PRACTICE PROBLEMS

Stuctural Engineering
ENGINEERING MECHANICS - STATICS
INSTRUCTION: Select the correct answer for each of the following
questions. Mark only one answer for each item by shading the box
corresponding to the letter of your choice on the answer sheet provided.
STRICTLY NO ERASURES ALLOWED. Use pencil no. 1 only.
MULTIPLE CHOICE
Situation 1:

Given that F1 = 600 N and = 30. See figure MECH

5.1.

8.

9.

How many are zero force members?

a.
5
c.
b.
4
d.
How many are two force members?
a.
19
c.
b.
20
d.

Situation 5:

1.

Which of the following most nearly gives the magnitude of the

resultant force acting on the eyebolt?
a.
750 N
c.
662 N
b.
630 N
d.
702 N

2.

Which of the following most nearly gives the direction of the

resultant force measured clockwise from the positive x axis?
a.
37.5
c.
24.4
b.
44.6
d.
53.0

Situation 2:

The force R is the resultant of the forces F1, F2 and

F3 acting on the rectangular plate. See figure SSDH
55.56.

10.

11.

13.
3.

Find F1 if = 30, R = 40 kN and F3 = 20 kN.

a.
24.78kN
c.
66.71kN
b.
73.44kN
d.
58.03kN

4.

Find F2.
a.
b.

Situation 3:

c.
d.

Given is the truss as shown in figure YUHK 33.

7
6

How many are load-carrying members?

a.
13
c.
b.
11
d.

10
12

Given is the truss as shown in figure ZGE 9.1.

How many are zero force members?

a.
5
c.
b.
4
d.

7
6

How many are load-carrying members?

a.
15
c.
b.
14
d.

17
16

Situation 7:
33.03kN
50.86kN

21
22

How many are zero force members?

a.
5
c.
b.
4
d.

Situation 6:

12.

7
6

The cantilever truss is loaded. See figure XCBE

99.99.

49.67kN
0.29kN

Resolve F1 and F2 into components along the u and v

axes. See figure MECH 4.8.

14.

Which of the following gives the reaction at E?

a.
85 kN
c.
70 kN
b.
60 kN
d.
65 kN

5.

Which of the following gives the component of F1 along u axis?

a.
386 N
c.
150 N
b.
260 N
d.
283 N

15.

Which of the following gives the force in member CD?

a.
57.7 kN
c.
63.5kN
b.
45.9 kN
d.
34.6 kN

6.

Which of the following gives the component of F1 along v axis?

a.
283 N
c.
260 N
b.
150 N
d.
386 N

16.

Which of the following gives the force in member BD?

a.
63.5kN
c.
57.7 kN
b.
34.6 kN
d.
45.9 KN

7.

Which of the following gives the component of F2 along u axis?

a.
260 N
c.
283 N
b.
386 N
d.
150 N

Situation 8:

Situation 4:

For the given truss, P = 3000 N and Q = 1000 N. See

figure MECH 6.81.

Given is a truss. See figure STRD 10.22.

Erickneil D. Realuyo

PRACTICE PROBLEMS
Stuctural Engineering

Situation 12:

17.

Which of the following gives the force in member CD?

a.
5.25 kN
c.
5.75 kN
b.
6.50 kN
d.
6.00 kN

18.

Which of the following gives the force in member JK?

a.
3.00 kN
c.
2.25 kN
b.
3.25 kN
d.
2.50 kN

Situation 9:

19.

20.

21.

For the given truss. See figure SAM 11.04.

15 kN
10 kN

Determine the horizontal reaction at F.

a.
32.3 kN
c.
b.
22.5 kN
d.

25.7 kN
30.1 kN

Determine the axial force in member BC.

a.
12.8 kN
c.
b.
6.0 kN
d.

18.8 kN
7.2 Kn

Situation 10:

Determine the required weight of block D for equilibrium.

a.
200 N
c.
175 N
b.
190 N
d.
230 N

23.

for
for equilibrium.
equilibrium.
Determine the required angle
a.
74.1
c.
72.8
b.
64.3
d.
67.5

24.

