{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Shigley's Solution Manual Ch.5

# Shigley's Solution Manual Ch.5 - Chapter 5 5-1 MSS DE 1 3 =...

This preview shows pages 1–6. Sign up to view the full content.

Chapter 5 5-1 MSS: σ 1 σ 3 = S y / n n = S y σ 1 σ 3 DE: n = S y σ σ = ( σ 2 A σ A σ B + σ 2 B ) 1 / 2 = ( σ 2 x σ x σ y + σ 2 y + 3 τ 2 xy ) 1 / 2 (a) MSS: σ 1 = 12, σ 2 = 6, σ 3 = 0 kpsi n = 50 12 = 4 . 17 Ans. DE: σ = (12 2 6(12) + 6 2 ) 1 / 2 = 10 . 39 kpsi, n = 50 10 . 39 = 4 . 81 Ans. (b) σ A , σ B = 12 2 ± 12 2 2 + ( 8) 2 = 16, 4 kpsi σ 1 = 16, σ 2 = 0, σ 3 = − 4 kpsi MSS: n = 50 16 ( 4) = 2 . 5 Ans. DE: σ = (12 2 + 3( 8 2 )) 1 / 2 = 18 . 33 kpsi, n = 50 18 . 33 = 2 . 73 Ans. (c) σ A , σ B = 6 10 2 ± 6 + 10 2 2 + ( 5) 2 = − 2 . 615, 13 . 385 kpsi σ 1 = 0, σ 2 = − 2 . 615, σ 3 = − 13 . 385 kpsi MSS: n = 50 0 ( 13 . 385) = 3 . 74 Ans. DE: σ = [( 6) 2 ( 6)( 10) + ( 10) 2 + 3( 5) 2 ] 1 / 2 = 12 . 29 kpsi n = 50 12 . 29 = 4 . 07 Ans. (d) σ A , σ B = 12 + 4 2 ± 12 4 2 2 + 1 2 = 12 . 123, 3 . 877 kpsi σ 1 = 12 . 123, σ 2 = 3 . 877, σ 3 = 0 kpsi MSS: n = 50 12 . 123 0 = 4 . 12 Ans. DE: σ = [12 2 12(4) + 4 2 + 3(1 2 )] 1 / 2 = 10 . 72 kpsi n = 50 10 . 72 = 4 . 66 Ans. B A

