PHINMA EDUCATION – ARAULLO UNIVERSITY

CIE 113 – MECHANICS OF DEFORMABLE BODIES

P2 EXAMINATION – SET A
INSTRUCTION: Select the correct answer for each of the following questions.
MARK ONLY ONE ANSWER for each item by shading the letter of your choice. You
may use a pen or a pencil. Strictly no erasures.

1. It is a measure of the force that can cause an object to rotate about

an axis.
A. Bending Moment C. Axial Force
B. Couple D. Twisting Moment

2. Quantity used to describe resistance to torsional deformation.

A. Poison’s Ratio C. Polar Moment of Inertia
B. Modulus of Rigidity D. Modulus of Elasticity

3. It is the rotation of the cross section at the end of the shaft.

A. Angular rotation C. Torsional shear stress
B. Angle of twist D. Torsional displacement

4. It is the location on the shaft where the maximum torsional shear

stress is developed.
A. Center C. Exterior surface
B. Throughout the section D. Midpoint of center and
exterior

5. The point where the beams moment diagram changes from concave up to
concave down or vice versa.
A. Point of Deformation C. Point of Contraction
B. Point of Contraflexure D. Point of Zero Shear

6. Which of the following gives the relationship between moment diagram

and shear diagram?
A. Area in shear diagram is the change in magnitude on moment
diagram
B. Area in shear diagram is the change in magnitude in load diagram
C. The slope of the shear diagram is the magnitude of the moment
diagram
D. Area in moment diagram is the change in magnitude on shear
diagram

7. A hollow steel tube with an inside diameter of 100mm must carry a

tensile load of 500 kN. Determine the outside diameter of the tube if
the stress is limited to 120 MPa.
A. 116 mm C. 120 mm
B. 117 mm D. 122 mm

8. A 10 mm2 cable is fixed on its upper end while a 300 kg box is on the
lower end. Determine the deformation on the cable if it has a length of
7 meters and E = 70 GPa.
A. 3.0 mm C. 21.51 mm
B. 6.8 mm D. 29.43 mm

Situation 1. A cylindrical steel pressure vessel 400 mm in diameter with a wall

thickness of 20 mm, is subjected to an internal pressure of 4.5 MN/m2.

9. Calculate the tangential stress in the steel vessel.

A. 21.0 MPa C. 40.5 MPa
B. 22.5 MPa D. 45.0 MPa

10. Calculate the longitudinal stress in the steel vessel.

A. 22.5 MPa C. 45.0 MPa
B. 21.0 MPa D. 40.5 MPa

PREPARED BY: ENGR. D. FLORES

ENGR. K. CUELLAR
 PHINMA EDUCATION – ARAULLO UNIVERSITY

CIE 113 – MECHANICS OF DEFORMABLE BODIES

P2 EXAMINATION – SET A
11. To what value may the internal pressure be increased if the stress
in the steel is limited to 120 MN/m2.
A. 16 MPa C. 12 MPa
B. 24 MPa D. 18 MPa

𝛼 = 10 𝑥10−6 /°𝐶.
Situation 2. A concrete pavement 6 meters long experience no stress at 27°C. Use

12. Determine the deformation at a temperature of 42°C.

A. 0.70 mm C. 0.90 mm
B. 0.80 mm D. 1.20 mm

13. Determine deformation at a temperature of 0°C.

A. 1.95 mm C. 1.14 mm
B. 1.62 mm D. 0.98 mm

14. Determine the stress at 70°C if E = 42 GPa.

A. 18.06 MPa C. 12.21 MPa
B. 13.56 MPa D. 10.84 MPa

Situation 3. FIGURE-01 shows a 2-in diameter solid steel cylinder that is built
into the support at C and subjected to the torques TA and TB. Use G = 12x106 psi.

15. Determine the maximum shear stresses in segments AB of the cylinder.

A. 6880 psi C. 3820 psi
B. 6808 psi D. 3280 psi

16. Determine the maximum shear stresses in segments BC of the cylinder.

A. 6808 psi C. 3280 psi
B. 6880 psi D. 3820 psi

17. Compute the angle of rotation.

A. 3.81° C. 2.63°
B. 2.89° D. 1.97°

Situation 4. The steel shaft, 3 ft long and 4 in. in diameter, carries the end
torque of 15 kip - ft. Determine the following if Use G =12 x 106 psi.

