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ch7-2 - SECTION 7.3 Principal Stresses and Maximum Shear...

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Problem 7.3-9 A shear wall in a reinforced concrete building is subjected to a vertical uniform load of intensity q and a horizontal force H , as shown in the first part of the figure. (The force H represents the effects of wind and earthquake loads.) As a consequence of these loads, the stresses at point A on the surface of the wall have the values shown in the second part of the figure (compressive stress equal to 1100 psi and shear stress equal to 480 psi). (a) Determine the principal stresses and show them on a sketch of a properly oriented element. (b) Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element. Solution 7.3-9 Shear wall SECTION 7.3 Principal Stresses and Maximum Shear Stresses 439 1100 psi 480 psi A A q H s x 5 0 s y 52 1100 psi t xy 480 psi (a) P RINCIPAL STRESSES 2 u p 5 2 41.11 8 and u p 5 2 20.56 8 2 u p 5 138.89 8 and u p 5 69.44 8 For 2 u p 5 2 41.11 8 : For 2 u p 5 138.89 8 : Therefore, s 1 5 180 psi and s 2 1280 psi and u p 2 5 69.44 8 u p 1 20.56 8 s x 1 1280 psi s x 1 5 180 psi 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 tan 2 u p 5 2 t xy s x 2 s y 0.87273 (b) M AXIMUM SHEAR STRESSES and t 5 730 psi and t 730 psi s aver 5 s x 1 s y 2 550 psi u s 2 5 u p 1 1 45 85 24.44 8 u s 1 5 u p 1 2 45 852 65.56 8 t max 5 B ¢ s x 2 s y 2 2 1 t xy 2 5 730 psi } } x O u p 2 5 69.44 8 180 psi 1280 psi y x O 730 psi u s 2 5 24.44 8 550 psi 550 psi y Problem 7.3-10 A propeller shaft subjected to combined torsion and axial thrust is designed to resist a shear stress of 63 MPa and a compressive stress of 90 MPa (see figure). (a) Determine the principal stresses and show them on a sketch of a properly oriented element. (b) Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element. 90 MPa 63 MPa

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Problems 7.3-11 through 7.3-16 An element in plane stress (see figure) is subjected to stresses s x , s y , and t xy . (a) Determine the principal stresses and show them on a sketch of a properly oriented element. (b) Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element. Data for 7.3-11 s x 5 3500 psi, s y 5 1120 psi, t xy 52 1200 psi Solution 7.3-11 Plane stress 440 CHAPTER 7 Analysis of Stress and Strain s x 90 MPa s y 5 0 t xy 63 MPa (a) P RINCIPAL STRESSES 2 u p 5 54.46 8 and u p 5 27.23 8 2 u p 5 234.46 8 and u p 5 117.23 8 For 2 u p 5 54.46 8 : For 2 u p 5 234.46 8 : s x 1 5 32.4 MPa s x 1 122.4 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 tan 2 u p 5 2 t xy s x 2 s y 5 1.4000 Therefore, s 1 5 32.4 MPa and s 2 122.4 MPa and (b) M AXIMUM SHEAR STRESSES and t 5 77.4 MPa and t 77.4 MPa s aver 5 s x 1 s y 2 45 MPa u s 2 5 u p 1 1 45 85 162.23 8 u s 1 5 u p 1 2 45 72.23 8 t max 5 B ¢ s x 2 s y 2 2 1 t xy 2 5 77.4 MPa u p 2 5 27.23 8 u p 1 5 117.23 8 Solution 7.3-10 Propeller shaft } } x O u p 2 5 27.23 8 32.4 MPa 122.4 MPa y x O 77.4 MPa u s 1 5 72.23 8 45 MPa 45 MPa y y x O t xy s x s y s x 5 3500 psi s y 5 1120 psi t xy 1200 psi (a) P RINCIPAL STRESSES 2 u p 5 2 45.24 8 and u p 5 2 22.62 8 2 u p 5 134.76 8 and u p 5 67.38 8 For 2 u p 5 2 45.24 8 : For 2 u p 5 134.76 8 : s x 1 5 620 psi s x 1 5 4000 psi 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
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ch7-2 - SECTION 7.3 Principal Stresses and Maximum Shear...

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