Seat No.

: ________
Republic of the Philippines
PROFESSIONAL REGULATION COMMISSION
Manila

BOARD OF CIVIL ENGINEERING

CIVIL ENGINEER Licensure Examination

Saturday, February 10, 2024 03:00 p.m. - 06:00 p.m.
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PRINCIPLES OF STRUCTURAL ENGINEERING AND DESIGN SET B

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. 2 only.

MULTIPLE CHOICE
Situation 1 – Given the following data of the earth dam shown:
Dimensions:
  m,    m,    m,    m
Unit weight of soil = 17.3 kN/m3
Unit weight of water = 9.81 kN/m3
1. Determine the factor of safety against overturning.
A. 10.4 C. 9.5
B. 11.8 D. 5.6
2. Determine the factor of safety against sliding assuming that the coefficient of friction
between the dam and the foundation is 0.45.
A. 2.1 C. 4.3
B. 3.2 D. 1.6
3. Compute the eccentricity (m) of the resultant foundation pressure.
A. 0.167 C. 0.098
B. 0.287 D. 0.053

Situation 2 – The stresses acting on an element is presented by the Mohr Circle shown.
4. Which of the following point represents the minimum principal stress?
A. C.
B. D. 
5. Which of the following represents the shear at failure plane at -axis:
A.  C. 
B.  D. 
6. Which of the following represents the maximum shearing stress?
A.  C. 
B.  D. 

Situation 3 – Given the following data of the concrete footing shown.

Dimensions:

  4 m  3 m
  .  m;   1.8 m
Unit weight of concrete = 24 kN/m3
Unit weight of soil = 17 kN/m3
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PRINCIPLES OF STRUCTURAL ENGINEERING AND DESIGN SET B

Column loads:
Axial load:      kN
Moment:   276 kN-m
7. Compute the maximum gross foundation pressure (kPa).
A. 184.2 C. 213.8
B. 115.2 D. 145.7
8. Compute the eccentricity (m) of the resultant foundation pressure.
A. 0.256 C. 0.367
B. 0.154 D. 0.667
9. Given: Axial load:      kN
Moment:   1100 kN-m
Compute the maximum gross foundation pressure (kPa).
A. 300 C. 280
B. 320 D. 360

Situation 4 – A decorative concrete beam with a tubular section is simply supported on a span
of 3 m. Given the following data:
Beam outside diameter = 600 mm
Beam inside diameter = 400 mm
Allowable tensile stress of concrete = 2.74 MPa
Allowable shearing stress of concrete = 0.40 MPa
Unit weight of concrete = 24 kN/m3
10. Compute the moment capacity (kN-m) of the beam.
A. 34.9 C. 54.5
B. 28.7 D. 46.6
11. What maximum concentrated load (kN) at midspan can the beam support based of allowable
shear stress.
A. 43 C. 65
B. 78 D. 53
12. If the circular hole is replaced by a 250 mm square hole, compute the moment capacity
(kN-m) of the beam.
A. 55 C. 77
B. 66 D. 44

Situation 5 – Given the following data for the figure shown.

Dimension,     600 mm × 500 mm
 = 10 – 28 mm diameter
Concrete, !  28 MPa
Yield strength of 28 mm bars, , "  415 MPa
Yield strength of 12 mm ties, # 275 MPa
Effective cover to centroid of main bar = 70 mm
Allowable shear stress = 0.89 MPa
Reduction factor for shear = 0.75
13. Calculate the maximum value of factored shear load $% (kN) if the spacing of transverse
reinforcement is 100 mm.
A. 765 C. 580
B. 625 D. 620

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PRINCIPLES OF STRUCTURAL ENGINEERING AND DESIGN SET B

14. Calculate the maximum value of factored shear load $% (kN) if the spacing of transverse
reinforcement is 100 mm.
A. 649 C. 680
B. 610 D. 712
15. If the factored shear force $%   kN, determine the required spacing (mm) of
transverse reinforcement.
A. 80 C. 110
B. 90 D. 70

Situation 6 – Refer to the figure below.

