m12_ps11_fall03

m12_ps11_fall03 - = -cos sin 11 + cos sin 22 + ( cos-sin 2...

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Problem M12 (Materials and Structures) The figure below shows a triangular element in a two dimensional plane. The element is defined by an angle q and the length of the opposite side dx 1 . The element is of uniform thickness, dx 3 . The element is acted on by a state of stress in the plane, s 11 , s 22 ˜ ˜ and s 12 . Stresses s 11 and 12 y corresponding to a rotated axis system, x ˜ b . By considering equilibrium of the forces acting on the triangular element drawn below show that: 11 = cos ˜ 2 q s 11 + sin 2 22 + 2 cos q sin 12 (1) and ˜ 2 12
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Unformatted text preview: = -cos sin 11 + cos sin 22 + ( cos-sin 2 ) 12 (2) Find the values of q that produce the maximum and minimum values of ˜ 11 , what are the corresponding values of ˜ 12 ?. Do not try to distinguish between the maximum and minimum values. Note: This is a "plane stress" problem, i.e. stresses only act in the plane of the drawing ( s 33 = s 13 = s 23 =0). This problem is at the heart of transforming stress, take the time to make sure that you understand the procedure....
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.

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