PAST BOARD EXAM PROBLEMS

Situation – Given the following data for a rectangular beam:

Beam dimensions, b x h = 300 mm x 450 mm
Effective depth, d = 380 mm
Concrete strength, f’c = 30 MPa
Steel strength, fy = 415 MPa
Unit weight of concrete = 24 kN/m^3

1. If the beam is simply supported on a span of 5 m and supports a superimposed dead load of 16
kN/m and live load of 14 kN/m, calculate the maximum moment (kN-m) at ultimate condition. Use U
= 1.4D + 1.7L
A. 158 C. 104
B. 195 D. 144

2. If the design moment at ultimate loads is 200 kN-m, determine the required number of 16 mm
diameter tension bars.
A. 4 C. 6
B. 8 D. 2

3. If the beam supports a factored (ultimate) load of 50 kN at midspan, calculate the required
number of 16 mm tension bars.
A. 4 C. 5
B. 3 D. 2

Situation – A 12 m simply supported beam is provided by an additional support at midspan. The beam
has a width of b = 300 mm and a total depth h = 450 mm. It is reinforced with a 4 – 25 mm ∅ at the
tension side and 2 - 25 mm ∅ at the compression side with 70 mm cover to centroid of
reinforcements. f’c = 30 MPa, fy = 415 MPa. Use 0.75 𝜌b = 0.023.

4. Determine the depth of the rectangular stress block.

A. 106.52 mm C. 116.31 mm
B. 213.66 mm D. 194.16 mm

5. Determine the nominal bending moment, Mn.

A. 122.33 kN-m C. 150.13 kN-m
B. 266.2 kN-m D. 236.16 kN-m

6. Determine the total factored uniform load including the beam weight considering moment capacity
reduction of 0.90.
A. 53.24 kN/m C. 42.75 kN/m
B. 16.94 kN/m D. 35.72 kN/m

Situation – A simply supported beam is reinforced with 4 – 28 mm ∅ at the bottom and 2 – 28 mm ∅ at

the top of the beam. Steel covering to centroid of reinforcement is 70 mm at the top and bottom of
the beam. The beam has a total depth of 400 mm and a width of 300 mm. f’c = 30 MPa, fy = 415 MPa.
Balanced steel ratio 𝜌b = 0.031.

7. Determine the depth of compression block.

A. 96.55 mm C. 54.12 mm
B. 89.54 mm D. 49.36 mm

8. Determine the design strength using 0.90 as the reduction factor.

A. 253.63 kN-m C. 451.38 kN-m
B. 164.32 kN-m D. 133.32 kN-m

9. Determine the live load at the mid-span in addition to a DL = 20 kN/m including the weight of
the beam if it has a span of 6 m.
A. 50.01 kN C. 12.36 kN
B. 41.35 kN D. 31.63 kN

Situation – A rectangular beam has a width of 280 mm and an effective depth of 500 mm. It has a
reinforcement area of 4072 mm2 at the bottom. Balanced steel ratio 𝜌b = 0.026. f’c = 25 MPa, fy =
414 MPa.

10. Determine the depth of the compression block.

A. 164.12 mm C. 114.65 mm
B. 260.17 mm D. 236.31 mm

11. Determine the tensile force carried by the steel bars.

A. 134.12 kN C. 1511.32 kN
B. 464.64 kN D. 1547.93 kN

12. Determine the resisting moment capacity of the beam, checked for moment capacity reduction
factor.
A. 204.4 kN-m C. 372.2 kN-m
B. 102.9 kN-m D. 351.2 kN-m

Situation – A beam has a width of 300 mm and an effective depth of 500 mm. f’c = 28 MPa, fy = 414
MPa. Es = 200,000 MPa.

CIE 120 – CONCRETE DESIGN

PAST BOARD EXAM PROBLEMS
13. Determine the depth of the compression block for a balanced condition.
A. 278.11 mm C. 214.63 mm
B. 251.48 mm D. 185.44 mm

14. Determine the balanced steel area required.

A. 4337 mm2 C. 1234 mm2
B. 3266 mm 2 D. 4569 mm2

15. Determine the moment capacity for maximum steel area requirements for a balanced condition.
A. 310.32 kN-m C. 164.32 kN-m
B. 327.62 kN-m D. 126.34 kN-m

