Structural Engineering

November and Construction

2013
Situation 1 – A student pushes the 600-N ladder horizontally as shown in the
Figure in order to prevent it from sliding.
1. Determine the vertical reaction at A.
A. 800 N C. 600 N
B. 400 N D. 550 N
2. Determine the horizontal reaction at A.
A. 110 N C. 160 N
B. 120 N D. 80 N
3. Determine the pushing force exerted by the student.
A. 532.8 N C. 487.9 N
B. 635.7 N D. 596.3 N

Situation 2 – The crane shown in the Figure carries the 35 kN load at B. The crane
weighs 8 kN.

Structural Engineering
November and Construction
2013
 4. What is the tension in cable AD?
A. 30.12 kN C. 32.65 kN
B. 35.69 kN D. 26.52 kN
5. What is the total reaction at C?
A. 56 kN C. 23.11 kN
B. 68 kN D. 60.58 kN
6. If the tension of cable AD is limited to 42 kN, what is the maximum value of the
load W?
A. 52.17 kN C. 57.77 kN
B. 65.85 kN D. 55.24 kN

Situation 3 – The parabolic cable supports the truss shown in the Figure. The truss
is pinned at D.
7. What is the tension at F where the tangent is zero?
A. 487.5 kN C. 386.7 kN
B. 528.7 kN D. 504.3 kN
8. What is the vertical reaction at pin D?
A. 48.87 kN C. 41.56 kN
B. 56.21 kN D. 37.47 kN
9. What is the vertical reaction at A?
A. 92.48 kN C. 74.96 kN
B. 97.73 kN D. 84.24 kN

Situation 4 – The pole GAF shown in the Figure is secure by a ball-and-socket joint
at F and by four steel wires at A. The diameter of steel wires is 6.5 mm. use E = 200
GPa for steel.
10.If P = 2 kN, what is the tensile stress in wire AD?
A. 142 MPa C. 178 MPa
B. 107 MPa D. 125 MPa
11.If P = 2 kN, what is the elongation of wire AD?
A. 15.07 mm C. 12.05 mm
B. 9.04 mm D. 10.24 mm

Structural Engineering
November and Construction
2013
 12.If the elongation of wire AD is 22 mm, by how much will point G, the tip of the
pole, move horizontally?
A. 51.9 mm C. 63.8 mm
B. 58.7 mm D. 47.5 mm

Situation 5 – The homogeneous stick shown in the Figure weighs 8 N. End “A” leans
against a vertical wall and end “B” is supported by a ball-and-socket joint. Neglect
all friction.

Structural Engineering
November and Construction
2013
13.Determine the value of P.
A. 3.2 N C. 1.9 N
 B. 2.5 N D. 2.8 N
14.Determine the reaction at A.
A. 2.56 N C. 1.97 N
B. 1.71 N D. 1.25 N
15.Determine the total reaction at B.
A. 6.63 N C. 5.24 N
B. 7.54 N D. 8.62 N

Situation 6 – The homogeneous boom AC

shown in the Figure weighs 35 kN and is
supported by a ball-and-socket joint at C
and two cables AD and AB.
16.What is the tension in cable AB?
A. 11.32 kN
B. 12.58 kN
C. 26.13 kN
D. 30.54 kN
17.What is the tension in cable AD?
A. 30.54 kN C. 12.58 kN
B. 26.13 kN D. 11.32 kN
18.What is the total reaction at C?
A. 68.57 kN C. 65.91 kN
B. 70.48 kN D. 73.58 kN

Situation 7 – The beam shown in the Figure is supported by two 16-mm-diameter

bolts at A and a 150 mm x 200 mm plate at B.

19.If P = 9 kN, what is the stress in the bolts at point A?