18. The maximum shear stress in the shaft.

A. 19.14 ksi C. 15.61 ksi
B. 14.32 ksi D. 11.87 ksi
19. The angle of twist of the shaft.
A. 0.971° C. 2.123°
B. 4.581° D. 1.231°

Situation 5. Refer to FIGURE-02. For the beam shown,

20. Which of the following gives the shear on segment AB.

A. 400 lb C. 800 lb
B. 600 lb D. 1200 lb

21. Which of the following gives the shear equation on segment BC.
A. 2000 – 400x C. -2000 + 400x
B. 2000 + 400x D. -2000 – 400x

A. 200𝑥2 + 2000𝑥 − 3200 C. 200𝑥2 + 2000𝑥 +

22. Which of the following gives the moment equation on segment BC.

3200
B. 200𝑥2 − 2000𝑥 − 3200 D. −𝟐𝟎𝟎𝒙𝟐 + 𝟐𝟎𝟎𝟎𝒙 −
𝟑𝟐𝟎𝟎

PREPARED BY: ENGR. D. FLORES

ENGR. K. CUELLAR
 PHINMA EDUCATION – ARAULLO UNIVERSITY

CIE 113 – MECHANICS OF DEFORMABLE BODIES

P2 EXAMINATION – SET A
Situation 6. The 12 kN -m torque is applied to the free end of the 6-m steel
shaft. The angle of rotation of the shaft is to be limited to 3°. Use G= 83
GPa.

23. Find the diameter “d” of the smallest shaft that can be used.
A. 110 mm C. 119 mm
B. 114 mm D. 128 mm

24. Determine the maximum shear stress in the shaft.

A. 56.1 MPa C. 41.3 MPa
B. 49.2 MPa D. 39.8 MPa

Situation 7. The rigid bar ABC in FIGURE-03 is supported by a pin at B and two
vertical steel rods. Initially the bar is horizontal, and the rods are stress-

decreased by 40. 𝛼 = 11.7 𝑥 10−6/°𝐶 and E=200 GPa.

free. Determine the stress in each rod if the temperature of the rod at A is

25. Determine the stress on bar at C.

A. 10.80 MPa C. 70.32 MPa
B. 16.19 MPa D. 86.40 MPa

26. Determine the stress on bar at A.

A. 10.80 MPa C. 70.32 MPa
B. 16.19 MPa D. 86.40 MPa

Situation 8. FIGURE-04 shows a homogeneous, rigid block weighing 12 kips that is

supported by three symmetrically placed rods. The lower ends of the rods were
at the same level before the block was attached. Determine the stress in each
rod after the block is attached and the temperature of all bars increases by
100°F.

27. Determine the stress in the steel rod.

A. 11 600 psi C. 10 500 psi
B. 3 600 psi D. 2 900 psi

28. Determine the stress in the bronze rod.

A. 11 600 psi C. 3 600 psi
B. 10 500 psi D. 2 900 psi

29. Which of the following gives the vertical displacement of the block?
A. 0.0252 in C. 0.0522 in
B. 0.252 in D. 0.522 in

Situation 9. Refer to FIGURE-05. For the beam shown,

A. −800𝑥 − 2400 C. −800𝑥 +

30. Which of the following is the shear equation for segment BC.

2400
B. 800𝑥 + 2400 D. 800 − 240

A. −400 𝑥2 − 2400𝑥 + 1600 C. −400 𝑥2 − 2400𝑥 +

31. Which of the following is the moment equation at segment BC.

1600
B. −400 𝑥2 + 2400𝑥 − 1600 D. 400 𝑥2 + 2400𝑥 −
1600

A. −400 𝑥2 + 2400𝑥 − 25,600 C. 400 𝑥2 + 2400𝑥 +

32. Which of the following is the moment equation at segment CD.

25,600
B. 400 𝑥2 + 2400𝑥 − 25,600 D. −400 𝑥2 − 2400𝑥 +
25,600

33. Which of the following is the shear diagram of the beam.

PREPARED BY: ENGR. D. FLORES

ENGR. K. CUELLAR
 PHINMA EDUCATION – ARAULLO UNIVERSITY

CIE 113 – MECHANICS OF DEFORMABLE BODIES

P2 EXAMINATION – SET A

A.

PREPARED BY: ENGR. D. FLORES

ENGR. K. CUELLAR
 PHINMA EDUCATION – ARAULLO UNIVERSITY

CIE 113 – MECHANICS OF DEFORMABLE BODIES

P2 EXAMINATION – SET A

34. Which of the following is the moment diagram of the beam.

PREPARED BY: ENGR. D. FLORES

ENGR. K. CUELLAR
 PHINMA EDUCATION – ARAULLO UNIVERSITY

CIE 113 – MECHANICS OF DEFORMABLE BODIES

P2 EXAMINATION – SET A

Situation 10.Refer to FIGURE-06. The steel shaft, 3 ft long and 4 in. in

diameter, carries the end torque of 15 kip - ft. Use G = 12 x 106 psi
for steel.

A. 12.3 𝑘𝑠𝑖 C. 14.3 𝑘𝑠𝑖

35. Determine the maximum shear stress in the shaft.

B. 13.6 𝑘𝑠𝑖 D. 15.2 𝑘𝑠𝑖

A. 1.32o C. 2.31o
36. Determine the angle of twist of the shaft.

B. 1.23o
D. 2.13o

Situation 11. Refer to FIGURE-07. The A-36 steel shaft has a diameter of 30
mm and is fixed at its ends A and B. G = 80 GPa. If it is subjected to
the torque.