Situation – A beam section is limited to a width b = 250 mm and a total depth of 500 mm. The beam
is subjected to a factored moment, Mu of 448 kN-m. f’c = 27.6 MPa, fy = 415 MPa, 𝜌b = 0.028. Use 80
mm concrete covering to the centroid of steel reinforcement.
16. Determine the ultimate moment capacity that is allowed for the section as singly reinforced.
A. 281.70 kN-m C. 198.12 kN-m
B. 109.45 kN-m D. 298.30 kN-m

17. Determine the total required area of reinforcement for tension if compression bars are needed.
A. 2930.3 mm2 C. 6413.3 mm2
B. 3515.0 mm 2 D. 1234.5 mm2

18. Determine the required area of reinforcement for compression.

A. 2103 mm2 C. 1608 mm2
B. 1303 mm 2 D. 2241 mm2

Situation – A beam section is limited to a width b = 250 mm and a total depth of 550 mm. The beam
is subjected to a factored moment of 356 kN-m. f’c = 20.73 MPa, fy = 346 MPa, 𝜌b = 0.027. Use 70 mm
concrete to the centroid of steel reinforcement.

19. Determine the ultimate moment capacity that is allowed for the section as singly reinforced.
A. 281.70 kN-m C. 198.12 kN-m
B. 109.45 kN-m D. 291.00 kN-m

20. Determine the total required area of reinforcement for tension if compression bars are needed.
A. 2939.1 mm2 C. 4413.3 mm2
B. 3515.0 mm2 D. 1234.5 mm2

21. Determine the required area of reinforcement for compression.

A. 410.3 mm2 C. 250.3 mm2
B. 509.1 mm 2 D. 320.3 mm2

Situation - Given the following data of the figure shown:

Beam width, b = 400 mm

h₁ = 100 mm; h₂ = 500 mm

As = 8-25 mm diameter bar
As’ = 4-25 mm diameter bar
Lateral ties, ds = 8 mm
a = 45 mm

Concrete compressive strength, fc’ = 34 MPa

Longitudinal bars, fy = 413 MPa
Transverse ties, fyh = 275 MPa
Clear concrete cover, cc = 40 mm

22. Compute the effective depth (mm) of the beam.

A. 487 C. 494
B. 517 D. 520

23. Compute the shear strength (kN) provided by concrete.

A. 205 C. 197
B. 236 D. 182

24. What is the maximum allowable tie spacing?

A. 300 C. 380
B. 325 D. 340

25. If the ties are spaced at 120 mm on centers, how much is the shear strength (kN) provided by
shear reinforcement.
A. 258 C. 189
B. 211 D. 238

26. Determine the design moment (kN-m) of the section neglecting the contribution of the compression
bars.
A. 526.3 C. 652.3

CIE 120 – CONCRETE DESIGN

PAST BOARD EXAM PROBLEMS
B. 724.7 D. 473.7

27. Given: Maximum size of coarse aggregates = 20 mm. Which of the following gives the minimum beam
width, b, to comply with the bar spacing requirements of the code?
A. 271 C. 300
B. 276 D. 291

Situation - The beam reinforcement for the negative moment at the column support is shown.
Given:
As = 6 of 28 mm diameter bars
A's = 4 of 28 mm diameter bars
Concrete Compressive Strength, fc’ = 34 MPa
Steel Yield Strength, fyl = 415 MPa for main bars
Steel Yield Strength, ſyv = 275 MPa for ties
Ties = 12 mm diameter at 100 mm on center spacing
Steel Ratio at Balanced Condition, ρb = 0.035
Effective cover to the Centroid of As = 80 mm
Effective Cover to the Centroid of A's = 70 mm

28. Calculate the moment capacity (kN-m) of the section, Mu.

A. 640 C. 416
B. 612 D. 438

29. Calculate the shear strength provided by the shear

reinforcement, Vs (kN).
A. 532 C. 475
B. 646 D. 704

30. Calculate the nominal shear strength of the section, Vn (kN).

A. 893 C. 532
B. 712 D. 827

Situation 17 - Given the following data of the figure shown:

Beam width, b = 350 mm

h₁ = 100 mm; h₂ = 500 mm

As = 6-28 mm diameter bar

As’ = 3-25 mm diameter bar
Lateral ties, ds = 12 mm
a = 56 mm

Concrete compressive strength, fc’ = 21 MPa

Longitudinal bars, fy = 415 MPa
Transverse ties, fyh = 275 MPa
Clear concrete cover, cc = 40 mm

31. Compute the effective depth (mm) of the beam.

A. 515.33 C. 536.45
B. 508.23 D. 480.25

32. Compute the shear strength (kN) provided by concrete.

A. 204 C. 197
B. 320 D. 140

33. What is the maximum allowable tie spacing?

A. 300 C. 380
B. 325 D. 340

34. If the ties are spaced at 100 mm on centers, how much is

the shear strength (kN) provided by shear reinforcement.
A. 204 C. 197
B. 320 D. 140