A. 37.30 MPa C. 55.95 MPa
B. 98.75 MPa D. 42.68 MPa
20.If P = 9 kN, what is the bearing stress in concrete at B?
A. 1.26 MPa C. 0.70 MPa
B. 11.05 MPa D. 0.87 MPa
21.If the allowable tensile stress of the bolts at A is 40 MPa, what is the maximum
value of P?
22.Structural Engineering
November 23.and Construction
2013
A. 6.434 kN C. 8.552 kN
B. 7.242 kN D. 6.874 kN
Situation 8 – The bolt shown in Figure S56-331 is
subjected to a total tensile force of 90 kN.
24.Determine the tensile stress in the body of
the bolt in MPa.
A. 70.54
B. 88.17
C. 79.36
D. 61.72
25.Determine the tensile stress at the root of the
bolt in MPa.
A. 87.1
B. 111.9
C. 99.5
D. 124.3
26.Determine the compressive stress at the head
as the bolt bears on the surface to resist the
tensile load.
A. 40.33 MPa C. 45.37 MPa
B. 50.41 MPa D. 35.29 MPa

Situation 9 – The beam shown in the Figure is

supported by the seat angle. The angle is fastened
to the column by two 16-mm-diameter bolts. The
beam reaction is 42 kN.
27.What is the bearing stress on contact surface
between the bolts and the angle?
A. 96.3 MPa
B. 87.5 MPa
C. 81.4 MPa
D. 101.7 MPa
28.What is the shearing stress in the bolts?
A. 126.3 MPa C. 115.6 MPa
B. 92.5 MPa D. 104.4 MPa
29.What is the bearing stress on contact surface between the beam and the
angle?
A. 2.41 MPa C. 2.92 MPa
B. 4.58 MPa D. 3.24 MPa

Structural Engineering
November and Construction
2013
Situation 10 – The strut shown in the Figure carries an axial load of P = 85 kN.
 30.Determine the bearing stress between
the pin and strut:
A. 265.6 MPa
B. 242.8 MPa
C. 278.4 MPa
D. 296.2 MPa
31.Determine the shearing stress in the pin.
A. 236.9 MPa
B. 195.8 MPa
C. 224.7 MPa
D. 211.4 MPa
32.Determine the shearing stress in the
bolts.
A. 85.7 MPa
B. 96.3 MPa
C. 91.5 MPa
D. 103.5 MPa

Situation 11 – A gravity dam is acted upon

by the forces (per meter length) shown in the
Figure. For this problem, F1 = 275 kN, F2 = 600
kN, F3 = 165 kN, a = 1.8 m, b = 2, c = 1.2 m,
angle θ = 60°.
33.Calculate the maximum foundation
pressure.
A. 196.5 kPa
B. 185.3 kPa
C. 154.2 kPa
D. 174.5 kPa
34.Calculate the minimum foundation pressure.
A. 82.4 kPa C. 87.7
kPa
B. 76.8 kPa D. 96.5 kPa
35.If the coefficient of friction between the base and the soil is 0.35, what is the
factor of safety against sliding?
A. 1.31 C. 2.15
B. 1.81 D. 1.63
36.A hallow circular shaft 2 m long is fixed at one end and free at the other end.
The outer diameter of the shaft is 300 mm and its thickness is 6 mm. If the
shaft is subjected to a torsional moment of 6 kN-m determine the angle of twist
of the shaft. Use G = 78 GPa.
A. 0.0736° C. 0.0214°
B. 0.0526° D. 0.0128°

Situation 12 – A solid circular shaft 2.5 long and 75 mm in diameter is subjected to

torsional moment. Use G = 78 GPa.
 37.Calculate the torsional rigidity of the shaft.
A. 224.8 kN-m2 C. 263.7 kN-m2
2
B. 242.3 kN-m D. 254.7 kN-m2
38.Calculate the torsional stiffness of the shaft.
A. 90.54 kN-m/rad C. 104.57 kN-m/rad
B. 96.92 kN-m/rad D. 85.63 kN-m/rad
39.Calculate the maximum shearing stress on the shaft due to a 3 kN-m torque at
its free end.
A. 30.58 MPa C. 42.54 MPa
B. 34.58 MPa D. 36.22 MPa

