Page 1 of 22

Republic of the Philippines

PROFESSIONAL REGULATION COMMISSION
Manila

BOARD OF CIVIL ENGINEERING

CIVIL ENGINEER Licensure Examination
Wednesday, November 6, 2024 8:00 am – 1:00 pm
---------------------------------------------------------------------
PRINCIPLES OF STRUCTURAL ANALYSIS AND DESIGN SET A
INSTRUCTION: Select the correct answer for each of the following
questions. Use the gform provided as your answer sheet.

SITUATIONAL.
SITUATION 1. – Refer to FIG. CE.01
A built-up section consisting of a wide flange W 350 x 90 and two 12-
mm plates welded to form a box section at the flanges tip with the
same depth. It is used as a column and fixed at both ends. The column
is braced at mid-height about the weak axis (Y-axis). Use Fy= 248 MPa.
Given:
Column Height= 10 m
Effective length factors:
K= 0.5 (for both ends fixed)
K= 0.7 (for one end fixed and other end pin)
Properties of W 350 x 90:
A= 11,550 mm^2
Ix= 266 x 10^6 mm^4
Iy= 44.54 x 10^6 mm^4
d= 350 mm
bf= 250 mm
tf= 16.4 mm
tw= 9.5 mm

1. Calculate the effective slenderness ratio of the column about the

x-axis.
A. 52.7 C. 132.8
B. 18.8 D. 37.7

2. Calculate the effective slenderness ratio of the column about the

y-axis.
A. 18.8 C. 72.0
B. 36.0 D. 25.7

3. Calculate the axial load capacity (kN) of the column section.

A. 2740 C. 2660
B. 2430 D. 2850
 Page 2 of 22

(PLEASE DO NOT DETACH)

ALLOWABLE STRESS
FOR COMPRESSION MEMBERS OF 248 MPA SPECIFIED YIELD STRESS

FIG. CE.01
 Page 3 of 22

SITUATION 2. – Refer to Fig. ST. 17.13.

The dam is used as a reservoir for collecting water where farmers can
rely on during dry spells. The following data are as follows:

H2= 3 m
t= 500 mm
Unit weight of concrete= 23.5 kN/m^3

Consider 1-m length of dam perpendicular to the figure. Assume that

the tensile stress can occur at the base of the dam.

Fig. ST. 17.13.

4. If the water level is at the top of the dam, compute the maximum
compressive stress (MPa) at the base.
A. 0.34 C. 1.13
B. 0.99 D. 1.54

5. If the allowable compressive stress at the base is 0.88 MPa, compute

the height of the water (m), H1.
A. 2.74 C. 2.28
B. 2.89 D. 2.56

6. At what height of water (m) will there be no tension at the base

of the dam?
A. 1.52 C. 1.10
B. 1.98 D. 1.22
 Page 4 of 22

SITUATION 3.- Refer to Fig. SAM.69.

The solid rod passes through a hole in the supported plate. When a
load P is applied to the rod, the rod head rests on the support plate.

Given:
Hole diameter, H= 20 mm
Rod diameter, d= 15 mm
Rod head diameter, a= 30 mm
Rod head thickness, t= 10 mm
Plate thickness, b= 12 mm

Normal stress produced in the rod by load P= 225 MPa.

Fig. SAM.69.

7. Compute the bearing stress (MPa) between the support plate and the
rod head.
A. 101.3 C. 220.9
B. 75.0 D. 176.7

8. Compute the average shear stress (MPa) produced in the rod head.
A. 84.4 C. 56.2
B. 220.9 D. 42.2

9. Compute the punching shear stress (MPa) produced in the support

plate by the rod head.
A. 52.7 C. 35.2
B. 56.2 D. 70.3
 Page 5 of 22

SITUATION 4.- Refer to Fig. PAS. 24.

The sheet pile shown in the figure is provided with tension rods
spaced 3 meters apart. The wooden stringers has d= 300 mm and can be
considered simply supported at each connection to the tension rod.
The sheet pile is assumed to be pinned at the dredge level (C).
Allowable bending stress of the stringer= 14.7 MPa
Allowable shearing stress of the stringer= 1.48 MPa
Given:
H1= 3.3 m
H2= 2.1 m
H3= 2.7 m
Unit weight of soil= 17.3 kN/m^3
Coefficient of active earth pressure= 1/3
Unit weight of water= 9.81 kN/m^3

Fig. PAS. 24.

