of length L 5 20 in. and thickness t 5 0.2 in. is bent by couples M 0 (see figure). The deflection d at the midpoint of the strip (measured from a line joining its end points) is found to be 0.25 in. Determine the longitudinal normal strain e at the top surface of the strip. Solution 5.4-5 Thin strip of steel t M 0 M 0 d L 2 L 2 L 5 20 in. t 5 0.2 in. d 5 0.25 in. The deflection curve is very flat (note that L / d 5 80) and therefore u is a very small angle. For small angles, ( u is in radians) d 5 r 2 r cos u 5 r (1 2 cos u ) Substitute numerical values ( r 5 inches): Solve numerically: r 5 200.0 in. N ORMAL STRAIN (Shortening at the top surface)
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Unformatted text preview: e 5 y r 5 t / 2 r 5 0.1 in. 200 in. 5 500 3 10 2 6 0.25 5 r 1 2 cos 10 r 5 r 1 2 cos L 2 r u 5 sin u 5 L / 2 r sin u 5 L / 2 r M M d L 2 L 2 r r u u Problem 5.4-6 A bar of rectangular cross section is loaded and supported as shown in the figure. The distance between supports is L 5 1.2 m and the height of the bar is h 5 100 mm. The deflection d at the midpoint is measured as 3.6 mm. What is the maximum normal strain e at the top and bottom of the bar? P h P a a d L 2 L 2 A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Institute of Technology.

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