Q3-Part-2

Prévia do material em texto

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MECHANICS OF MATERIALS 
 
Beer • Johnston • DeWolf 
 Sample Problem 2.1 
 
 
 
 
 
 
 
 
The rigid bar BDE is supported by two 
links AB and CD. 
Link AB is made of aluminum (E = 70 
GPa) and has a cross-sectional area of 500 
mm2. Link CD is made of steel (E = 200 
GPa) and has a cross-sectional area of (600 
mm2). 
For the 30-kN force shown, determine the 
deflection a) of B, b) of D, and c) of E. 
SOLUTION: 
• Apply a free-body analysis to the bar 
BDE to find the forces exerted by 
links AB and DC. 
• Evaluate the deformation of links AB 
and DC or the displacements of B 
and D. 
• Work out the geometry to find the 
deflection at E given the deflections 
at B and D. 
 
 
 
© 2002 The McGraw-Hill Companies, Inc. All rights reserved. 2 - 13 
T
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E
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MECHANICS OF MATERIALS 
 
Beer • Johnston • DeWolf 
 Sample Problem 2.1 
 
SOLUTION: 
Free body: Bar BDE 
Displacement of B: 
 B 
 
 
PL 
AE 
 
 
 60 103 N

0.3m 


 MB  0 
500 10-6 m2 
 514 106 m 
 B 
Displacement of D: 
70 109 Pa 
 
 0.514 mm 
0  30 kN 0.6 m FCD  0.2 m 
 PL 
FCD 
MD 
 90 kN 
 0 
tension 
 D 
AE 
  90 103 N0.4 m
0  30 kN 0.4 m FAB  0.2 m 600 10-6 m2 200 109 Pa
FAB  60 kN compression  300 106 m 
 
 
 D  0.300 mm 

© 2002 The McGraw-Hill Companies, Inc. All rights reserved. 2 - 14 
T
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E
d
itio
n
 
MECHANICS OF MATERIALS 
 
Beer • Johnston • DeWolf 
 Sample Problem 2.1 
 
 
Displacement of D: 
 
BB 
 
BH 
DD HD 
0.514 mm 
0.300 mm 
 
200 mm x
x 
x  73.7 mm 
 
 
EE 
 
HE 
DD HD 
 E 
0.300 mm 
 
400  73.7mm
73.7 mm 
 E  1.928 mm 
 
 
 
 E  1.928 mm 



© 2002 The McGraw-Hill Companies, Inc. All rights reserved. 2 - 15