HW28 - PROBLEM 7.31 7.31 Solve Probs 7.7 and 7.11 using...

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Unformatted text preview: PROBLEM 7.31 7.31 Solve Probs. 7.7 and 7.11, using Mohr’s circle. 7.5 through 7.8 For the given state of stress, determine (a) the principal planes, (b) 7.9 through 7.12 For the given state of stress, determine (a) the orientation of the planes of maximum in-plane shearing stress, (b) the maximum in—plane shearing mess, (c) the corresponding normal stress. SOLUTION 5,.=-GOMPQ S,:—4DMP« 6mm: €;_Z'6'3 = “‘50 “PO. Poin'is >< 461,423,) = (- 6mm, ~35HPQ Y-‘(fi‘m 11.3): (-wMPa, 35 MPa) C: (Gave) 0 ) -‘ (“SDHPAJ O) = 36.4 MP4 -50-36.’-I = —86.‘f MP4 -.S'0+36.'+ ' -|3.G MP4 93+ 45° = 7.97“ 9» +45" ’ ”17.77" 12 = 3G}! MP6; 6‘... = —50 MW» PROBLEM 7.34 7.34 SOIVC Prob. 7.10, usmg MOhl' S cn‘cle_ 7.9 through 7.12 plan“ of maximum in-planc shearing stress, (6) the mp0!) ' g normal stmss. SOLUTION P0in+$ X: (6x0 —'1:3)=(.2 165316;) Y: (5:,J 7,19) = (ID lag-3kg) c: (6% o ) : (651:5?) o) 0.75 ' ’ circle. PROBLEM 7.39 7.39 Solve Prob. 7.17, usmg Mohr s 7.17 and 7.18 The grain ofa wooden member forms an angle of15° with the vertical. For the state of stress shown, determine (a) the in—plan'e shearing stress parallel to the grain, (b)thenormal su'essperpendiailartothegrain. SOLUTION 6x:—3Mpa. G“):-|.8 M‘Pq 221:0 sm=flzL§t = —2.4 MPa. 29 = -30° a: 0.6 MPa. 12: 0.6 MPa. (a) 2163’ ': “EXI $13130 1‘ - R sin 30‘ 7 -0.6 Siva 30. ? -O.3 MP‘L l (m 6:.- : G... — Ex'mso‘ = ~2fl - 0.4 cosso" .- — 2.92 MPa. l 7.40 Solve Prob. 7.18, using Mohr’s circle. 7.17 and 7.18 The grain ofa wooden member forms an angle of15° with the vertical. For the state of stress shown, determine (a) the in-plane shearing stress parallel to the PROBLEM 7.40 400 psn - . . gfirgg/éfi 8min, (b) the normal stress perpendicular to the gram. { [IXV‘ZW SOLUTION ”if, :53 = = o ’r = 00 s‘ xiii 55%;? 5* 5: *1 4 P . ‘— 15° 6'“,e :. 5x + 61 = O 2 (a) 73.]. 2 R :05 30" r 400 cos 30" = 346 psi, 4 0)) 6-" t 6;", " Rsin 30‘ 7 —‘+00 Sivx30a = -200 P$i 4 PROBLEM 7.54 7.54 through 7.57 Determine the principal planes and the principal Sufism for the state of plane stras multing fi'om the superposmon of the two stata of sums shown. 25 “Pa SOLUTION Molnw‘s cichc 'Fol‘ 2nd shes: sick 6x:,20+20 as 40' = 30 MPG. 6:, = 20—20025 ‘0' : l0 MP4 Tl: : 20 $;fl 6°. 5 \7.32 MFA Resup‘l‘qd 5+ asses 20 al 5,=35+3o= 55qu [:_.,° 5 r 25 + Io = 35 M90. 7:) = O +1132 = l7.32 HPa. tn (MP0) - (62%;) = %(é$+55) = 50 MP4 _ (2 X1232 ) C5 _35 = 1.1547 9‘: 29.6 95:14.6 «a ’= 22.9/ M94. 625 “+1? 72.9: MP“ 61,: GM — 12 , 27.061 HPaL. ...
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