Situation 13 – The state of stress of

the material is illustrated by the Mohr
Circle shown in the Figure.
40.What is the maximum normal
stress, σx?
A. 120 MPa
B. 40 MPa
C. 110 MPa
D. 80 MPa
41.What is the minimum normal
stress, σy?
A. 40 MPa
B. 30 MPa
C. 80 MPa
D. 50 MPa
42.Calculate the maximum shearing
stress.
A. 50 MPa
B. 20 MPa
C. 30 MPa
D. 40 MPa

Situation 14 – An element is subjected to a pure shearing stress as shown in the

Figure.
43.What is the normal axial stress on the element?
A. 40 MPa C. 120 MPa
B. 80 MPa D. 0
44.What is the shearing stress on the element?
A. 80 MPa C. 120 MPa
B. 0 D. 40 MPa
45.What is the angle of the plane of maximum shear from the principal plane?
A. 45° C. 90°
B. 30° D. 60°
Situation 15
– The hallow pole shown in the Figure has an outside
diameter of 300 mm thickness of 6 mm. The pole
weighs 150 N per linear meter.
46.What is the maximum compressive stress at the
base?
A. 5.24 MPa
B. 4.75 MPa
C. 3.65 MPa
D. 6.87 MPa
47.What is the maximum tensile stress at the base?
A. 4.36 MPa
B. 2.87 MPa
C. 2.45 MPa
D. 3.51 MPa
48.What is the maximum shearing stress in the
pole?
A. 0.162 MPa C. 0.554 MPa
B. 0.324 MPa D. 0.287 MPa

Situation 16 – The concrete pad shown in Figure C05-563 is subjected to uniform

loads.
49.Determine the base pressure.
A. 96 kN/m C. 192 kN/m
B. 104 kN/m D. 128 kN/m
50.Determine the maximum moment in the slab.
A. 436 kN-m C. 336 kN-m
B. 384 kN-m D. 192 kN-m
51.Determine the location of zero bending moment measured from the left end of
the slab.
A. 5 m C. 4 m
B. 7 m D. 6 m
Situation 17 – The barge shown in the Figure supports the loads w 1 and w2 for this
problem, w1 = 145 kN/m, w = 290 kN/m, L1 = 3 m, L2 = 3 m.
52.What is the length of the barge “L” so that the upward pressure is uniform?
A. 15 m C. 20 m
B. 12 m D. 18 m
53.What is the shear at 3 m from the left end?
A. -162 kN C. -194 kN
B. -151 kN D. -174 kN
54.At what distance from the left end will the shear in the barge be zero?
A. 4 m C. 5 m
B. 5.5 m D. 4.5 m

Situation 18 – The semi-circular arch is

loaded as shown in the Figure. For this
problem, P1 = 1.8 kN, P2 = 0.90 kN, and P3
= 0.45 kN.
55.What is the resultant of the three
forces?
A. 2.04 kN
B. 3.12 kN
C. 2.85 kN
D. 2.46 kN

56.Determine the reaction at B.

 A. 1.75 kN C. 1.06 kN
B. 1.63 kN D. 1.24 kN
57.Determine the reaction at A.
A. 1.06 kN C. 1.63 kN
B. 1.75 kN D. 1.24 kN

58.A 6 m long timber beam 220 mm wide by 400 mm deep is simply supported at
its ends and carries a uniformly distributed load throughout its length. If the
allowable deflection is L/360, find w. Use E = 9.5 GPa.
A. 14 kN/m C. 12 kN/m
B. 13 kN/m D. 11 kN/m

59.A 10-meter long beam is simply supported at the right end and at 2 meters
from the left end. It is required to determine the maximum shear at the middle
of the supported length due to a uniformly distributed moving load. What is the
total length of the beam that must be subjected by the uniform load?
A. 4 m C. 3 m
B. 6 m D. 5 m

Situation 19 – Classify the structures shown in Figure 346-23 as stable, unstable,

determinate or indeterminate. If indeterminate, state the degree of indeterminacy.
60.Figure 346-23a is:
A. Indeterminate to the second degree
B. Unstable
C. Determinate
D. Indeterminate to the first degree
61.Figure 346-23b is:
A. Indeterminate to the second degree
B. Indeterminate to the third degree
C. Unstable
D. Indeterminate to the first degree
62.Figure 346-23c is:
A. Indeterminate to the third degree
B. Unstable
C. Indeterminate to the first degree
D. Indeterminate to the second degree
Situation 20 – The floor framing plan of a commercial building is shown in the
Figure. When the columns at E and H are deleted, beam BEHK becomes a single-
span girder which can be assumed fixed at B and K. The concentrated load on girder
BEHK at E and H are each 272 kN and the uniform load on the entire span is 5 kN/m.

