1.

A round steel shell with outer and inner diameter 12 mm and 8 mm, respectively, encloses a brass core
(Ebrass = 96 GPa) with diameter 6 mm. The steel shell and brass core are initially 1 m in length. A load P is
applied to both shell and core through a cap plate. Find the load P required to compress both shell and
core by 0.10 mm.
a) 2179 N c) 1528 N
b) 1739 N d) 1655 N

2. The light rigid bar ABCD as shown is pinned at B and connected to two vertical rods. Assuming that the
bar was initially horizontal and the rods stress-free, determine the allowable load P if the stresses are not to
exceed 60 MPa and 150 MPa in the aluminium and steel, respectively.

a) 57.38 kN c) 51.75 kN
b) 43.71 kN d) 42.56 kN

3. A pipe carrying steam at 3.5 MPa has an outside diameter of 450 mm and a wall thickness of 10 mm. A
gasket is inserted between the flange at one end of the pipe and a flat plate used to cap the end. How
many 40-mm-diameter bolts must be used to hold the cap on if the allowable stress in the bolts is 80 MPa,
of which 55 MPa is the initial stress?

a) 11 c) 15
b) 13 d) 17

4. The rigid bar ABC in Fig. P-268 is pinned at B and attached to the two vertical rods. Initially, the bar is
horizontal and the vertical rods are stress-free. Determine the stress in the aluminum rod if the temperature
of the steel rod is decreased by 40°C. Neglect the weight of bar ABC.

a) 6.25 MPa c) 9.45 MPa

b) 8.35 MPa d) 10.15 MPa
5. Determine the maximum tensile stress in the beam shown.

a) 8.35 MPa c) 10.26 MPa

b) 7.33 MPa d) 5.96 MPa

6. Determine the maximum compressive stress in the beam shown.

a) 8.35 MPa c) 10.26 MPa

b) 7.33 MPa d) 5.96 MPa

7. The intensity of the triangular load carried by the T-section varies from zero at the free end to wo at
the support. Find the maximum safe value of wo given that the working stresses are 4000 psi in tension
and 10 000 psi in compression.

a) 400 lb/ft c) 360 lb/ft

b) 320 lb/ft d) 450 lb/ft

8. The thin-walled tube is used as a beam to support the uniformly distributed load of intensity wo. The
largest allowable value of wo is based on the working stress in bending of 100 MPa. Compute the
corresponding maximum shear stress in the beam.

a) 15.4 MPa c) 12.2 MPa

b) 35.5 MPa d) 20.3 MPa
9. A point in the cross-section where if the load is applied, the member will experience no added twist.
a) Center of mass c) Shear center
b) Centroid d) Center of rigidity

10. Imagine a concrete rectangular pad lying flat on the ground. No load is applied other than its own
weight. Draw the shear diagram.

A C

B D

11. Imagine a concrete rectangular pad lying flat on the ground. No load is applied other than its own
weight. Draw the moment diagram.

A
C

B
D

12. What is the maximum shearing stress that will be developed in a solid steel shaft subjected to a
torque of 12 kN·m if its angle of twist is limited to 3° in a length of 6 m? Use G = 83 GPa.
a) 38.11 MPa c) 46.33 MPa
b) 44.92 MPa d) 41.27 MPa

13. A flanged bolt coupling consists of eight 10-mm-diameter steel bolts on a bolt circle 400 mm in
diameter, and six 10-mm-diameter steel bolts on a concentric bolt circle 300 mm in diameter. What
torque can be applied without exceeding a shearing stress of 60 MPa in the bolts?
a) 13.27 kN·m c) 10.72 kN·m
b) 8.98 kN·m d) 12.10 kN·m

14. As shown in the figure below, determine the slope at A in rad. E=200 GPa and I=3000x10^6 mm^4.
 a) 0.00019 c) 0.00043
b) 0.00082 d) 0.00077

15. As shown in the figure below, determine the slope at B in rad. E=200 GPa and I=3000x10^6 mm^4.

a) 0.000014 c) 0.000098
b) 0.000053 d) 0.000036

16. As shown in the figure below, determine the slope at C in rad. E=200 GPa and I=3000x10^6 mm^4.

a) 0.000051 c) 0.000037
b) 0.000094 d) 0.000069

17. As shown in the figure below, determine the deflection at C in rad. E=200 GPa and I=3000x10^6
mm^4.

a) 0.081 c) 0.002
b) 0.027 d) 0.061

18. As shown in the figure below, determine the moment at A in kN-m.

 a) 205 c) 168
b) 137 d) 152

19. As shown in the figure below, determine the moment at B in kN-m.

a) 105 c) 120
b) 115 d) 125

20. A steel propeller shaft is to transmit 4.5 MW at 3 Hz without exceeding a shearing stress of 50 MPa
or twisting through more than 1° in a length of 26 diameters. Compute the proper diameter if G = 83
GPa.
a) 289.71 mm c) 273.21 mm
b) 352.08 mm d) 322.11 mm