35. Determine the design moment (kN-m) of the section neglecting the contribution of the compression
bars.
A. 602 C. 541
B. 611 D. 679

36. Determine the design moment (kN-m) of the section considering the contribution of the
compression bars.
A. 602 C. 541
B. 611 D. 679

37. Given: Maximum size of coarse aggregates = 20 mm. Which of the following gives the minimum beam
width, b, to comply with the bar spacing requirements of the code?
A. 271 C. 300
B. 276 D. 291

CIE 120 – CONCRETE DESIGN

PAST BOARD EXAM PROBLEMS
Situation - Given the following data of a reinforced concrete cantilever beam:
Beam dimension, b x h = 300 mm x 600 mm
Beam length, L = 4 m
Clear concrete cover to 10 mm stirrups = 40 mm
Longitudinal bars: Top bars: 4 - 25 mm diameter (one line)
Bottom bars: 2 - 25 mm diameter
Superimposed dead load = 10.2 kN/m (including slab wt.)
Unit weight of concrete = 24 kN/m
Steel strength: Longitudinal bars = 414 MPa
Lateral bars = 275 MPa
Concrete strength, fc’ = 27.6 MPa
U = 1.2D + 1.6L

Reduction factors:
Flexure = 0.90
Shear = 0.75
Neglect compression bars and use pb = 0.0285 Determine the following:

38. The effective depth (mm) of the beam.

A. 537.5 C. 560
B. 535 D. 543.5

39. The total dead load in kN/m.

A. 12.36 C. 5.88
B. 14.52 D. 4.32

40. The area (mmi of tension steel reinforcement.

A. 2945 C. 1963
B. 1472 D. 982

41. The depth (mm) of the concrete compression block

A. 165.3 C. 57.8
B. 95.7 D. 115.5

42. The nominal moment strength (kN-m) of the beam.

A. 206 C. 458
B. 351 D. 389

43. The maximum uniform live load (kN/m) that the beam can support.
A. 13 C. 15
B. 16 D. 17

44. The minimum beam width (mm) to comply with bar spacing requirements of the code.
A. 290 C. 285
B. 300 D. 275

Situation 11 - Given the following data for the figure shown.

Dimension, w x L = 560 mm x 720 mm
As = 10 - 28 mm
diameter Ties = 12 mm diameter
fc' = 27.5 MPa
Main bar, fy =415 MPa
ties, fyh = 275 MPa
Clear concrete cover = 40 mm
Factored shear forces: Vux = 800 kN; Vuy = 500 kN
Allowable concrete shear stress, Fvc, = 0.87 MPa
Hint: Vc = Fvc bw d
Reduction factor for shear = 0.75

45. What is the gross area As (mm2) of the section?

A. 386200 C. 432500
B. 536200 D. 403200

46. What effective depth d (mm) to be used to compute for Vcy?

A. 654 C. 494
B. 524 D. 510

47. What width bw, (mm) to be used to compute for Vcx?

A. 720 C. 520
B. 700 D. 560

48. Calculate the required spacing (mm) of lateral reinforcement for the factored shear Vuy.
A. 170 C. 210
B. 190 D. 240

49. Calculate the required spacing (mm) of lateral reinforcement for the factored shear Vux.
A. 120 C. 160
B. 80 D. 90

CIE 120 – CONCRETE DESIGN

PAST BOARD EXAM PROBLEMS
Situation - Given the following data of a rectangular tied column:
Kn = 0.6, ρg = 0.04
Reduction factor, = 0.65

50. If the column dimension is 550 mm x 550 mm, determine the design axial strength (kN) of the
column.
A. 2689 B. 2242
C. 3152 D. 3757

51. If the column dimension is 550 mm x 550 mm, determine the design moment (kN-m) of the column.
A. 470 B. 723
C. 821 D. 678

52. Using a steel ratio ρg = 0.03 and Kn = 0.6, what is the required column depth “h” (mm) with the
same gross area.
A. 906 B. 750
C. 680 D. 830

Situation - The initial design of a rectangular tied column resulted to the following:

Column section:
Width (w)= 400 mm
Depth (h) = 600 mm
Concrete compressive strength, fc’ = 27.5 MPa
Reinforcing steel yield strength, fy = 413 MPa
From the interaction diagram:
Rn = 0.20
Kn = 0.80
The resulting steel ratio ρg = 0.05
Strength reduction factor (ϕ)= 0.65

