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ch01-03 stress & strain & properties

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

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1–10. The boom DF of the jib crane and the column DE<br />

have a uniform weight of 50 lb/ft. If the hoist and load weigh<br />

300 lb, determine the resultant internal loadings in the crane<br />

on cross sections through points A, B, and C.<br />

5 ft<br />

D<br />

B<br />

A<br />

2 ft 8 ft 3 ft<br />

F<br />

C<br />

300 lb<br />

7 ft<br />

E<br />

Equations of Equilibrium: For point A<br />

; + © F x = 0; N A = 0<br />

Ans.<br />

+ c © F y = 0; V A - 150 - 300 = 0<br />

V A = 450 lb<br />

Ans.<br />

a +©M A = 0; -M A - 150(1.5) - 300(3) = 0<br />

M A = -1125 lb # ft = -1.125 kip # ft<br />

Ans.<br />

Negative sign indicates that M A<br />

acts in the opposite direction to that shown on FBD.<br />

Equations of Equilibrium: For point B<br />

; + © F x = 0; N B = 0<br />

Ans.<br />

+ c © F y = 0; V B - 550 - 300 = 0<br />

V B = 850 lb<br />

Ans.<br />

a +© M B = 0; -M B - 550(5.5) - 300(11) = 0<br />

M B = -6325 lb # ft = -6.325 kip # ft<br />

Ans.<br />

Negative sign indicates that M B<br />

acts in the opposite direction to that shown on FBD.<br />

Equations of Equilibrium: For point C<br />

; + © F x = 0; V C = 0<br />

Ans.<br />

+ c © F y = 0; -N C - 250 - 650 - 300 = 0<br />

N C = -1200 lb = -1.20 kip<br />

Ans.<br />

a +©M C = 0; -M C - 650(6.5) - 300(13) = 0<br />

M C = -8125 lb # ft = -8.125 kip # ft<br />

Ans.<br />

Negative signs indicate that N C<br />

and M C<br />

act in the opposite direction to that shown<br />

on FBD.<br />

6

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