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ch01-03 stress & strain & properties

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01 Solutions 46060 5/6/10 2:43 PM Page 66<br />

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently<br />

exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.<br />

1–98. The aluminum bracket A is used to support the<br />

centrally applied load of 8 kip. If it has a constant thickness<br />

of 0.5 in., determine the smallest height h in order to<br />

prevent a shear failure. The failure shear <strong>stress</strong> is<br />

t fail = 23 ksi. Use a factor of safety for shear of F.S. = 2.5.<br />

A<br />

h<br />

Equation of Equilibrium:<br />

+ c ©F y = 0; V - 8 = 0 V = 8.00 kip<br />

Allowable Shear Stress: Design of the support size<br />

t allow = t fail<br />

F.S = V A ; 23(1<strong>03</strong> )<br />

2.5<br />

= 8.00(1<strong>03</strong> )<br />

h(0.5)<br />

8 kip<br />

h = 1.74 in.<br />

Ans.<br />

1–99. The hanger is supported using the rectangular pin.<br />

Determine the magnitude of the allowable suspended load<br />

P if the allowable bearing <strong>stress</strong> is (s b ) allow = 220 MPa, the<br />

allowable tensile <strong>stress</strong> is (s t ) allow = 150 MPa, and the<br />

allowable shear <strong>stress</strong> is t allow = 130 MPa. Take t = 6 mm,<br />

a = 5 mm, and b = 25 mm.<br />

75 mm<br />

a<br />

a<br />

20 mm<br />

b<br />

10 mm<br />

Allowable Normal Stress: For the hanger<br />

(s t ) allow = P A ; 150A106 B =<br />

P = 67.5 kN<br />

Allowable Shear Stress: The pin is subjected to double shear. Therefore, V = P 2<br />

t allow = V A ; P>2<br />

130A106 B =<br />

(0.01)(0.025)<br />

P = 65.0 kN<br />

P<br />

(0.075)(0.006)<br />

Allowable Bearing Stress: For the bearing area<br />

t<br />

P<br />

37.5 mm<br />

37.5 mm<br />

(s b ) allow = P A ; 220A106 B =<br />

P>2<br />

(0.005)(0.025)<br />

P = 55.0 kN (Controls!)<br />

Ans.<br />

66

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