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
116 Solutions Manual Instructor’s Solution Manual to Accompany Mechanical Engineering Design 5-2 S y = 50 kpsi MSS: σ 1 σ 3 = S y / n n = S y σ 1 σ 3 DE: ( σ 2 A σ A σ B + σ 2 B ) 1 / 2 = S y / n n = S y / ( σ 2 A σ A σ B + σ 2 B ) 1 / 2 (a) MSS: σ 1 = 12 kpsi, σ 3 = 0, n = 50 12 0 = 4 . 17 Ans. DE: n = 50 [12 2 (12)(12) + 12 2 ] 1 / 2 = 4 . 17 Ans. (b) MSS: σ 1 = 12 kpsi, σ 3 = 0, n = 50 12 = 4 . 17 Ans . DE: n = 50 [12 2 (12)(6) + 6 2 ] 1 / 2 = 4 . 81 Ans. (c) MSS: σ 1 = 12 kpsi, σ 3 = − 12 kpsi, n = 50 12 ( 12) = 2 . 08 Ans. DE: n = 50 [12 2 (12)( 12) + ( 12) 2 ] 1 / 3 = 2 . 41 Ans. (d) MSS: σ 1 = 0, σ 3 = − 12 kpsi, n = 50 ( 12) = 4 . 17 Ans. DE: n = 50 [( 6) 2 ( 6)( 12) + ( 12) 2 ] 1 / 2 = 4 . 81 5-3 S y = 390 MPa MSS: σ 1 σ 3 = S y / n n = S y σ 1 σ 3 DE: ( σ 2 A σ A σ B + σ 2 B ) 1 / 2 = S y / n n = S y / ( σ 2 A σ A σ B + σ 2 B ) 1 / 2 (a) MSS: σ 1 = 180 MPa, σ 3 = 0, n = 390 180 = 2 . 17 Ans. DE: n = 390 [180 2 180(100) + 100 2 ] 1 / 2 = 2 . 50 Ans. (b) σ A , σ B = 180 2 ± 180 2 2 + 100 2 = 224 . 5, 44 . 5 MPa = σ 1 , σ 3 MSS: n = 390 224 . 5 ( 44 . 5) = 1 . 45 Ans. DE: n = 390 [180 2 + 3(100 2 )] 1 / 2 = 1 . 56 Ans.
Chapter 5 117 (c) σ A , σ B = − 160 2 ± 160 2 2 + 100 2 = 48 . 06, 208 . 06 MPa = σ 1 , σ 3 MSS: n = 390 48 . 06 ( 208 . 06) = 1 . 52 Ans. DE: n = 390 [ 160 2 + 3(100 2 )] 1 / 2 = 1 . 65 Ans. (d) σ A , σ B = 150, 150 MPa = σ 1 , σ 3 MSS: n = 390 150 ( 150) = 1 . 30 Ans. DE: n = 390 [3(150) 2 ] 1 / 2 = 1 . 50 Ans. 5-4 S y = 220 MPa (a) σ 1 = 100, σ 2 = 80, σ 3 = 0 MPa MSS: n = 220 100 0 = 2 . 20 Ans. DET: σ = [100 2 100(80) + 80 2 ] 1 / 2 = 91 . 65 MPa n = 220 91 . 65 = 2 . 40 Ans. (b) σ 1 = 100, σ 2 = 10, σ 3 = 0 MPa MSS: n = 220 100 = 2 . 20 Ans. DET: σ = [100 2 100(10) + 10 2 ] 1 / 2 = 95 . 39 MPa n = 220 95 . 39 = 2 . 31 Ans. (c) σ 1 = 100, σ 2 = 0, σ 3 = − 80 MPa MSS: n = 220 100 ( 80) = 1 . 22 Ans. DE: σ = [100 2 100( 80) + ( 80) 2 ] 1 / 2 = 156 . 2 MPa n = 220 156 . 2 = 1 . 41 Ans. (d) σ 1 = 0, σ 2 = − 80, σ 3 = − 100 MPa MSS: n = 220 0 ( 100) = 2 . 20 Ans. DE: σ = [( 80) 2 ( 80)( 100) + ( 100) 2 ] = 91 . 65 MPa n = 220 91 . 65 = 2 . 40 Ans.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
118 Solutions Manual Instructor’s Solution Manual to Accompany Mechanical Engineering Design 5-5 (a) MSS: n = O B O A = 2 . 23 1 . 08 = 2 . 1 DE: n = OC O A = 2 . 56 1 . 08 = 2 . 4 (b) MSS: n = OE O D = 1 . 65 1 . 10 = 1 . 5 DE: n = OF O D = 1 . 8 1 . 1 = 1 . 6 (c) MSS: n = O H OG = 1 . 68 1 . 05 = 1 . 6 DE: n = OI OG = 1 . 85 1 . 05 = 1 . 8 (d) MSS: n = OK O J = 1 . 38 1 . 05 = 1 . 3 DE: n = OL O J = 1 . 62 1 . 05 = 1 . 5 O ( a ) ( b ) ( d ) ( c ) H I G J K L F E D A B C Scale 1" 200 MPa B A
Chapter 5 119 5-6 S y = 220 MPa (a) MSS: n = O B O A = 2 . 82 1 . 3 = 2 . 2 DE: n = OC O A = 3 . 1 1 . 3 = 2 . 4 (b) MSS: n = OE O D = 2 . 2 1 = 2 . 2 DE: n = OF O D = 2 . 33 1 = 2 . 3 (c) MSS: n = O H OG = 1 . 55 1 . 3 = 1 . 2 DE: n = OI OG = 1 . 8 1 . 3 = 1 . 4 (d) MSS: n = OK O J = 2 . 82 1 . 3 = 2 . 2 DE: n = OL O J = 3 . 1 1 . 3 = 2 . 4 B A O ( a ) ( b ) ( c ) ( d ) H G J K L I F E D

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}