10. Compute the design moment (kN-m) of the stringer.

A. 56.7 C. 119.8
B. 63.8 D. 44.1

11. Compute the value of stringer’s width “b” (mm) based on bending.
A. 260 C. 290
B. 545 D. 200

12. Compute the value of stringer’s width “b” (mm) based on shear.
A. 255 C. 540
B. 290 D. 200
 Page 6 of 22

SITUATION 5. Refer to Fig. JAZ. 37.

The 6 m long prestressed cantilever beam carries a uniformly
distributed dead load due to beam’s weight and a concentrated load of
18 kN at the free end. The strands are 12 mm in diameter with total
prestressing force of 540 kN applied at an eccentricity “e” above the
neutral axis of the gross-section.
Given:
Unit weight of concrete= 23.5 kN/m^3
b= 400 mm
d= 600 mm
Prestress loss at service loads= 15%

Fig. JAZ. 37.

13. Calculate the resulting final compressive stress (MPa) if the

prestressing force is applied at the centroid of the beam.
A. 2.25 C C. 1.91 C
B. 2.25 T D. 1.91 T

14. Calculate the resulting final compressive stress (MPa) in the top
fiber of the beam at the fixed end if the prestressing force is
applied at an eccentricity e=100 mm.
A. 12.6 C C. 4.91 T
B. 12.6 T D. 4.91 C

15. Calculate the required eccentricity e (mm) such that the resulting
stress in the top fiber of the beam at the fixed end is zero.
A. 356 C. 488
B. 288 D. 424

SITUATION 6.
A steel beam is simply supported on a span of 12 meters.
Given:
Section W 410 mm x 100 kg/m:
Area, A = 12,710 mm^2
Depth, d = 410 mm
Flange width, bf = 260 mm
Flange thickness, tf = 17 mm
 Page 7 of 22

Web thickness, tw = 10 mm
Moment of inertia, Ix = 397 x 10^6 mm^4
Moment of inertia, Iy = 49 x 10^6 mm^4
Modulus of elasticity, E = 200 GPa
Plastic modulus, Zx = 2.13 x 10^6 mm^3
Plastic modulus, Zy = 0.58 x 10^6 mm^3
Tensile yield stress, Fy = 345 MPa

Loads causing bending about the major axis:

Dead load (including beam weight) = 12 kN/m
Live load at midspan = P(kN)

16. Determine the load P(kN) based on the design flexural strength of
the beam, Mu. Given: Resistance factor for flexure, ø = 0.90,
Factored load combination = 1.2D + 1.6L.
A. 83.8 C. 134.8
B. 99.1 D. 52.4

17. Determine the load P(kN) based on the design shear strength of
the beam, Vu.
Factored shear stress= 0.6 Fy
Resistance Factor for shear= 1.0
A. 953 C. 3180
B. 1061 D. 762

18. At service load, the allowable midspan deflection due to live

load= L/360 of span. Determine P (kN) based on the allowable
deflection.
A. 134.5 C. 88.2
B. 73.5 D. 80.8

SITUATION 7.- Refer to Fig. STT.021.

A bell crank mechanism is in equilibrium given the following data:
P1= 7 kN
Angle theta= 65o
a= 0.2 m
b= 0.15 m
c= 8 mm
e= 6 mm

Fig. STT.021.
 Page 8 of 22

Allowable shear stress in the pin= 40 MPa

Allowable bearing stress in the bell crank= 100 MPa
Allowable bearing stress in the support bracket= 95 MPa

19. Calculate the minimum diameter “d” (mm) for pin B without exceeding
the allowable shear stress in the pin.
A. 18 C. 15
B. 20 D. 12

20. Calculate the minimum diameter “d” (mm) for pin B without exceeding
the allowable bearing stress of the bell crank.
A. 18 C. 22
B. 15 D. 20

21. Calculate the minimum diameter “d” (mm) for pin B without exceeding
the allowable bearing stress in the support bracket.
A. 18 C. 12
B. 10 D. 15