25.

26.

Which of the following most nearly gives the vertical reaction at

A?
a.
324 kN
c.
216 kN
b.
432 kN
d.
108 kN

28.

Which of the following most nearly gives the tension in the cable
at midspan?
a.
432 kN
c.
324 kN
b.
108 kN
d.
216 kN

29.

If the allowable tension in the cable is 320 kN, which of the

following most nearly gives the sag at midspan?
a.
4.88 m
c.
4.30 m
b.
5.49 m
d.
5.17 m
A cable weighing 50 N/m of length is suspended.
With the small sag-to-span ratio, approximation as a
parabolic cable maybe used. See figure MECH 7.0.

Block B weighs 200 N and block C weighs 100 N.

See figure MECH 8.89.

22.

Situation 11:

27.

Situation 13:

Determine the vertical reaction at A.

a.
14 kN
c.
b.
11 kN
d.

The suspended girder shown in figure DDFU 099 is

supported by a series of hangers, equally spaced
along a parabolic cable.

30.

Which of the following most nearly gives the horizontal distance

of the lowest point of the cable to A?
a.
33.12 m
c.
22.79 m
b.
18.51 m
d.
27.82 m

31.

Which of the following most nearly gives the tension of the cable
at A?
a.
1838 N
c.
1139 N
b.
1442 N
d.
2102 N

32.

Which of the following most nearly gives the tension of the cable
at a point 10 m (horizontal) from B?
a.
1475 N
c.
1361 N
b.
1983 N
d.
2081 N

Situation 14:

The 36-m cable weighs 1.5 kN/m. See figure MECH

8.8.

A cable is subjected to concentrated loads at B and

C. See figure MECH 7.77.

Compute the axial love in segment CD.

a.
2023 N
c.
b.
2961 N
d.

2334 N
2556 N

Compute the value of 2.

a.
19.08
b.
33.05

52.61
49.78

33.

37.25 m
32.42 m

34.

c.
d.

Compute the total length of the cable.

a.
21.72 m
c.
b.
29.48 m
d.

Determine the sag H.

a.
8.77 m
b.
9.11 m

c.
d.

7.32 m
6.81 m

Determine the maximum tension on the cable.

a.
37.5 kN
c.
34.3 kN
b.
28.1 kN
d.
24.6 kN

Erickneil D. Realuyo

PRACTICE PROBLEMS
Stuctural Engineering
Situation 15:

A 200 N-block is being pushed by a force P. See

figure EMM 33.05.

35.

What is the value of the friction force if P = 20 N?

a.
20 N
c.
60 N
b.
40 N
d.
50 N

36.

What is the value of the friction force if P = 50 N?

a.
20 N
c.
60 N
b.
40 N
d.
50 N

37.

What is the value of the friction force if P = 70 N?

a.
90 N
c.
40 N
b.
60 N
d.
70 N

38.

What is the value of the friction force if P = 90 N?

a.
90 N
c.
40 N
b.
60 N
d.
70 N

Situation 16:

Situation 19:

The weight of the cylindrical tank is negligible in

comparison to the weight of water it contains (density
of water= 1000 kg/m3). The coefficient of static
friction between the tank and the horizontal surface is
s. Take the radius of the cylinder equal to 0.8 m.
See figure MECH 4.51.

A 500 N block is resting on an inclined plane. See

figure EMM 11.06.

39.

Find the minimum value of P necessary to have an impending

motion if = 30.
a.
163.4 N
c.
129.9 N
b.
120.1 N
d.
86,6 N

47.

Assuming a full tank, find the smallest force Q required to tip the
tank.
a.
13.93 kN
c.
10.20 kN
b.
16.55 kN
d.
18.22 kN

40.

