07-02ChapGere.0011 - D A u 5 0 5600 2 u = 53.13 8 2 u s 2 =...

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Problem 7.4-3 An element in uniaxial stress is subjected to compressive stresses of magnitude 5600 psi, as shown in the figure. Using Mohr’s circle, determine (a) the stresses acting on an element oriented at a slope of 1 on 2 (see figure) and (b) the maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements. Solution 7.4-3 Uniaxial stress SECTION 7.4 Mohr’s Circle for Plane Stress 449 y x O 5600 psi 1 2 x 5600 psi y 0 xy 0 (a) E LEMENT AT A SLOPE OF 1 ON 2 (All stresses in psi) 2 53.130 26.57 R 2800 psi Point C : Point D : Point D : t x 1 y 1 R sin 2 u 2240 psi s x 1 R R cos 2 u 1120 psi t x 1 y 1 R sin 2 u 2240 psi s x 1 R R cos 2 u 4480 psi s x 1 2800 psi u arctan 1 2 26.565 (b) M AXIMUM SHEAR STRESSES Point S 1 : max R 2800 psi Point S 2 : min R 2800 psi aver R 2800 psi u s 2 45 2 u s 2 90 u s 1 45 2
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Unformatted text preview: D A ( u 5 0) 5600 2 u = 53.13 8 2 u s 2 = ] 90 8 C S 1 S 2 R O ± x 1 B ( u 5 90 8 ) t x 1 y 1 2 u s 1 R R x O 2240 psi u 5 26.57 8 1120 psi 4480 psi y D D' x O 2800 psi u s 1 5 45 8 2800 psi 2800 psi y S 2 S 1 Problem 7.4-4 An element in biaxial stress is subjected to stresses s x 5 2 60 MPa and s y 5 20 MPa, as shown in the figure. Using Mohr’s circle, determine (a) the stresses acting on an element oriented at a counterclockwise angle u 5 22.5° from the x axis and (b) the maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements. y x O 20 MPa 60 MPa A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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