21. As shown in the figure below, determine the reaction at B in kN.

a) 61.8 c) 80.5
b) 63.6 d) 71.9
22. As shown in the figure below, determine the moment (kN-m) at the point of the applied moment.

a) 36.1 c) 48.1
b) 10 d) 91.6
SITUATION (Item 23). The rigid pole and cross-arm assembly are shown in the figure, Determine the
components of tension in cable CD if the force acting on it is 2kN.

a) <1.07 -0.534 -1.603> c) <0 -0.534 1.603>

b) <-1.07 0.534 0> d) <-1.07 0.534 -1.603>

SITUATION (Item 24). Determine the moment of force in cable CD about the point O.
a) <6.414 0 -2.138> c) <2.138 6.414 0>
b) <0 6.414 -2.138 d) <6.414 2.318 0>

SITUATION (Item 25). A 20-kg uniform plate is held in position by cable AB as shown in the figure. If the
force in cable AB is 200N. Determine the combined moment about the x-axis.

a) 159.13N-m c) 68.67N-m
b) 21.79N-m d) 90.46N-m

SITUATION (Item 26). If the combined moment of the forces acting on the plate (weight and cable
tension) about the z-axis is zero. Determine the force acting on the cable.
a) 98.1N c) 195.2N
b) 170.8N d) 151.82N
27. _____________ of a force system is a force or a couple that will have the same effect to the body,
both in translation and rotation, if all the forces are removed and replaced by the resultant.
a) Resultant c) Component
b) Magnitude d) Direction

28. Three vectors A, B, and C are shown in the figure below. Find one vector (magnitude and direction)
that will have the same effect as three vectors shown.
 a) R=71.79 N at 139.85degrees c) R=71.79 N at 239.85degrees
b) R=81.79 N at 139.85degrees d) R=81.79 N at 239.85degrees

29. The forces which meet at one point and have their lines of action in different planes are called.
a) Non-coplanar concurrent forces c) Non-coplanar non-concurrent forces
b) Coplanar non-concurrent forces d) Intersecting forces

30. The ratio of driving tensions for flat belts, neglecting centrifugal tension, is (where T1, and T2 =
Tensions on the tight and slack sides of belt respectively, μ = Coefficient of friction, between the belt and
pulley, and θ = Angle of contact)
a) T1/T2= ln(μθ) c) T1/T2= μθ
b) T1/T2= log(μθ) d) T1/T2=e^(μθ)

31. The maximum bending moment due to a moving load on a simply supported beam, occurs
a) at the mid span c) under the load
b) at the supports d) anywhere on the beam

32. In a loaded beam, the point of contraflexure occurs at a section where

a) bending moment is minimum c) bending moment is maximum
b) bending moment is zero or changes d) shearing force is maximum
sign

33. If the shear force along a section of a beam is zero, the bending moment at that section is
a) zero c) minimum
b) maximum d) average of maximum-minimum

34. In the beam shown, determine the shear 3m from the left end.

a) 0 c) 50
b) 100 d) 125

35. Classify the structure shown if it is statically determinate, statically indeterminate or unstable.

a) statically determinate c) statically indeterminate to 6th degree

b) statically indeterminate to 9th degree d) unstable
36. The truss shown in the figure is supported by a parabolic cable, hinge at points C and E. Considering
the truss as pinned at D, determine the maximum tension in the cable.
a) 485.13 kN c) 398.05 kN

b) 420.11 kN d) 327.11 kN

37. For the truss shown, determine the maximum tensile force that my occur at member DG if the loads 2
kN (left) and 3 kN (right) will be passing through the truss. Consider the loads will move from left to right
and their distance with each other is 3 m.

a) 0.92 kN c) 1.42 kN
b) 1.88 kN d) 0.81 kN

SITUATION: (38 - 40) For the figure shown: If the compressive force on member AD is 12 kN. Which of
the following gives the nearest value of force F?

a) 40.25 c) 50.65
b) 29.60 d) 38.99

39. If the compressive force on member AD is 12 kN. Which of the following gives the nearest value of
compressive force on member BD?
a) 11.97 c) 15.85
b) 16.22 d) 18.65
40. If the compressive force on member AD is 12 kN. Which of the following gives the nearest value of
compressive force on member CD?
a) 22.92 c) 20.27
b) 16.88 d) 29.57

SITUATION: (41 - 42). Knowing that the tension on cable BD is 15 kN. Which of the following gives the
nearest value of tension at AC? The pole is supported by Ball and socket joint.