Find the maximum value of P necessary to have an impending

motion if = 30.
a.
336.6 N
c.
379.9 N
b.
351.3 N
d.
391.6 N

48.

Assuming a full tank, find the smallest s that would allow tipping
to take place.
a.
0.204
c.
0.315
b.
0.267
d.
0.231

41.

Find the value of P that will still make the block in equilibrium
condition.
a.
382 N
c.
110 N
b.
71 N
d.
279 N

49.

If the force Q = 1000 N initiates tipping, determine the depth of

water in the tank.
a.
164.7 mm
c.
215.3 mm
b.
201.2 mm
d.
151.7 mm

50.

xed cylinders
cylinders carries
carries the
the 44-kg
The rope running over two xed
-kg mass
at one end. Determine the force P that must be applied to the
other end to initiate motion. The coefficient of static friction
between the rope and the cylinders is 0.15.

Situation 17:

The Coefficient of friction for all contact surfaces is

0.15. The weight of blocks A and B are 250 N and
125 N, respectively.

42.

Determine the force F necessary to cause an upward impending

motion of block A.
a.
146.47 N
c.
112.50 N
b.
127.72 N
d.
167.33 N

43.

Determine the force F necessary to cause a downward

impending motion of block A.
a.
30.97 N
c.
25.71 N
b.
52.80 N
d.
49.72 N

Situation 18:

a.
b.
Situation 20:

The masses of A, B and C are 10 kg, 15kg and 70

kg, respectively. Use s = 0.35 for all contacts. See
figure MECH 1.1.

44.

Calculate the normal force exerted by the horizontal plane to

block B if block C is to move upward.
a.
1424.6 N
c.
357.1 N
b.
498.6 N
d.
1509.4 N

45.

Calculate the normal force exerted by the wall to block A if block

C is to move upward.
a.
953.3 N
c.
314.9 N
b.
212.7 N
d.
899.7 N

46.

Calculate the force P required to start block C to move upward.

a.
807.6 N
c.
955.0 N
b.
731.2 N
d.
1076.4 N
51.

52.

64.1 N
37.5 N

c.
d.

55.2 N
42.9 N

An 80-N box X is placed on a folding table. Neglect

friction and the weights of the members. determine
all forces acting on member EFG and the tension in
the cable connecting points B and D.

Calculate the normal force acting at G.

a.
50 N
c.
b.
60 N
d.

70 N
80 N

Calculate the reaction at E.

a.
33.50 N

114.27 N

c.

Erickneil D. Realuyo

PRACTICE PROBLEMS
Stuctural Engineering
b.
53.

111.12 N

d.

26.67 N
60.

Calculate the change in length a if initially, a = 300 mm, b = 150

mm and c = 200 mm.
a.
1.054 mm
c.
0.75 mm
b.
1.429 mm
d.
2.107 mm

61.

Calculate the change in length of the space diagonal.

a.
0.37 mm
c.
0.78 mm
b.
0.81 mm
d.
0.43 mm

62.

Calculate the volumetric strain.

a.
0.0011
b.
1.0152

Calculate the tension in the cable connecting points B and D.

a.
24.5 N
c.
20.0 N
b.
18.5 N
d.
22.2 N

Situation 21:

The uniform cylinder has a mass of 150 kg. Neglect

friction and the weight of bar AB.

Situation 24:

54.

55.

56.

Determine the normal force at C.

a.
1920.91 N
c.
b.
1477.99 N
d.

1373.13 N
1234.74 N

Determine the tension in the cable at B.

a.
1477.99 N
c.
b.
1234.74 N
d.

1373.13 N
1920.91 N

Determine the reaction at A.

a.
1477.99 N
b.
1920.91 N

1234.74 N
1373.13 N

Situation 22:

c.
d.

The welded tubular frame is secured to the horizontal

x-y plane by a ball-and-socket joint at A and receives
support from the loose-fitting ring at B. Under the
action of the 2-kN load, rotation about a line from A
to B is prevented by the cable CD, and the frame is
stable in the position shown in figure SA - 0211.
Neglect the weight of the frame.

