PROBLEM Solve Probs. 7.5 and 7.9, using Mohr s circle.
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1 PROBLEM 7.1 Solve Probs. 7.5 and 7.9, using Mohr s circle. PROBLEM 7.5 through 7.8 For the given state of stress, determine (a) the principal planes, (b) the principal stresses. PROBLEM 7.9 through 7.12 For the given state of stress, determine (a) the orientation of the planes of maimum in-plane shearing stress, (b) the maimum in-plane shearing stress, (c) the corresponding normal stress. 60 MPa, 40 MPa, 5 MPa 2 Plotted points for Mohr s circle: 50 MPa X :(, ) ( 60 MPa, 5 MPa) Y :(, ) ( 40 MPa, 5 MPa) C:(, 0) ( 50 MPa, 0) (a) GX 5 tan.500 CG b b a a R CG GX MPa (b) min R min 86.4 MPa ma R ma 1.60 MPa (a) d B e A (b) ma R 6.4 MPa ma 6.4 MPa (c) 50 MPa 50.0 MPa e d PROPRIETARY MATERIAL. Copright 2015 McGraw-Hill Education. This is proprietar material solel for authorized instructor use. Not authorized for sale or distribution in an manner. This document ma not be copied, scanned, duplicated, forwarded, distributed, or posted 1059
2 PROBLEM 7.5 Solve Prob. 7.1, using Mohr s circle. PROBLEM 7.1 through 7.16 For the given state of stress, determine the normal and shearing stresses after the element shown has been rotated through (a) 25 clockwise, (b) 10 counterclockwise. 0, 8 ksi, 5 ksi Plotted points for Mohr s circle: 2 X :(0, 5 ksi) Y :(8 ksi, 5 ksi) C:(4 ksi, 0) FX 5 tan 2 p 1.25 FC p 4 ksi R FC FX ksi (a) R cos 2.40 ksi R sin ksi (b) R cos ksi R cos ksi R sin 6.07 ksi R cos 6.05 ksi PROPRIETARY MATERIAL. Copright 2015 McGraw-Hill Education. This is proprietar material solel for authorized instructor use. Not authorized for sale or distribution in an manner. This document ma not be copied, scanned, duplicated, forwarded, distributed, or posted 106
3 PROBLEM 7.9 Solve Prob. 7.17, using Mohr s circle. PROBLEM 7.17 The grain of a wooden member forms an angle of 15 with the vertical. For the state of stress shown, determine (a) the in-plane shearing stress parallel to the grain, (b) the normal stress perpendicular to the grain psi Plotted points for Mohr s circle: X (0, 250 psi) Y (0, 250 psi) C (0, 0) (a) Rcos 2 (250 psi)cos0 217 psi 217 psi (b) Rsin 2 (250 psi)sin psi psi PROPRIETARY MATERIAL. Copright 2015 McGraw-Hill Education. This is proprietar material solel for authorized instructor use. Not authorized for sale or distribution in an manner. This document ma not be copied, scanned, duplicated, forwarded, distributed, or posted 1068
4 PROBLEM 7.44 Solve Prob. 7.22, using Mohr s circle. PROBLEM 7.22 Two members of uniform cross section mm are glued together along plane a-a that forms an angle of 25 with the horizontal. Knowing that the allowable stresses for the glued joint are 800 kpa and 600 kpa, determine the largest centric load P that can be applied. 0 0 PA / A (50 10 )(80 10 ) m P (1 cos 50 ) 2A 2A P 1 cos50 (2)(4 10 )( ) P 1cos50 P.9010 N Choosing the smaller value, P 2 A (2)(410 )(60010 ) sin 50 P N 2A sin50 sin50 P.90 kn PROPRIETARY MATERIAL. Copright 2015 McGraw-Hill Education. This is proprietar material solel for authorized instructor use. Not authorized for sale or distribution in an manner. This document ma not be copied, scanned, duplicated, forwarded, distributed, or posted 107
5 PROBLEM 7.99 A spherical gas container having an inner diameter of 5 m and a wall thickness of 24 mm is made of steel for which E 200 GPa and Knowing that the gage pressure in the container is increased from zero to 1.8 MPa, determine (a) the maimum normal stress in the container, (b) the corresponding increase in the diameter of the container. p 1.8 MPa 1 1 (5) m r d t 2 2 pr (1.8)(2.476) MPa 2 t (2)(24 10 ) (a) 1 2 (b) ( 1 2) 1 ( ) E E MPa d d 1 (5)( ) m d mm PROPRIETARY MATERIAL. Copright 2015 McGraw-Hill Education. This is proprietar material solel for authorized instructor use. Not authorized for sale or distribution in an manner. This document ma not be copied, scanned, duplicated, forwarded, distributed, or posted 118
6 PROBLEM Determine the largest internal pressure that can be applied to a clindrical tank of 5.5-ft outer diameter and 5 -in. wall thickness if the ultimate normal stress of the steel used is 65 ksi and a factor of safet of is desired. U 65 ksi 1 1 ksi 1 10 psi FS d (5.5)(12) r t in. 2 2 pr t1 (0.625)(1 10 ) 1 p p 251 psi t r 2.75 PROPRIETARY MATERIAL. Copright 2015 McGraw-Hill Education. This is proprietar material solel for authorized instructor use. Not authorized for sale or distribution in an manner. This document ma not be copied, scanned, duplicated, forwarded, distributed, or posted 1148
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