SITUATION 8.
An 8-m fixed-ended beam is loaded with a concentrated load P=200 kN
at midspan and a uniform load 30 kN/m throughout the length of the
beam.
Properties of the section:
Outside diameter= 300 mm
Thickness= 10 mm
E= 200 GPa

22. Calculate the maximum deflection (mm) of the restrained beam.

A. 44.5 C. 29.7
B. 53.6 D. 31.2

23. To prevent excessive deflection, a support is added at midspan.

Calculate the reaction (kN) at the added support.
A. 240 C. 120
B. 200 D. 320

24. To prevent excessive deflection, a support is added at midspan.

Calculate the maximum positive moment (kN-m) due to uniform load
of 30 kN/m.
A. 40 C. 60
B. 100 D. 20
 Page 9 of 22

SITUATION 9.-Refer to Fig. XUX. 17.

A 78-kg man walks up the inclined plank of negligible weight. The
length of the plank from A to B is 12 m.
Given:
Angle theta= 30o
Coefficient of static friction at A= 0.35
Coefficient of static friction at B= 0.25

Fig. XUX. 17.

25. Determine the reaction (N) at A.

A. 459.4 C. 344.1
B. 424.9 D. 372.2

26. Determine the reaction (N) at B.

A. 344.1 C. 372.2
B. 459.4 D. 424.9

27. Determine the distance “x” (m) at which the plank would begin to
slide.
A. 6.7 C. 6.4
B. 5.2 D. 5.8

SITUATION 10.- Refer to Fig. STL. 123.

The bracket welded to the flange of the supporting column carries the
load P= 150 kN.
Given:
a= 145 mm
b= 300 mm
c= 400 mm
 Page 10 of 22

Fig. STL. 123.

28. Calculate the force per unit length (N/mm) on the weld group if
the load acts at the centroid of the weld group.
A. 254.2 C. 500
B. 177.5 D. 337.1

29. Calculate the critical force (N/mm)on the weld group due to the
torsional effect of the eccentric load P.
A. 1409 C. 815.1
B. 1009 D. 895.4

30. Determine the weld thickness (mm) required to resist the eccentric
load P.
Allowable weld shear stress, Fv= 145 MPa
A. 8 C. 12
B. 10 D. 16

SITUATION 11.
A composite section having an effective width of flange of 2100 mm
and a slab thickness of 150 mm. The steel beam is a W 530 x 101 of
A36 Steel with Fy= 250 MPa.
Concrete fc’= 20.7 MPa
Modular ratio, n=9
Assume full shoring and full composite action.

Properties of W 530 x 101:

A= 12,900 mm^2
d= 537 mm
Ix= 617 x 10^6 mm^4
Weight= 101.4 kg/m

31. Calculate the moment of inertia (10^6 mm^4) of the effective

transformed area.
A. 2669.8 C. 827.5
B. 1794.8 D. 1487.8
 Page 11 of 22

32. Calculate the maximum tensile stress (MPa) in the beam due to a
standard truck load consisting of 17.8 kN front wheel load and
71.2 kN rear wheel load. Distance between wheels= 4.3 m. Include
24% impact factor. Simple span= 10 m.
A. 66.7 C. 64.9
B. 53.8 D. 116.7

33. Determine the uniformly distributed load (kN/m) which excludes

the weight of the steel and the concrete slab that the beam could
support if it has a resisting moment capacity of 580 kN-m.
Span length= 10 m
Unit weight of concrete= 24 kN/m^3
A. 32.8 C. 46.4
B. 54.9 D. 37.9

SITUATION 12.- Refer to Fig. SNM 12.17.

Given:
P= 40 kN
R= 3.2 m
Angle theta= 25 degrees
Line AB is along the horizontal axis.

Fig. SNM 12.17.

34. Determine the maximum shear stress (MPa) due to flexure alone at
cross-section D. Hint: Max. shear stress= VQ/Ib
Given: Outside diameter= 100 mm
Thickness= 6 mm
A. 36.7 C. 35.1
B. 21.2 D. 45.0

35. Determine the maximum shear stress (MPa) due to torsion alone at
cross-section D.
Given: Outside diameter= 100 mm
Thickness= 6 mm
 Page 12 of 22

A. 152.6 C. 134.3
B. 305.2 D. 688.2

36. Determine the maximum bending stress (MPa) at cross-section D.

Given: Outside diameter= 120 mm
Thickness= 15 mm
A. 86.2 C. 142.4
B. 466.5 D. 552.8

SITUATION 13.
A channel is used as a purlin of a truss whose top chord is sloped
4:1 (H:V). Assume all loads pass through the centroid. Span length is
6m.

