ESM 2204 – Mechanics of Deformable BodiesSample Test 1

Name (last, first):

INSTRUCTIONS: You can only use your calculator. The use of books, notes, phones,and computers is prohibited at any time during the test. You must show all your work. Nocredit will be given on any problem without any work shown. Partial credit will be awardedif and only if work is neat and easy to follow. You must write the final answer to eachproblem (with appropriate units) in the corresponding box.

HONOR PLEDGE: I have neither given nor received unauthorized aid on this test.

Signature:

1

[10%] The rod ABC is made of an aluminum for which E=70 GPa. Knowing that P = 6kN and Q = 42 kN, determine the displacement of (a) point A, (b) point B.

20 mm diameter

60 mm diameter

A

B

C

0.4 m

0.5 m

(a)=

(b)=

2

[15%] The change in diameter of a large steel bolt is carefully measured as the nut is tightened.Knowing that E = 29× 106 psi and ν = 0.30, determine the internal force in the bolt, if thediameter is observed to decrease by 0.5×10−3 in.

4 in

force in bolt=

3

[15%] An acetal polymer block is fixed to rigid plates at its top and bottom surfaces. If thetop plate displaces 2 mm horizontally when it is subjected to a horizontal force P = 2 kN,determine the shear modulus of the polymer. The width of the block is 100 mm. Assumethat the polymer is linearly elastic and use small angle analysis.

400 mm

200 mm

P 5 2 kN

shear modulus=

4

[10%] The yoke-and-rod connection is subjected to a tensile force of 10 kN. Determine theaverage normal stress in rod B and rod C.

25 mm

40 mm

30 mm

A

5 kN

5 kN

B

C

10 kN

10 kN60 mm

80 mm

50 mm

Normal stress in rod B=

Normal stress in rod C=

5

[25%] Workout Problem: The concrete post (Ec = 3.6 × 106 psi and αc = 5.5 × 10−6/oF)is reinforced with six steel bars (Es = 29 × 106 psi and αs = 6.5 × 10−6/oF), each having adiameter of 0.875 in. Determine the normal stresses induced in the steel and in the concreteby a temperature rise of 65 oF.

72 ft

10 in10 in

Normal stress in steel=

Normal stress in concrete=

6

[25%] Workout Problem: The rigid link is supported by a pin at A and two steel wires, eachhaving an unstretched length of 15 in. and cross-sectional area of 0.0115 in2. Determine theforce developed in the wires when the link supports the vertical load of 400 lb. Note thatEs = 29 × 103 ksi.

7 in.

5 in.

15 in.

6 in.

400 lb

A

B

C

FB =

FC =

7