63. Determine
the shear at B.
A. 300.75 kN C. 290.75 kN
B. 325.45 kN D. 280.50 kN
64.Determine the maximum shear at E.
A. 278.25 kN-m C. 245.75 kN-m
B. 296.34 kN-m D. 260.78 kN-m
65.What is the maximum positive moment in the beam?
A. 204.7 kN-m C. 268.7 kN-m
B. 198.5 kN-m D. 238.4 kN-m
Situation 21 – The steel truss shown in the Figure is loaded with three
concentrated loads applied at B, D, and F. Use F y = 248 MPa and E= 200 GPa.
66.Determine the reaction at G.
A. 14 kN C. 26 kN
B. 27 kN D. 21 kN
67.What is the axial stress in the member DI?
A. 4.53 MPa C. 5.28 MPa
B. 6.24 MPa D. 7.32 MPa
68.What is the allowable load of member DI? Given the following properties of DI:
Area = 1858 mm2, rx = 26.7 mm, ry = 34 mm.
A. 98.5 kN C. 112.5 kN
B. 104.9 kN D. 126.4 kN

Situation 22 – The entrance of a building has a roof that supports the load “w’ as
shown in the Figure. The supports at A and B can be considered hinge. The column
AC is fixed at C.
Properties of AC:
L = 445 x 106 mm2 d = 466.10 mm
2
A = 11,355 mm E = 200 GPa
rx = 190.11 mm Fy = 248 MPa
ry = 43.02 mm
69.Compute the allowable axial load on member AC. Use 2001 NSCP.
A. 1156 kN C. 1039 kN
B. 952 kN D. 1234 kN
70.If the allowable load on AC is 900 kN, compute the value of w.
A. 144 kN/m C. 120 kN/m
B. 136 kN/m D. 112 kN/m
71.If the load w = 112 kN/m, compute for the load on AC.
A. 800 kN C. 700 kN
B. 850 kN D. 750 kN
Situation 23 – The deck of a bridge consist of ribbed metal deck with 100 mm
concrete slab on top (See Figure 16-19). The superstructure supporting the deck is
made of wide flange steel beams strengthened by cover plate 16 mm x 275 mm
one at the top and one at the bottom, and is spaced 1.2 m on centers. The beams
are simple supported over a span of 25 m. The loads on each beam are as follows:

Dead load = 12 kN/m (including beam weight and deck)

Wheel live loads:
Front wheel = 17.8 kN
Rear wheel = 71.2 kN
Wheel base = 4.75 m
15
Impact factor = ≤ 30%, where L = length in m.
L+37
Properties of W 850 x 185:
A = 23,750 tw = 15 mm
d = 850 mm lx = 2662 x 106 mm4
bf = 290 mm ly = 81.52 x 106 mm4
tf = 20mm

72.Calculate the maximum bending stress in the beam due to dead load.
A. 90.25 MPa C. 98.66 MPa
B. 88.45 MPa D. 95.86 MPa
73.Calculate the maximum bending stress in the beam due to live load plus
impact.
A. 60.2 MPa C. 72.5 MPa
B. 86.3 MPa D. 65.4 MPa
74.Calculate the maximum average web shear stress in the beam due to live load
plus impact.
A. 7.54 MPa C. 8.34 MPa
 B. 10.21 MPa D. 9.32 MPa

Situation 24 – Channel sections are used as a purlin. The top chords of the truss
are sloped at 4H to 1V. The trusses are spaced 6 m on centers and the purlins are
spaced 1.2 m on centers.