a) 25.22 c) 36.25
b) 10.18 d) 11.25

42. Determine the vertical reaction on the ball and socket support.
a) 27.64 c) 36.25
b) 15.90 d) 16.73

SITUATION: (43 - 45). Determine the stiffness of Spring, Steel and Brass assembly as shown.

a) 8256.25 c) 2563.23
b) 9141.75 d) 5632.20

44. Determine the Maximum Deflection Caused by the Impact of 50 kg mass.

a) 24.61 c) 23.39
b) 44.16 d) 29.80

45. Determine the Deflection at the interface of Brass and Steel.

a) 17.63 c) 15.23
b) 15.87 d) 29.80

SITUATION: (46 - 48). Determine the normal stress along z-direction on the steel block so that the strain
along z is zero. Use v=0.20.
 a) 50 c) 20
b) 25 d) 40

47. Determine the Strain along x-direction of the steel block.

a) 0.0003 c) 0.000225
b) 0.0052 d) 0.00056

48. Determine the Strain along y-direction of the steel block.

a) 0.00001 c) -0.000075
b) 0.2365 d) 0.000065

49. Determine the Volumetric Strain of the material shown, if E=100 GPa and v=0.25.

a) 0.0002 c) 0.0034
b) 0.0004 d) -0.0001

SITUATION: (50 - 51). A closed thin cylindrical tank with diameter D and thickness t is subjected to an
internal pressure p. Determine the axial stress that force F should developed, so that the in-plane
shearing stress in the lateral surface of the tank is zero at any angle θ is zero.

a) pD/8t c) pD/2t
b) pD/4t d) 0

51. An open ended thin cylindrical tank with diameter D and thickness t is subjected to an internal
pressure p. Determine the axial stress that force F should developed, so that the in-plane shearing stress
in the lateral surface of the tank is zero at any angle θ is zero.
a) pD/8t c) pD/2t
b) pD/4t d) 0

SITUATION: (52 - 53). Given L=200mm, W=150 mm, Given: σ_A=-2MPa; σ_B=-5MPa; σ_C=-8MPa.
Determine the value of ey.
a) 7.5mm c) 2.5mm
b) 3.2mm d) 1.5mm

53. Determine the normal stress at point D.

a) -2MPa c) -5MPa
b) -8MPa d) 0

SITUATION (54 - 56). A 5m steel beam carries a concentrated live load P at the midspan and a uniformly
distributed deadload of 15kN/m acting all throughout the beam. Determine the maximum deflection due
to deadload.
a) 134.70 c) 155.05
b) 122.07 d) 234.56

55. Determine the required moment of inertia to not exceed the deflection due to dead load to 16mm.
 a) 38.15 c) 38.15x10^5
b) 38.15x10^4 d) 38.15x10^6

56. Determine the value of P so that the deflection due to live load and deflection due to dead load is
equal.
a) 46.88 c) 43.44
b) 137.67 d) 23.78

57. For the beam shown, determine the reaction at B.

a) 40.233 c) 37.125
b) 38.735 d) 36.982

58. If each box weighs 150 lb, determine the least horizontal force P that the man must exert on the top
box in order to cause motion. The coefficient of static friction between the boxes is 0.65, and the
coefficient of static friction between the box and the floor is 0.35.

a) 90 lb c) 80 lb
b) 95 lb d) 85 lb

59. Determine the smallest horizontal force P required to lift the 200 kg crate. The coefficient of static
friction at all contacting surfaces is 0.3. Neglect the mass of the wedge.

a) 1878.37 N c) 1979.37 N
b) 1978.37 N d) 1778.37 N
60. Determine the moment of inertia of the beam's cross-sectional area about the x-axis.

a) 115.35 x 10^6 mm^4 c) 114.62 x 10^6 mm^4

b) 113.45 x 10^6 mm^4 d) 115 x 10^6 mm^4

SITUATION (61-64). A beam with a span of 15 m is supported by a hinge at the left end and a roller 3 m
from the right end. The beam is to support a uniform highway load of 5 kN/m and a concentrated moving
load of 10 kN. Let C be a point 6 m from the left support. Determine the length of the beam that needs to
be loaded to produce the maximum shear at C.
a) 3 m c) 9 m
b) 6 m d) 12 m

62. What is the value of the maximum positive shear at C?

a) 10 kN c) 12.50 kN
b) 8 kN d) 7.5 kN

63. Determine the length of the beam that needs to be loaded to produce the maximum bending moment
at C.
a) 3 m c) 9 m
b) 6 m d) 12 m

64. What is the maximum bending moment at C?

a) 90 kN-m c) 110 kN-m
b) 100 kN-m d) 120 kN-m

65. It represents the variation of either the reaction, shear, moment, or deflection at a specific point in a
member as a concentrated force moves over the member.
a) Shear and Moment Diagram
b) Moving Load Diagram
c) Response Spectrum
d) Influence Line