Properties of the channel:

Sx = 6.19 x 10^4 mm^3
Sy= 1.38 x 10^4 mm^3
Weight = 76 N/m

Roof Loads:
Dead Load =0.72 kPa
Live Load = 1.0 kPa
Wind Pressure = 1.44 kPa
Wind pressure coefficient:
At windward side = 0.18 (pressure)
At leeward side = 0.6 (suction)
Allowable stresses:
Fbx = Fby = 207 MPa
For D+L+W load combination, a 1/3 increase in allowable stresses is
permitted.

37. Calculate the maximum spacing (m)of purlins due to dead load plus
live load only.
A. 1.0 C. 0.8
B. 0.7 D. 0.9

38. Calculate the maximum spacing (m)of purlins due to dead load, live
load and wind load on the windward side.
A. 0.9 C. 1.1
B. 1.0 D. 1.2

39. Calculate the maximum spacing (m)of purlins due to dead load, live
load and wind load on the leeward side.
A. 1.0 C. 1.4
B. 1.2 D. 1.3

SITUATION 14. – Refer to Fig. RCD. 169.

Given the following data for the column section shown:
W x L=600 mm x 800 mm
Main reinforcement= 16-25mm dia. bars
Lateral ties= 10 mm dia. bars
 Page 13 of 22

Reinforcing steel yield strength:

Main reinforcement, fy= 415 MPa
Lateral ties, fyv= 275 MPa
Clear concrete cover= 40 mm
Spacing of ties= 150 mm
Concrete, fc’= 28 MPa

Fig. RCD. 169.

40. What is the nominal shear strength (kN) of the column for the
shear parallel to the y-axis?
A. 833 C. 696
B. 466 D. 774

41. What is the design shear strength (kN) of the column for the shear
parallel to the x-axis?
A. 717 C. 584
B. 537 D. 622

42. If the column is subjected to a factored axial load of 1250 kN,

compute the maximum spacing (mm) of lateral reinforcement if the
design shear strength of the column parallel to the x-axis is 700
kN.
A. 184 C. 368
B. 205 D. 103

SITUATION 15.- Refer to Fig. BMN. 123.

The beam bridge is shown below.
Given:
a= 8 m c= 10 m e= 15 m
b= 20 m d= 5 m

Fig. BMN. 123.

 Page 14 of 22

43. At what length (m) should the uniformly distributed load be applied
to produce a maximum reaction at F?
A. 15 C. 25
B. 20 D. 30

44. At what length (m) should the uniformly distributed load be applied
to produce a maximum reaction at B?
A. 46 C. 28
B. 36 D. 38

45. At what length (m) should the uniformly distributed load be applied
to produce a maximum reaction at E?
A. 35 C. 38
B. 30 D. 46

SITUATION 16.- Refer to Fig. SAM. 147 and FIG. CE.02

Given:
L1= L2= L3= L4= 8.0 m
S1= 2.5 m
S2= 3.0 m

Total dead load= 4.6 kPa

Live load= 4.8 kPa
The interior beam KLMNO is to be analyzed for the maximum forces
considering live load pattern. At ultimate condition, U=1.2D+1.6L.
All supports are simply supported.

Fig. SAM. 147

46. What is the maximum reaction (kN) at O?

A. 39 C. 345
B. 123 D. 114

47. What is the maximum moment (kN-m) of the beam at support N?

A. 249 C. 280
B. 267 D. 182

48. What is the maximum shear (kN) at span NO?

A. 178.5 C. 175.6
B. 176.3 D. 167.3
 Page 15 of 22

(PLEASE DO NOT DETACH)

BEAM DIAGRAMS AND DEFLECTIONS

For Various static loading conditions

FIG. CE.02
 Page 16 of 22

SITUATION 17.- Refer to Fig. STA. 019.