A. 32.25 𝑀𝑝𝑎 C. 37.73 𝑀𝑝𝑎

37. Determine the maximum shear stress in regions AC.

B. 36.32𝑀𝑝𝑎 D. 34.07 𝑀𝑝𝑎

A. 12.25 𝑀𝑃𝑎 C. 14.15 𝑀𝑃𝑎

38. Determine the maximum shear stress in region BC.

B. 16.32 𝑀𝑝𝑎 D. 18.86 𝑀𝑃𝑎

A. 0.72𝑜 C. 0.67𝑜
39. Determine the angle of twist at C.

B. 0.77𝑜 D. 0.62𝑜

Situation 12. Refer to FIGURE-08. The compound shaft is attached to a rigid

wall at each end. For the bronze segment AB, the diameter is 75 mm and G
= 35 Gpa. For the steel segment BC, the diameter is 50 mm and G = 83 Gpa. Given
that a = 2 m and b = 1.5 m.

40. Compute the largest torque T that can be applied as shown in the
figure if the maximum shear stress is limited to 60 MPa in the bronze

A. 5.11 𝑘𝑁 𝑚 C. 6.37 𝑘𝑁 𝑚
and 80 MPa in the steel.

B. 4.32 𝑘𝑁 𝑚 D. 7.43 𝑘𝑁 𝑚

A. 4.97 𝑘𝑁 𝑚 C. 1.96 𝑘𝑁 𝑚
41. What is the reaction at A?

B. 3.14 𝑘𝑁 𝑚 D. 3.10 𝑘𝑁 𝑚

A. 4.97 𝑘𝑁 𝑚 C. 1.96 𝑘𝑁 𝑚
42. What is the reaction at C?

B. 3.14 𝑘𝑁 𝑚 D. 3.10 𝑘𝑁 𝑚

Situation 13. Refer to FIGURE-09. The thin-walled tube is subject to a

torque of 750 N m.

A. 15.6 𝑀𝑃𝑎 C. 10.4 𝑀𝑃𝑎

43. What is the average shear stress at A?

B. 13.7 𝑀𝑃𝑎 D. 12.1 𝑀𝑃𝑎

A. 15.6 𝑀𝑃𝑎 C. 10.4 𝑀𝑃𝑎

44. What is the average shear stress at B?

B. 13.7 𝑀𝑃𝑎 D. 12.1 𝑀𝑃𝑎

PREPARED BY: ENGR. D. FLORES

ENGR. K. CUELLAR
 PHINMA EDUCATION – ARAULLO UNIVERSITY

CIE 113 – MECHANICS OF DEFORMABLE BODIES

P2 EXAMINATION – SET A

Situation 14. Refer to FIGURE-10. Cantilever beam loaded as shown.

A. −20𝑥 C. −60
45. What is the shear equation at segment AB?

B. −40𝑥 D. −10𝑥2

A. −10𝑥2 C. −5𝑥
46. What is the moment equation at segment AB?

B. −5𝑥2 D. −20𝑥

A. 3 𝑚 C. 0
47. What is the distance of maximum moment from point A?

B. 5 𝑚 D. 7
𝑚

Situation 15. A solid steel shaft 5 m long is stressed at 80 MPa when twisted
through 4°. Using G = 83 GPa.

A. 138 𝑚𝑚 C. 338 𝑚𝑚
48. Compute the shaft diameter.

B. 238 𝑚𝑚 D. 38 𝑚𝑚

A. 5.19 𝑥 106 𝑊 C. 5.19 𝐾𝑊

49. What power can be transmitted by the shaft at 20 Hz?

B. 519 𝑀𝑊 D. 5.19 𝐺𝑊

50. These are beams in which the reactions of the supports may

A. 𝑆𝑡𝑎𝑡𝑖𝑐𝑎𝑙𝑙𝑦 𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑡𝑒 𝐵𝑒𝑎𝑚 C. 𝑃𝑟𝑜𝑝𝑝𝑒𝑑

be determined by the use of the equations of static equilibrium.

𝐵𝑒𝑎𝑚
B. 𝑆𝑡𝑎𝑡𝑖𝑐𝑎𝑙𝑙𝑦 𝐼𝑛𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑡𝑒 D. 𝐶𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠
𝐵𝑒𝑎𝑚 𝐵𝑒𝑎𝑚

PREPARED BY: ENGR. D. FLORES

ENGR. K. CUELLAR
 PHINMA EDUCATION – ARAULLO UNIVERSITY

CIE 113 – MECHANICS OF DEFORMABLE BODIES

P2 EXAMINATION – SET A

FIGURE-01 FIGURE-02

FIGURE-03 FIGURE-04

FIGURE-05 FIGURE-06

FIGURE-07 FIGURE-08

FIGURE-09 FIGURE-10

PREPARED BY: ENGR. D. FLORES

ENGR. K. CUELLAR