63.

Determine the tension T in the cable CD.

a.
4.08kN
c.
b.
3.64kN
d.

Determine the reaction at B is support B allows translation in ydirection.

a.
4.08 kN
c.
2.83 kN
b.
3.64 kN
d.
1.25 kN

59.

Determine the reaction at A.

a.
4.08 kN
b.
3.64 kN

Situation 23:

c.
d.

2.83 kN
1.25 kN

A cube is subjected to the following forces as shown.

Fx = 10,000 kN, Fy = 20,000 kN and Fz = 5,000 kN.
Fx, Fy and Fz are forces parallel to axes x, y and z,
respectively. Use Poissons ratio of 0.3 and Youngs
modulus of 70 GPa.

4802.21 N mm
2814.25 N mm

64.

Determine the x component of the resultant couple.

a.
1197.79 N mm
c.
2814.25 N mm
b.
4802.21 N mm
d.
3185.75 N mm

65.

Determine the magnitude of the resultant couple.

a.
6288.50 N mm
c.
8152.66 N mm
b.
9944.27 N mm
d.
7133.43 N mm
A propped beam is subjected to a linearly varying
load of 60 kN/m at the fixed end and zero at the other
end. The beam has a length of 10 m and a
trapezoidal section with upper base of 300 mm, lower
base of 400 mm and a depth of 500 mm.

66.

Which of the following most nearly gives the maximum flexural

stress at the section where the maximum positive moment is
acting?
a.
12.94 MPa
c.
28.93 MPa
b.
26,30 MPa
d.
11.76 MPa

67.

Which of the following most nearly gives the maximum flexural

stress at the section where the maximum negative moment is
acting?
a.
12.94 MPa
c.
28.93 MPa
b.
26,30 MPa
d.
11.76 MPa

68.

Which of the following most nearly gives the maximum tensile

stress at the section where the maximum negative moment is
acting?
a.
12.94 MPa
c.
28.93 MPa
b.
26,30 MPa
d.
11.76 MPa

2.83kN
1.25kN

58.

1.0011
0.0152

The gear box is subjected to the three couples as

shown. Given that C1 = 6000 N -mm, C2 = 4200 N mm, and C3 = 6600 N -mm.

Determine the x component of C3.

a.
1197.79N mm
c.
b.
3185.75 N mm
d.

Situation 25:

57.

c.
d.

Situation 26:

A steel rod having a length of 50 m is suspended

vertically from one end. It supports a tensile load of
250 kN at the lower end. The unit weight of the steel
3
is 7,850 kg/m . The allowable tensile stress for steel
is 140 MPa. Use E = 200 GPa.

69.

Which of the following most nearly gives the required diameter of

the steel rod if its allowable stress is not exceeded?
a.
48.35 mm
c.
52.03 mm
b.
47.68 mm
d.
50.19 mm

70.

Using the value obtained in the previous problem, which of the

following most nearly gives the deformation caused by the
applied load?
a.
31.59 mm
c.
34.04 mm
b.
29.40 mm
d.
35.00 mm

71.

Which of the following most nearly gives the total deformation of

the steel rod?
a.
34.52 mm
c.
32.07 mm
b.
35.48 mm
d.
29.88 mm

Situation 27:

72.

A solid circular pole has a height of 3 m and a

diameter of 250 mm. The pole carries a compressive
load of 3 kN at an eccentricity of 100 mm and a
lateral force of 0.45 kN at its top. The unit weight of
the pole is 22kN/m3.

Which of the following most nearly gives the maximum

compressive stress at the base of the pole?
a.
0.95 MPa
c.
1.03 MPa
b.
1.20 MPa
d.
1.14 MPa

Erickneil D. Realuyo

PRACTICE PROBLEMS
Stuctural Engineering
73.