The force acting per meter length of the dam and the dimensions are
as follows:
W= 650 kN a= 1.2 m
F1= 275 kN b= 2.1 m
F2= 165 kN c= 1.8 m
Angle theta= 60 degrees d= 5.4 m

Fig. STA. 019.

49. What is the maximum bearing pressure (MPa) at the base of the dam?
A. 282.1 C. 162.8
B. 569.7 D. 196.1

50. What is the minimum bearing pressure (MPa) at the base of the dam?
A. 108.5 C. 112.7
B. 298.4 D. 126.4

51. The coefficient of friction at the base of the dam is 0.30, find
the frictional force (kN) which resists the sliding of the dam.
A. 39.6 C. 132.1
B. 67.8 D. 219.8

SITUATION 18.
An axially loaded rectangular tied column is to be designed for the
following service loads:
Dead Load= 1,500 kN
Live Load= 835 kN
Required Strength= 1.2D + 1.6L

Effective cover to centroid of steel reinforcement= 70 mm

Concrete fc’= 27.5 MPa
Steel, Fy= 415 MPa
Reduction factor= 0.65
 Page 17 of 22

52. What is the required column width (mm) for vertical steel ratio
of 3%?
Column width in one direction= 350 mm
A. 500 C. 370
B. 250 D. 550

53. If the column section is circular, calculate the required diameter

(mm) if it is reinforced with 8-25 mm dia. bars.
A. 430 C. 550
B. 500 D. 600

54. Given:
Column section= 450 mm x 450 mm
No. of vertical reinforcement bars= 16
Steel ratio= 0.03
Determine the minimum diameter of vertical bars (mm).
A. 20 C. 28
B. 25 D. 32

SITUATION 19.
An 8 m. high retaining wall is subjected to lateral earth pressure
increasing from 34 kPa at the top to 136 kPa at the base. Flexural
rigidity EI = 4.5 x 1014 N-mm2. Analyze per meter length of the wall.

55. What is the moment (kN-m) at the base of the cantilever retaining
wall?
A. 1564 C. 2176
B. 1877 D. 2672

56. What is the force (kN) to be applied at the propped end to limit
the deflection to 35 mm?
A. 122.17 C. 91.37
B. 86.15 D. 112.71

57. What is the moment (kN-m) at the base when the wall is propped at
the top?
A. 707.2 C. 416.4
B. 815.6 D. 526.7

SITUATION 20.- Refer to Fig. SAL. 261.

A combined footing and its corresponding shear diagram due to factored
load is shown.
Dimensions:
e = f = h = 0.4 m W = 2 m
g = 3.5 m
Shear diagram:
a = 156.8 kN
b = -610.8 kN
c = 761.2 kN
 Page 18 of 22

Concrete strength, fc’= 27.5 MPa

Steel strength, fy= 414 MPa
Main bar diameter= 20 mm
Effective depth= 500 mm
Columns A and B= 400 mm x 400 mm
Reduction factors at ultimate condition:
Moment= 0.90
Shear= 0.75

Fig. SAL. 261.

58. Calculate the critical wide-beam shear stress (MPa).

A. 0.57 C. 0.75
B. 1.01 D. 0.93

59. Calculate the required number of bars (pcs) at critical moment.

A. 10 C. 16
B. 11 D. 17

60. Calculate the punching shear stress (MPa) at Column B if the

column at B carries a factored axial load of Pu= 1428.4 kN.
A. 0.94 C. 1.69
B. 0.71 D. 1.27

SITUATION 21.
A hollow circular pole 3m high is fixed at the base. It is 6 mm thick
and its outside diameter is 300 mm. The pole is subjected to a torque
and a lateral force at the free and.
Given:
Torque= 25 kN-m
Lateral Force= 5 kN
Shear modulus of elasticity= 78 GPa
 Page 19 of 22

Allowable shear stress= 45 MPa

61. What is the maximum shear stress (MPa) at the outside surface of
the pole due to the torque?
A. 31.3 C. 62.6
B. 4.72 D. 60.7

62. What is the angle of twist (in degrees) due to the torque?
A. 0.92o C. 0.80o
B. 1.24 o D. 0.46o

63. What is the maximum bending stress at the base of the pole due to
the lateral load?
A. 37.6 C. 75.1
B. 5.7 D. 68.9

SITUATION 22.
The basic data for proportioning trial batches for normal weight
concrete with an average compressive strength of 25 MPa at 28 days
are as follows:

Slump................................. 75 mm to 100 mm
Water-cement ratio by weight ......... 0.63
Specific gravity of cement............ 3.15
Specific gravity of coarse aggregate... 2.68
Specific gravity of fine aggregate..... 2.64
Water (net mixing)..................... 200 kg/m^3
Weight of coarse aggregate............. 10.1 kN/m^3
Entrapped air.......................... 1%
Unit weight of concrete................ 23.6 kN/m^3

64. Calculate the required volume of coarse aggregates (m^3) per

cubic meter of concrete.
A. 1.03 C. 2.34
B. 0.38 D. 0.76

65. For a 8 cu.m. of concrete, how much cement (kN) is needed?

A. 28.4 C. 39.7
B. 32.0 D. 24.9

66. If the combined solid volume of cement, water, coarse aggregate

and entrapped air is 0.72 m3, what is the weight of the dry sand
in kN?
A. 7.3 C. 21.27
B. 18.6 D. 11.65
 Page 20 of 22

SITUATION 23.- Refer to Fig. ARC. 123.

A semi-circular steel arch is subjected to equal but oppositely
directed forces T at A and B as shown.
Given:
d= 2.5 m
h= 1.2 m

Fig. ARC. 123.

67. If T= 20 kN, determine the bending moment (kN-m) at point E.

A. 7.0 C. 25.0
B. 24.0 D. 12.5

68. If T= 20 kN, determine the shear force (kN) acting at point E.

A. 19.2 C. 5.6
B. 20 .0 D. 24.0

69. If T= 20 kN, determine the normal force (kN) acting at point E.

A. 5.6 C. 20.8
B. 24.0 D. 19.2

SITUATION 24.- Refer to Fig. FIT. 110.

The lap joint of a tension member is shown below. The plate is 260 mm
wide and 12 mm thick. Steel is A36 with Fy= 250 MPa and Fu= 400 MPa.
Bolt diameter= 22 mm
Bolt hole diameter= 25 mm
S1= 65 mm
S2= 40 mm
S3= 65 mm
t= 12 mm

Allowable tensile stress on gross area= 0.6Fy

Allowable tensile stress on net area= 0.5Fu
Allowable shear stress on plate= 0.3Fu
 Page 21 of 22

Fig. FIT. 110.

70. Determine the maximum safe value of P (kN) based on tension on

gross area.
A. 936 C. 234
B. 468 D. 624

71. Determine the maximum safe value of P (kN) based on tension on

net area.
A. 333 C. 888
B. 666 D. 444

72. Determine the maximum safe value of P (kN) based on block shear.
A. 385.2 C. 448.8
B. 522.2 D. 472.8

SITUATION 25.- Refer to Fig. BBM. 014.

The beam reinforcement for a 5-meter cantilever beam are as follows:
Given:
As= 6-28 mm diameter bars
As’= 4-28 mm diameter bars
Concrete strength, fc’= 34 MPa
Reinforcing Steel Yield Strength, fyl= 415 MPa
Reinforcing Steel Yield Strength, fyv= 275 MPa
Lateral ties= 12 mm diameter at 100 mm spacing O.C.
Steel ratio at balanced condition= 0.035
Dimensions:
h1= 100 mm
h2= 500 mm
b= 350 mm
Effective cover to centroid of As= 80 mm
Effective cover to centroid of As’= 70 mm
 Page 22 of 22

Dead Load= 20 kN/m (beam weight already included)

At ultimate condition, U=1.2D + 1.6L

Fig. BBM. 014.

73. Calculate the design moment capacity (kN-m) of the section.

A. 534 C. 480
B. 613 D. 681

74. Calculate the factored shear force, Vu, (kN) that can be supported
by the section.
Allowable concrete shear stress= 1.15 MPa
Reduction factor for shear= 0.75
A. 642 C. 856
B. 400 D. 532

75. Calculate the maximum live load (kN) at the free end that can be
carried by the beam based on shear.
A. 334 C. 326
B. 552 D. 244

“ENGINEER NA AKO NGAYONG NOVEMBER 2024! CLAIM IT!”

Engr._____________________________
(Your Name)

---------------------NOTHING FOLLOWS------------------