Loads:
Dead load = 550 Pa
Live load = 720 Pa
Wind load = 1440 Pa
Wind coefficients:
Windward = 0.2
Leeward = 0.6

Properties of C200 x 76
Sx = 6.19 x 104 mm3
Sy = 1.38 x 104 mm3
Weight, w = 79 kN/m
Allowable bending stresses, Fbx = Fby = 207 MPa

75.Determine the computed bending stress, fbx, due to combination of dead and
live loads only.
A. 196 MPa C. 113 MPa
B. 176 MPa D. 151 MPa
76.Determine the computed bending stress, fby, due to combination of dead and
live loads only.
A. 169 MPa C. 143 MPa
B. 127 MPa D. 103 MPa
77.Determine the value of the interaction equation using the load combination of
0.75 (D + L + W) at the windward side.
A. 0.96 C. 1.25
B. 1.59 D. 1.87
Situation 25 – The section of a solid
concrete beam is shown in the Figure. Unit
weight of concrete is 23.5 kN/m3. Fc = 27.5
MPa, fct = 2.75 MPa. The beam is simply
supported over a span of 5 m.
78.What is the cracking moment of the
beam?
A. 46.32 kN-m
B. 72.15 kN-m
C. 61.25 kN-m
D. 55.55 kN-m
79.If the cracking moment of the beam is
40 kN-m, what is the maximum
superimposed uniform load can the
beam carry?
A. 8.86 kN/m
B. 9.65 kN/m
C. 7.54 kN/m
D. 14.36 kN/m
80.If the beam is reinforced with 3-25-mm-diameter bars placed 435 mm from the
top, what is the new cracking moment? Assume n = 8.
A. 71.45 kN/m C. 68.57 kN/m
B. 65.22 kN/m D. 60.87 kN/m

Situation 26 – A reinforced concrete beam has a width of 300 mm and an overall

depth of 400 mm. The beam is reinforced with four 28-mm-diameter tension bars
and two 28-mm diameter compression bars. Use fc = 20.7 MPa and fy = 415 MPa.
Distance from centroid of bars to extreme concrete fiber is 70 mm.
81.Calculate the depth of compression block.
A. 122 mm C. 114 mm
B. 134 mm D. 148 mm
82.What is the ultimate moment capacity of the section?
A. 214.7 kN-m C. 244.4 kN-m
B. 271.6 kN-m D. 238.7 kN-m
83.If the beam is simply supported over a length of 6 m, what additional
concentrated live load can be applied at the midspan if its ultimate moment
capacity is 400 kN-m? Unit weight of concrete is 23.5 kN/m 3.
A. 200 kN C. 150 kN
B. 125 kN D. 175 kN

Situation 27 – The floor framing plan of a reinforced concrete is shown in Figure

C100-21. Beam DEF is poured monolithically with the slab making it to be
considered as T-beam. The columns are each 350 mm x 350 mm. The NSCP
coefficients for continuous beam is also given in Figure CODE-523. For this problem,
t = 100 mm, bw = 350 mm, fy = 415 MPa, fc = 28 MPa, fyh = 275 MPa.
 84. Calculate the
factored uniform load wu that the beam can carry based on the design strength
of the beam at support.
A. 69.1 kN/m C. 72.5 kN/m
B. 54.7 kN/m D. 63.3 kN/m
85.Calculate the factored uniform load wu that the beam can carry based on the
design strength of the beam at midspan.
A. 65.2 kN/m C. 72.4 kN/m
B. 61.2 kN/m D. 58.7 kN/m
86.If the factored uniform loaf wu = 60 kN/m, determine the required nominal
shear strength at critical section near the support at E.
A. 195 kN C. 164 kN
B. 199 kN D. 187 kN
Situation 28 – For the column shown in the Figure, f c = 28 MPa, fy = 415 MPa,
flexural rigidity EI = 910,000 N-m2
Situation 29 – The section of a concrete column is shown in the Figure. The column
is reiforced with 10 25-mm-diameter bars with f y = 415 MPa. Use fc = 21 MPa.