- Text
- Determine,
- Shear,
- Portion,
- Solutions,
- Pearson,
- Saddle,
- Copyright,
- Currently,
- Reproduced,
- Diameter,
- Strain,
- Properties

**03** Solutions 46060 5/7/10 8:45 AM Page 22 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 3–30. The block is made of titanium Ti-6A1-4V and is subjected to a compression of 0.06 in. along the y axis, and its shape is given a tilt of u = 89.7°. Determine P x , P y , and g xy . y Normal Strain: e y = dL y = -0.06 = -0.0150 in.>in. L y 4 Ans. Poisson’s Ratio: The lateral and longitudinal **strain** can be related using Poisson’s ratio. e x = -ve y = -0.36(-0.0150) 4 in. u 5 in. x = 0.00540 in. >in. Ans. Shear Strain: b = 180° - 89.7° = 90.3° = 1.576**03**2 rad g xy = p 2 - b = p 2 - 1.576**03**2 = -0.00524 rad Ans. 3–31. The shear **stress**–**strain** diagram for a steel alloy is shown in the figure. If a bolt having a diameter of 0.75 in. is made of this material and used in the double lap joint, determine the modulus of elasticity E and the force P required to cause the material to yield. Take n = 0.3. The shear force developed on the shear planes of the bolt can be determined by considering the equilibrium of the FBD shown in Fig. a : + ©F x = 0; V + V - P = 0 V = = P 2 P t(ksi) 60 0.00545 P/2 P/2 g(rad) From the shear **stress**–**strain** diagram, the yield **stress** is t y = 60 ksi. Thus, t y = V y A ; 60 = P>2 p 4 A0.752 B P = 53.01 kip = 53.0 kip Ans. From the shear **stress**–**strain** diagram, the shear modulus is Thus, the modulus of elasticity is G = G = 60 ksi 0.00545 = 11.01(1**03** ) ksi E 2(1 + y) ; 11.01(1**03** ) = E 2(1 + 0.3) E = 28.6(10 3 ) ksi Ans. 22

**03** Solutions 46060 5/7/10 8:45 AM Page 23 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *3–32. A shear spring is made by bonding the rubber annulus to a rigid fixed ring and a plug. When an axial load P is placed on the plug, show that the slope at point y in the rubber is dy>dr =-tan g = -tan1P>12phGr22. For small angles we can write dy>dr = -P>12phGr2. Integrate this expression and evaluate the constant of integration using the condition that y = 0 at r = r o . From the result compute the deflection y = d of the plug. r o d P r i r y h y P Shear Stress–Strain Relationship: Applying Hooke’s law with t A = . 2p r h g = t A G = P 2p h G r dy dr P = -tan g = -tan a 2p h G r b (Q.E.D) If g is small, then tan g = g. Therefore, At r = r o , y = 0 Then, y = P 2p h G ln r o r At r = r i , y = d dy dr = - P 2p h G r P dr y = - 2p h G L r y = - 0 = - C = P 2p h G ln r + C P 2p h G ln r o + C P 2p h G ln r o d = P 2p h G ln r o r i Ans. 23

- Page 1 and 2:
FM_TOC 46060 6/22/10 11:26 AM Page

- Page 3 and 4:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 5 and 6:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 7 and 8:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 9 and 10:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 11 and 12:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 13 and 14:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 15 and 16:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 17 and 18:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 19 and 20:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 21 and 22:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 23 and 24:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 25 and 26:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 27 and 28:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 29 and 30:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 31 and 32:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 33 and 34:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 35 and 36:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 37 and 38:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 39 and 40:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 41 and 42:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 43 and 44:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 45 and 46:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 47 and 48:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 49 and 50:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 51 and 52:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 53 and 54:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 55 and 56:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 57 and 58:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 59 and 60:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 61 and 62:
01 Solutions 46060 5/6/10 2:43 PM P

- Page 63 and 64: 01 Solutions 46060 5/6/10 2:43 PM P
- Page 65 and 66: 01 Solutions 46060 5/6/10 2:43 PM P
- Page 67 and 68: 01 Solutions 46060 5/6/10 2:43 PM P
- Page 69 and 70: 01 Solutions 46060 5/6/10 2:43 PM P
- Page 71 and 72: 01 Solutions 46060 5/6/10 2:43 PM P
- Page 73 and 74: 01 Solutions 46060 5/6/10 2:43 PM P
- Page 75 and 76: 02 Solutions 46060 5/6/10 1:45 PM P
- Page 77 and 78: 02 Solutions 46060 5/6/10 1:45 PM P
- Page 79 and 80: 02 Solutions 46060 5/6/10 1:45 PM P
- Page 81 and 82: 02 Solutions 46060 5/6/10 1:45 PM P
- Page 83 and 84: 02 Solutions 46060 5/6/10 1:45 PM P
- Page 85 and 86: 02 Solutions 46060 5/6/10 1:45 PM P
- Page 87 and 88: 02 Solutions 46060 5/6/10 1:45 PM P
- Page 89 and 90: 02 Solutions 46060 5/6/10 1:45 PM P
- Page 91 and 92: 02 Solutions 46060 5/6/10 1:45 PM P
- Page 93 and 94: 03 Solutions 46060 5/7/10 8:45 AM P
- Page 95 and 96: 03 Solutions 46060 5/7/10 8:45 AM P
- Page 97 and 98: 03 Solutions 46060 5/7/10 8:45 AM P
- Page 99 and 100: 03 Solutions 46060 5/7/10 8:45 AM P
- Page 101 and 102: 03 Solutions 46060 5/7/10 8:45 AM P
- Page 103 and 104: 03 Solutions 46060 5/7/10 8:45 AM P
- Page 105 and 106: 03 Solutions 46060 5/7/10 8:45 AM P
- Page 107 and 108: 03 Solutions 46060 5/7/10 8:45 AM P
- Page 109 and 110: 03 Solutions 46060 5/7/10 8:45 AM P
- Page 111 and 112: 03 Solutions 46060 5/7/10 8:45 AM P
- Page 113: 03 Solutions 46060 5/7/10 8:45 AM P
- Page 117 and 118: 03 Solutions 46060 5/7/10 8:45 AM P
- Page 119 and 120: 03 Solutions 46060 5/7/10 8:45 AM P
- Page 121 and 122: 03 Solutions 46060 5/7/10 8:45 AM P