PROBLEM 7.31 SOLUTION. β = τ max = 36.4 MPa. Solve Probs. 7.5 and 7.9, using Mohr s circle.
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1 PROBLEM 7.1 Solve Probs. 7.5 an 7.9, using Mohr s circle. PROBLEM 7.5 through 7.8 For the given state of stress, etermine (a) the principal planes, (b) the principal stresses. PROBLEM 7.9 through 7.1 For the given state of stress, etermine (a) the orientation of the planes of maimum in-plane shearing stress, (b) the maimum in-plane shearing stress, (c) the corresponing normal stress. = 60 MPa, = 40 MPa, τ = 5 MPa Plotte points for Mohr s circle: + = = 50 MPa X :(, τ ) = ( 60 MPa, 5 MPa) Y :(, τ ) = ( 40 MPa, 5 MPa) C:(, 0) = ( 50 MPa, 0) (a) GX 5 tan β = = =.500 CG 10 β = θb = β = 7.0 θ b = 7.0 α = 180 β = θa = α = 5.97 θ a = 5.0 R = CG + GX = = 6.4 MPa (b) min = R = min = 86.4 MPa ma = + R = ma = 1.6 MPa (a ) θ = θ + 45 = 7.97 θ = 8.0 B θ = θ + 45 = θ = 98.0 e ma A τ = R = 6.4 MPa τ ma = 6.4 MPa (b ) = = 50 MPa = 50.0 MPa e PROPRIETARY MATERIAL. 01 The McGraw-Hill Companies, Inc. All rights reserve. No part of this Manual ma be isplae, reprouce, or istribute in an form or b an means, without the prior written permission of the publisher, or use beon the limite istribution to teachers an eucators permitte b McGraw-Hill for their iniviual course preparation. A stuent using this manual is using it
2 PROBLEM 7.5 Solve Prob. 7.1, using Mohr s circle. PROBLEM 7.1 through 7.16 For the given state of stress, etermine the normal an shearing stresses after the element shown has been rotate through (a) 5 clockwise, (b) 10 counterclockwise. = 0, = 8 ksi, τ = 5 ksi Plotte points for Mohr s circle: + = = 4 ksi X :(0, 5 ksi) Y :(8 ksi, 5 ksi) C:(4 ksi, 0) FX 5 tan θ p = = = 1.5 FC 4 θ = 51.4 p R = FC + FX = = 6.40 ksi (a) θ = 5. θ = 50 ϕ = = 1.4 = R cosϕ =.40 ksi τ = R sinϕ τ = 0.15 ksi = + R cosϕ = ksi (b) θ = 10. θ = 0 ϕ = = 71.4 = R cosϕ = 1.95 ksi τ = R sinϕ τ = 6.07 ksi = + R cosϕ = 6.05 ksi PROPRIETARY MATERIAL. 01 The McGraw-Hill Companies, Inc. All rights reserve. No part of this Manual ma be isplae, reprouce, or istribute in an form or b an means, without the prior written permission of the publisher, or use beon the limite istribution to teachers an eucators permitte b McGraw-Hill for their iniviual course preparation. A stuent using this manual is using it
3 PROBLEM 7.9 Solve Prob. 7.17, using Mohr s circle. PROBLEM 7.17 The grain of a wooen member forms an angle of 15 with the vertical. For the state of stress shown, etermine (a) the in-plane shearing stress parallel to the grain, (b) the normal stress perpenicular to the grain. = 4 MPa = 1.6 MPa τ = 0 + = =.8 MPa Plotte points for Mohr s circle: X :(, τ ) = ( 4MPa,0) Y :(, τ ) = (1.6MPa,0) C:(,0) = (.8MPa,0) θ = 15. θ = 0 CX = 1.MPa R = 1.MPa (a) τ = CX sin 0 = Rsin 0 = 1.sin 0 τ = MPa (b) = CX cos 0 =.8 1. cos 0 =.84 MPa PROPRIETARY MATERIAL. 01 The McGraw-Hill Companies, Inc. All rights reserve. No part of this Manual ma be isplae, reprouce, or istribute in an form or b an means, without the prior written permission of the publisher, or use beon the limite istribution to teachers an eucators permitte b McGraw-Hill for their iniviual course preparation. A stuent using this manual is using it
4 PROBLEM 7.44 Solve Prob. 7., using Mohr s circle. PROBLEM 7. Two steel plates of uniform cross section mm are wele together as shown. Knowing that centric 100-kN forces are applie to the wele plates an that the in-plane shearing stress parallel to the wel is 0 MPa, etermine (a) the angle β, (b) the corresponing normal stress perpenicular to the wel. P = = = Pa = 15 MPa A (10 10 )(80 10 ) = 0 τ = 0 From Mohr s circle: (a) 0 sin β = = 0.48 β = (b) = cos β = 117. MPa PROPRIETARY MATERIAL. 01 The McGraw-Hill Companies, Inc. All rights reserve. No part of this Manual ma be isplae, reprouce, or istribute in an form or b an means, without the prior written permission of the publisher, or use beon the limite istribution to teachers an eucators permitte b McGraw-Hill for their iniviual course preparation. A stuent using this manual is using it
5 PROBLEM 7.98 A spherical gas container mae of steel has a 5-m outer iameter an a wall thickness of 6 mm. Knowing that the internal pressure is 50 kpa, etermine the maimum normal stress an the maimum shearing stress in the container. = 5m t = 6mm = 0.006m, r = t =.494m pr (50 10 Pa)(.494 m) 6 = = = Pa t (0.006m) ma min = 7.74 MPa 0 (Neglectingsmallraialstress) = 7.7 MPa 1 τma = ( ma min ) τ ma = 6.4 MPa PROPRIETARY MATERIAL. 01 The McGraw-Hill Companies, Inc. All rights reserve. No part of this Manual ma be isplae, reprouce, or istribute in an form or b an means, without the prior written permission of the publisher, or use beon the limite istribution to teachers an eucators permitte b McGraw-Hill for their iniviual course preparation. A stuent using this manual is using it
6 PROBLEM The unpressurize clinrical storage tank shown has a -in. wall thickness 16 an is mae of steel having a 60-ksi ultimate strength in tension. Determine the maimum height h to which it can be fille with water if a factor of safet of 4.0 is esire. (Specific weight of water = 6.4 lb/ft.) 0 = (5)(1) = 00 in. 1 r = t = 150 = in. 16 U 60 ksi all = = = 15 ksi = psi FS pr all = t ( ) (15 10 ) 16 t all p = = = psi = 70 lb/ft r But p = γ h, p 70 lb/ft h = = h = 4. ft γ 6.4 lb/ft PROPRIETARY MATERIAL. 01 The McGraw-Hill Companies, Inc. All rights reserve. No part of this Manual ma be isplae, reprouce, or istribute in an form or b an means, without the prior written permission of the publisher, or use beon the limite istribution to teachers an eucators permitte b McGraw-Hill for their iniviual course preparation. A stuent using this manual is using it
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