07-02ChapGere.0007

# 07-02ChapGere.0007 - max 2 2 t xy 2 20 30 40 20 40 60 13 45...

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SECTION 7.3 Principal Stresses and Maximum Shear Stresses 445 Problem 7.3-18 At a point on the surface of a machine component the stresses acting on the x face of a stress element are s x 5 45 MPa and t xy 5 30 MPa (see figure). What is the allowable range of values for the stress s y if the maximum shear stress is limited to t 0 5 34 MPa? Solution 7.3-18 Allowable range of values y x O t xy s y s x = 100 MPa s x 5 45 MPa t xy 5 30 MPa s y 5 ? Find the allowable range of values for s y if the maximum allowable shear stresses is t 0 5 34 MPa. Eq. (1) or Eq. (2) t max 2 5 ¢ s x 2 s y 2 2 1 t xy 2 t max 5 B ¢ s x 2 s y 2 2 1 t xy 2 S OLVE FOR s y Substitute numerical values: 5 45 MPa 6 32 MPa Therefore, 13 MPa # s y # 77 MPa G RAPH OF t max From Eq. (1): Eq. (3) t max 5 B ¢ 45 2 s y 2 2 1 (30) 2 s y 5 45 MPa 6 2 Ï (34 MPa) 2 2 (30 MPa) 2 s y 5 s x 6 2 Ï t
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Unformatted text preview: max 2 2 t xy 2 20 30 40 20 40 60 13 45 77 ] 20 Eq. (3) s y (MPa) 30 MPa 34 MPa ( 5 t o ) t max (MPa) 10 100 80 Problem 7.3-19 An element in plane stress is subjected to stresses s x 5 6500 psi and t xy 5 2 2800 psi (see figure). It is known that one of the principal stresses equals 7300 psi in tension. (a) Determine the stress s y . (b) Determine the other principal stress and the orientation of the principal planes; then show the principal stresses on a sketch of a properly oriented element. y x O 6500 psi s y 2800 psi A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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