592_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

592_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 586 1:18 PM Page 586 CHAPTER 7 Analysis of Stress and Strain Solution 7.3-8 sx txy 13 MPa 21 MPa PRINCIPAL ANGLES atan a up 2 sx sy tmax 25.92° up2 + 90° s1 s2 56.2 MPa up1 sx + sy cos 12up12 + txy sin 12up12 sy 2 sx + sy sx + 2 saver a sy sx 2 45° sy sx 2 b + txy2 us1 tmax ; ; 19.08° saver 26.7 MPa ; 29.5 MPa cos 12up22 + txy sin 12up22 + 2 up1 64.08° sy sx A MAXIMUM SHEAR STRESSES b 2 up1 2 .8 MPa us1 2txy up2 s1 s2 sy 46 MPa 2 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). 2 q 1100 psi H 480 psi A A (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 sx Shear wall sy 0 txy 1100 psi 480 psi s2 (a) PRINCIPAL STRESSES tan 2up 2up 2up sx1 For 2up For 2up 2txy sx 0.87273 sy 41.11° and up 20.56° 138.89° and up 69.44° sx + sy sy sx + 2 41.11°: 138.89°: Therefore, s1 2 sx1 sx1 cos 2u + txy sin 2u 180 psi 1280 psi 180 psi and up1 1280 psi and up2 20.56° f 69.44° ; ...
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