m13_ps12_fall03

# m13_ps12_fall03 - 13 with x 1 x 2 and x 3 b The bending...

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Unified Engineering Fall 2003 Problem M13 (Materials and Structures) a) The state of axial stress through the thickness of a beam in pure bending (i.e. loaded only by a moment) is given by: M ˆ ˜ x 3 for –h < x 3 < +h s 11 = I M is the bending moment (which is constant in x 1 ), and I is the second moment of area of the cross-section of the beam (which is also constant). If 12 = 32 = 22 = 33 = 0 what can you say about the variation of the shear stress
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Unformatted text preview: 13 with x 1 , x 2 and x 3 ? b) The bending moment M now varies as a function of x 1 according to M = cx 1 The axial M ˆ stress is still give by 11 = ˜ x 3 . Again, 12 = 32 = 22 = 33 = . How does 13 I vary with x 1 , x 2 and x 3 ? Note 13 = for –h = x 3 and x 3 = +h (the top and bottom surfaces of the bean are free surfaces and do not have any stress acting on them)....
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