Which of the following most nearly gives the maximum tensile

stress at the base of the pole?
a.
1.03 MPa
c.
1.14 MPa
b.
0.95 MPa
d.
1.20 MPa

74.

Which of the following most nearly gives the maximum shearing

stress at the base of the pole?
a.
9.17 kPa
c.
13.75 kPa
b.
11.38 MPa
d.
12.22 kPa

75.

Six steel cables support a circular moulding of diameter 2 m. The

cables are spaced equally along the perimeter of the moulding.
The moulding weighs 2.50kN/m and is attached at a point 3 m
above its center. If the allowable stress of each cable is 124
MPa, which of the following most nearly gives the minimum
diameter of each cable?
a.
5.12 mm
c.
5.24 mm
b.
5.32 mm
d.
5.19 mm

76.

A hollow circular tube has an outer diameter of 75 mm and a wall

thickness of 5mm. It is supported at one end and carries a torque
of 3 kN-m at its free end. Which of the following most nearly
gives the shearing stress in the tube?
a.
85.07 MPa
c.
72.49 MPa
b.
79.51 MPa
d.
83.10 MPa

77.

A simple beam 6 m long weighs 3.75 kN/m. If the cracking

moment of the beam is35.20 kN-m, which of the following most
nearly gives the additional uniformly distributed load that it can
carry?
a.
2.55 kN/m
c.
6.30 kN/m
b.
4.07 kN/m
d.
7.82 kN/m

78.

A cantilever beam 2.80 m long carries a uniformly distributed

load of 10 kN/m and a concentrated load of 25 kN at a point 2 m
from the support. Which of the following most nearly gives the
moment at the support?
a.
82.09 kN-m
c.
89.20 kN-m
b.
82.90 kN-m
d.
80.92 kN-m

79.

A 12-m long beam is simply supported at the right end and at 3

m from the left end. The beam is subjected to a uniformly
distributed moving load. Which of the following most nearly gives
the length of the beam over which the uniformly distributed load
could be placed to produce maximum negative moment at
midspan?
a.
7.50 m
c.
3.00 m
b.
4.50 m
d.
9.00 m

80.

Within the elastic region, the stress is directly proportional to the

strain.
a.
Youngs modulus
b.
Poissons ratio
c.
St. Venants Principle
d.
Hookes Law

81.

In the deformation of axially loaded members, it is the ratio of the

lateral strain to the longitudinal strain.
a.
St. Venantss Principle c.
Elastic limit
b.
Poissons ratio
d.
Youngs modulus

82.

Within the elastic range, it is the constant of proportionality that

defines the linear relationship between stress and strain.
a.
St. Venantss Principle c.
Elastic limit
b.
Poissons ratio
d.
Youngs modulus

83.

An iron column of annular cross-section has an outer diameter of

200 mm and is subjected to a force of 75 kN. Find the thickness
of the wall if the allowable compressive stress is 10 MPa.
a.
12.57 mm
c.
15.75 mm
b.
12.75 mm
d.
17.75 mm

84.

A 25-m long 10-mm in diameter steel rod is suspended at its top

end and supports an 8-kN load at the other end. The unit weight
3
of the steel is 77 kN/m . Which of the following most nearly gives
the total elongation of the steel rod?
a.
12.94 mm
c.
12.85 mm
b.
12.60 mm
d.
12.73 mm

85.

Which of the following deals with forces at rest?

a.
dynamics
c.
statics
b.
kinetics
d.
kinematics

86.

Which of the following is the force which determines whether the

body will remain in equilibrium or will have a varying state of
motion?
a.
impulse
c.
equilibrant
b.
weight
d.
resultant

87.

Which of the following is the retarding force acting opposite a

body in motion?
a.
drag force
c.
static friction
b.
inertia
d.
kinetic friction

88.

Which structural member has a ratio of its unsupported length to

its least lateral dimension of not less than 3 and is used primarily
to carry axial loads?
a.
pedestal
c.
column
b.
beam
d.
corbel

Erickneil D. Realuyo