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ch01-03 stress & strain & properties

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01 Solutions 46060 5/6/10 2:43 PM Page 30<br />

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1–43. Solve Prob. 1–42 assuming that pins D and E are<br />

subjected to single shear.<br />

3 ft 3 ft<br />

500 lb<br />

A<br />

Support Reactions: FBD(a)<br />

a +©M E = 0; 500(6) + 300(3) - D y (6) = 0<br />

D y = 650 lb<br />

B<br />

C<br />

3 ft<br />

; + ©F x = 0; 500 - E x = 0 E x = 500 lb<br />

1.5 ft<br />

1.5 ft<br />

3 ft<br />

+ c ©F y = 0; 650 - 300 - E y = 0 E y = 350 lb<br />

Average shear <strong>stress</strong>: Pins D and E are subjected to single shear as shown on FBD<br />

(b) and (c).<br />

D<br />

300 lb<br />

E<br />

For Pin D, V D = F D = D y = 650 lb<br />

(t D ) avg = V D<br />

A D<br />

=<br />

650<br />

p<br />

4 (0.252 )<br />

= 13242 psi = 13.2 ksi<br />

Ans.<br />

For Pin E, V E = F E = 2 500 2 + 350 2 = 610.32 lb<br />

(t E ) avg = V E<br />

= 610.32<br />

p<br />

A E 4 (0.252 )<br />

= 12433 psi = 12.4 ksi<br />

Ans.<br />

*1–44. A 175-lb woman stands on a vinyl floor wearing<br />

stiletto high-heel shoes. If the heel has the dimensions<br />

shown, determine the average normal <strong>stress</strong> she exerts on<br />

the floor and compare it with the average normal <strong>stress</strong><br />

developed when a man having the same weight is wearing<br />

flat-heeled shoes. Assume the load is applied slowly, so that<br />

dynamic effects can be ignored. Also, assume the entire<br />

weight is supported only by the heel of one shoe.<br />

Stiletto shoes:<br />

A = 1 2 (p)(0.3)2 + (0.6)(0.1) = 0.2014 in 2<br />

s = P A = 175 lb<br />

= 869 psi<br />

2<br />

0.2014 in<br />

1.2 in.<br />

0.5 in.<br />

Ans.<br />

0.3 in.<br />

0.1 in.<br />

Flat-heeled shoes:<br />

A = 1 2 (p)(1.2)2 + 2.4(0.5) = 3.462 in 2<br />

s = P A =<br />

175 lb<br />

= 50.5 psi<br />

2<br />

3.462 in<br />

Ans.<br />

30

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