07-01ChapGere.0007

07-01ChapGere.0007 - 100 mm 250 mm 5 arctan 0.4 5 21.80 8 x...

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Problem 7.2-13 At a point on the surface of a machine the material is in biaxial stress with s x 5 3600 psi and s y 52 1600 psi, as shown in the first part of the figure. The second part of the figure shows an inclined plane aa cut through the same point in the material but oriented at an angle u . Determine the value of the angle u between zero and 90° such that no normal stress acts on plane aa . Sketch a stress element having plane aa as one of its sides and show all stresses acting on the element. Solution 7.2-13 Biaxial stress SECTION 7.2 Plane Stress 431 Problem 7.2-12 Solve the preceding problem for a plate of dimensions 100 mm 3 250 mm subjected to a compressive stress of 2.5 MPa in the long direction and a tensile stress of 12.0 MPa in the short direction (see figure). Solution 7.2-12 Biaxial stress (welded joint) 12.0 MPa Weld 2.5 MPa 100 mm 250 mm s x 52 2.5 MPa s y 5 12.0 MPa t xy 5 0 52 0.5 MPa s x 1 5 s x 1 s y 2 1 s x 2 s y 2 cos 2 u 1 t xy sin 2 u u 5 arctan
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Unformatted text preview: 100 mm 250 mm 5 arctan 0.4 5 21.80 8 x O 5.0 MPa u 5 21.80 8 0.5 MPa 10.0 MPa y S TRESSES ACTING ON THE WELD s w 5 10.0 MPa t w 5 2 5.0 MPa s y 1 5 s x 1 s y 2 s x 1 5 10.0 MPa t x 1 y 1 5 2 s x 2 s y 2 sin 2 u 1 t xy cos 2 u 5 5.0 MPa t w u s w 5.0 MPa u 5 21.80 8 10.0 MPa y x a a O 1600 psi 3600 psi u s x 5 3600 psi s y 5 2 1600 psi t xy 5 Find angle u for s 5 0. s 5 normal stress on plane a-a 5 1000 1 2600 cos 2 u (psi) For we obtain [ 2 u 5 112.62 8 and u 5 56.31 8 cos 2 u 5 2 1000 2600 s x 1 5 0, s x 1 5 s x 1 s y 2 1 s x 2 s y 2 cos 2 u 1 t xy sin 2 u S TRESS ELEMENT u 5 56.31 8 5 2 2400 psi t x 1 y 1 5 2 s x 2 s y 2 sin 2 u 1 t xy cos 2 u s y 1 5 s x 1 s y 2 s x 1 5 2000 psi s x 1 5 x O 2400 psi u 5 56.31 8 2000 psi y a a u s A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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