HW 3 - Homework set 3 Solutions PDF

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Homework set 3 Solutions...

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PROBLEM 2.4 Two gage marks are placed exactly 250 mm apart on a 12-mm-diameter aluminum rod with E = 73 GPa and an ultimate strength of 140 MPa. Knowing that the distance between the gage marks is 250.28 mm after a load is applied, determine (a) the stress in the rod, (b) the factor of safety.

SOLUTION (a )

  L  L0  250.28 mm  250 mm  0.28 mm



 L0



0.28 mm 250 mm

 1.11643 10 4

  E  (73  10 9 Pa) (1.11643 10 4 )  8.1760  107 Pa

  81.8 MPa  (b )

F.S.  

u  140 MPa 81.760 MPa

 1.71233

F.S.  1.712 

P

PROBLEM 2.20 The rod ABC is made of an aluminum for which E  70 GPa. Knowing that P  6 kN and Q  42 kN, determine the deflection of (a) point A, (b) point B.

A

20-mm diameter

0.4 m

B

Q 0.5 m

60-mm diamete r

C

SOLUTION

AAB  A BC 

 4

 4

2 d AB  2  d BC

 4

 4

(0.020) 2  314.16  10 6 m 2 (0.060) 2  2.8274  10 3 m 2

PAB  P  6  103 N PBC  P  Q  6  103  42  103  36  103 N LAB  0.4 m LBC  0.5 m

 AB 

PAB LAB (6  103 )(0.4) 6   109.135  10 m AAB E A (314.16 10 6 )(70  10 9 )

 BC 

PBC LBC ( 36  10 3 )(0.5)   90.947  106 m ABC E (2.8274  103 )(70  109 )

(a)

 A   AB  BC  109.135  106  90.947  106 m  18.19 106 m

(b)

 B   BC  90.9 10 6 m  0.0909 mm

or

 A  0.01819 mm  

B  0.0909 mm  

30 kips

A

30 kips

B

30 kips

D

PROBLEM 2.22

8 ft C

For the steel truss ( E  29  106 psi) and loading shown, determine the deformations of the members BD and DE, knowing that their crosssectional areas are 2 in2 and 3 in2, respectively.

8 ft E 8 ft F G 15 ft

SOLUTION Free body: Portion ABC of truss

M E  0 : FBD (15 ft)  (30 kips)(8 ft)  (30 kips)(16 ft)  0 FBD   48.0 kips

Free body: Portion ABEC of truss

F x  0 : 30 kips  30 kips  FDE  0  FDE   60.0 kips



BD 

PL ( 48.0  103 lb)(8  12 in.)  AE (2 in 2 )(29  106 psi)

DE 

PL ( 60.0  103 lb)(15  12 in.)  AE (3 in2 )(29 106 psi)

BD  79.4 10 3 in.  DE  124.1  10 3 in. ...