Given:
  3 m;  3 m;  1 m;  6 m; &  150 kN
Slope, $:   4:3
Section properties (all members):
Area,   18,900 mm2 (  3.26×106 mm3
Determine the following:
16. Force ) (kN) so that the shear stress of column * is zero. Given:   60 kN, +  ,°.
A. 137.2 C. 120.0
B. 150.5 D. 127.3
17. Force ) (kN) so that the column * is purely axial. Given,   60 kN.
A. 100.6 C. 90.0
B. 120.0 D. 110.5
18. Maximum compressive stress (MPa) of the column *. Given: +  0, )  60 kN,   120 kN.
A. 62 C. 68
B. 13 D. 79

P
Situation 7 – The 12-mm-diameter steel rod shown has a length   18 m, is subject to its own
weight. An ore bucket with weight  is attached at the end of the rod. Unit weight of
steel, .  77 kN/m3.
19. What is the value of  (kN) if the maximum elongation in the rod, /0  10 mm.
A. 12.410 C. 13.014
B. 12.488 D. 13.448
20. If   20 kN, find the longitudinal strain.
A. 0.00089 C. 0.00075
B. 0.00098 D. 0.00057
21. Find the ductility of the rod if due to a heavy load at failure the diameter of the
broken part is 11.25 mm.
A. 6.25 C. 13.8%
B. 6.67 D. 12.1%

Situation 8 – The hook is subjected to three forces A, B, and C as shown and gives no
resultant. θ = 60°.
22. Compute the force (kN) at C if A = 75 kN and B = 50 kN.
A. 50.00 C. 43.30
B. 56.18 D. 66.14
23. Compute the value of α if A = 75 kN and B = 50 kN.
A. 49.11° C. 60.12°
B. 40.89° D. 61.02°
24. Compute the force (kN) at A if C = 55 kN and B = 50 kN.
A. 58.91 C. 58.91
B. 46.89 D. 56.89

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PRINCIPLES OF STRUCTURAL ENGINEERING AND DESIGN SET B

y C

A B

Situation 9 – Refer to the plane truss shown.

Given:
P = 10 kN; a = 2 m; b = 4 m; s = 2.5 m
25. How much is the reaction (kN) at A?
A. 9.375 C. 20.295
B. 14.625 D. 18.825
26. How much is the reaction (kN) at B?
A. 9.375 C. 20.295
B. 14.625 D. 18.825
27. Find P (kN) so that the reaction at A will be equal to 25 kN.
A. 17 C. 19
B. 18 D. 20

Situation 10 – Given the following data for the butt connection shown in the figure.
s1 = 40 mm, s2 = 60 mm, s3 = 30 mm, s4 = 45 mm
t1 = 20 mm, t2 = 10 mm
Fy = 248 MPa; Fu = 400 MPa
Allowable stresses:
Tension on gross area = 0.6Fy
Tension on net area = 0.5Fu
Shear on net area = 0.3Fu
Bearing on plate = 1.2Fu
Bolt: Diameter = 22 mm; Fv = 100 MPa
Effective Hole diameter = 25 mm.
28. Find P (kN) based upon tension on gross plate area.
A. 595 C. 559
B. 638 D. 611
29. Find P (kN) based upon tension on net area of plate.
A. 720 C. 680
B. 500 D. 610
30. Find P (kN) based upon bolt shear.
A. 720 C. 684
B. 638 D. 611

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PRINCIPLES OF STRUCTURAL ENGINEERING AND DESIGN SET B

31. The dimensions of a concrete beam are b = 300 mm, d = 450 mm. If the concrete strength is
f’c = 27 MPa for normal weight concrete and allowable steel stress is fy = 415 MPa,
calculate the depth of neutral axis (mm) for a balance failure.
A. 169 C. 193
B. 266 D. 227
32. Determine the type of failure for a beam cross-section 300 mm wide, 680 mm deep
reinforced for tension at the bottom with 8-25 mm bars with effective depth of 590 mm.
Use f’c = 21 MPa and fy = 414 MPa.
A. concrete crush first C. steel yields first
B. balance failure D. unbalance failure
33. A rectangular concrete beam is 250 mm wide is reinforced with 3-20mm bars at an effective
depth of 380 mm. Compressive strength of concrete and steel yield strength are 21 MPa and
275 MPa, respectively. Calculate the nominal moment capacity, in kN-.
A. 74 C. 83
B. 81 D. 90
34. A 5-m long beam is fixed at the left end and is supported by a spring at the right end.
The spring stiffness is equal to 60 kN/m. Determine the deflection (mm) of the spring, if
the entire length of the beam is subjected to a uniformly distributed load of 756 N/m.
For the beam, E = 10 GPa and I = 80 x 106 mm4. Hint: Fspring = kx
A. 18 C. 21
B. 15 D. 19.5

