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446_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 446_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 05Ch05.qxd 9/24/08 440 4:59 AM Page 440 CHAPTER 5 Stresses in Beams (Basic Topics) ds1 dx 0 dA x dA) a b L 2(dB dA x ‹ L 2(dB 1 dA) 2a dB dA 1b (a) GRAPH OF x/L VERSUS dB/dA (EQ. 2) Maximum bending stress occurs at the support when 0 1… Eq. (2) dB … 1.5 dA ; (b) MAXIMUM STRESS (AT SUPPORT B) Substitute x/L 1 into Eq. (1): smax 32PL ; pdB3 Fully Stressed Beams q Problems 5.7-6 to 5.7-8 pertain to fully stressed beams of rectangular cross section. Consider only the bending stresses obtained from the flexure formula and disregard the weights of the beams. B Problem 5.7-6 A cantilever beam AB having rectangular cross sections with constant width b and varying height hx is subjected to a uniform load of intensity q (see figure). How should the height hx vary as a function of x (measured from the free end of the beam) in order to have a fully stressed beam? (Express hx in terms of the height hB at the fixed end of the beam.) A hx hB x L hx hB b b Solution 5.7-6 Fully stressed beam with constant width and varying height hx hB b height at distance x height at end B width (constant) qx 2 2 AT DISTANCE x: M sallow hx 3q A bsallow x M S 3qx 2 bhx2 3q A bsallow AT THE FIXED END (x hB S bhx2 6 L Therefore, hx hB x L L): hx hB x L ; ...
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