prob_03_01_02 - Problem 3.1-2. Imagine that stresses in the...

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Problem 3.1-2. Imagine that stresses in the xy plane are reported to be: σ x 6 a 1 x 2 = y 12 a 1 x 2 = τ xy 12 a 1 y 2 = where a 1 is a constant. Consider the square region 0<= x <= b , 0<= y <= b . Find: a) expressions for the tractions Φ x and Φ y on each side of this square, in terms of x, y , b , and a 1 . b) If body forces are zero, is this state of stress in fact possible? Explain. Solution: 1 2 3 4 x y b b a) Apply Eq. 3.1-14, adapted for 2-dimensions, n =0 Φ x l x m xy + = y l xy m y + = For Side 1-2 l 1 = m 0 = xb = x x = 6 a 1 b 2 = y xy = 12 a 1 y 2 = For Side 2-3 l 0 = m 1 = yb = x xy = 12 a 1 b 2 = y y = 12 a 1 x 2 = For Side 3-4 l 1 = m 0 = x 0 = x x = 0 = y xy
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This note was uploaded on 01/11/2011 for the course MAE 5020 taught by Professor Folkman during the Fall '10 term at Utah State University.

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