Situation 11 – A rectangular concrete beam having b = 270 mm and d = 430 mm is reinforced with
six 25-mm-diameter bars with fy = 415 MPa. The beam is simply supported over a span of 6
m and carries a total dead load of 22 kN/m. Use f’c = 24 MPa and 1b = 0.0247.
35. Calculate the depth of compression block, in mm.
A. 236 C. 218
B. 197 D. 185
36. Calculate the nominal moment strength, in kN-m.
A. 250 C. 276
B. 385 D. 425
37. Calculate the maximum service live load that can be supported by the beam, in kN/m.
A. 26.3 C. 21.5
B. 30.2 D. 18.3

Situation 12 – Refer to the figure shown:

Loads on beam GHI:

Dead Load = 4.3 kPa (including slab weight)
Live Load = 4.8 kPa
Load Combination, U = 1.2D + 1.6L
Dimensions:
L1 = L2 = 6.3 m S = 2.5 m
Beam b × h = 300 mm × 400 mm
Slab thickness, t = 100 mm
Unit weight of concrete = 23.5 kN/m3

For two spans loaded, the negative moment at the interior support is wL2/8.

For one span loaded, the negative moment at the interior support is wL2/16.

For maximum stress, apply pattern loading for live load.

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PRINCIPLES OF STRUCTURAL ENGINEERING AND DESIGN SET B

38. Calculate the total factored dead load for beam GHI, in kN/m.
A. 19.2 C. 15.4
B. 12.9 D. 15.4
39. Compute the maximum factored vertical reaction (in kN) at the exterior support G in beam
GHI.
A. 83.4 C. 89.4
B. 98.3 D. 78.4
40. Determine the maximum factored negative moment (kN-m) in beam GHI.
A. 142.9 C. 101.2
B. 111.6 D. 124.2

Situation 13 – To prevent excessive deflection of a 3-m long cantilever beam subjected to a

load of 2 kN/m, its free end is attached to a tension rod.

Beam properties:
A = 1900 mm² Ix = 5.12 x 106 mm4
E = 200 MPa

41. What is the maximum deflection (mm) before attaching the tension rod?
A. 14.7 C. 18.9
B. 17.4 D. 19.8
42. If the resulting tensile in the rod is 2.5 kN when attached to the beam, find the maximum
moment at the fixed end (kN-m).
A. 1.50 C. 1.43
B. 1.56 D. 1.26
43. Determine the maximum span moment (kN-m) if the tension in the rod is 2.5 kN.
A. 1.50 C. 1.43
B. 1.56 D. 1.26

Situation 14 – A 6-meter simple beam is supported with a pin and roller supports at each end A
and B, respectively. It is designed to carry a uniform distributed load, w = 15 kN/m. Use
E = 200 GPa and I = 70×106 mm4.
44. Calculate the maximum moment (kN-m) in the beam.
A. 67.5 C. 87.5
B. 75.6 D. 57.8
45. Calculate the maximum deflection (mm) in the beam.
A. 12.9 C. 18.1
B. 15.7 D. 21.6
46. If the deflection at midspan is limited to L/360, what is the maximum uniform distributed
load the beam can carry? Assume EI is constant.
A. 12 C. 14
B. 13 D. 15

SUBMIT THIS TEST QUESTION SET TOGETHER WITH THE ANSWER SHEET TO YOUR
WATCHERS.
BRINGING THE TEST QUESTION SET OUT OF THE ROOM WILL BE A GROUND FOR
DISCIPLINARY ACTION.