53. For the steel ratio, how many 20 mm diameter bars are required?
A. 22 C. 16
B. 20 D. 18

54. How much is the nominal axial capacity of the column, Pn (kN)?
A. 5280 C. 5820
B. 2580 D. 2580

55. To limit the steel ratio, ρg to 3% where Kn = 0.8 and the eccentricity of Pn is e = 150 mm, what
should be the column depth, h (mm)?
A. 750 C. 800
B. 1000 D. 890

CIE 120 – CONCRETE DESIGN

PAST BOARD EXAM PROBLEMS
Situation – A spiral column has a diameter of 500 mm. It is reinforced with 32 mm diameter bars, it
carries a nominal moment of 700 kN-m. ρ = 0.07.

56. Determine the value of Kn.

A. 1.82 C. 1.45
B. 1.00 D. 1.15

57. Determine the value of the eccentric nominal load (kN) that it could support.
A. 5400 C. 6550
B. 5250 D. 4700

58. How many 30 mm diameter bars is needed for the spiral column.
A. 17 C. 14
B. 20 D. 19

Situation - A round spiral column with a diameter of 400 mm is reinforced as shown in the figure in
the interaction diagram.
Where:
Kn = 0.400
Rn = 0.195
Concrete compressive strength, fc’ = 27.5 MPa
Reinforcing steel yield strength, fy = 413 MPa
From the interaction diagram:
The resulting steel ratio ρg = 0.03
Strength reduction factor (ϕ)= 0.75

59. What is the required size (mm) of reinforcing bar for the given layout?
A. 25 C. 16
B. 32 D. 18

60. What is the design axial load Pu (kN)?

A. 1036.5 C. 1306.5
B. 1382.3 D. 1603.5

61. How much is the design moment Mu (kN-m)?

A. 270 C. 249
B. 205 D. 154

CIE 120 – CONCRETE DESIGN

PAST BOARD EXAM PROBLEMS
Situation - A 600-mm-diameter spiral column is reinforced with 16-mm-diameter longitudinal bars.
Use fy = 415 MPa and fc’ = 27.5 MPa.

62. Using a steel ratio of 1.7%, determine the minimum number of bars.
A. 26 C. 24
B. 28 D. 22

Given:
Axial dead load = 1800 KN
Axial live load = 1700 KN
U = 1.2D + 1.6L
63. Determine the minimum number of bars.
A. 12 C. 16
B. 14 D. 18

64. Determine the effective slenderness ratio of the column if the column length is 6 mand K = 0.5.
Take I = 0.70Ig.
A. 25.8 C. 21.5
B. 20.0 D. 23.9

Situation - Given the following data of a circular spiral column:

Concrete strength fc’ = 34 MPa
Steel yield strength, fy = 413 MPa
Steel ratio = 2.5%
Nominal strength = 4500 kN
Spiral bar diameter = 10 mm
Clear concrete cover = 40 mm

65. Determine the minimum required column diameter in mm.

A. 410 C. 400
B. 430 D. 420

66. If the column diameter is 600 mm and is reinforced with six 28-mm-diameter bars, compute the
design axial strength (kN) of the column. Use ф = 0.75.
A. 5824 C. 6113
B. 8151 D. 6325

67. What is the minimum pitch of spiral (mm) according to the provisions of NSCP?
A. 35 C. 80
B. 50 D. 65

CONCRETE MIXTURES

Situation - Given the following data for a concrete mixture:

Target concrete strength = 40 MPa
Slump = 75mm to 150 mm
Water-cement ratio = 0.48
Water content per cubic meter of concrete = 180 kg/m3
Entrapped air = 1%
Fine aggregates = 33% of total volume of aggregates

Specific gravity of materials:

Cement=3.15 Fine aggregates = 2.68
Coarse aggregates = 2.64
Unit weight of concrete = 23.4 kN/m3

68. Calculate the required weight (kg) of cement and water per cubic meter of concrete.
A. 530 C. 632
B. 587 D. 555

69. Calculate the required weight (kg) of fine aggregates per cubic meter of concrete.
A. 611 C. 562
B. 745 D. 452

70. Calculate the required weight (kg) of coarse aggregates per cubic meter of concrete.
A. 1222 C. 904
B. 1124 D. 1490

Situation - Given the following data for proportioning trial batches for normal weight concrete
with an average compressive strength of 34 MPa at 28 days:
Slump = 7 mm to 100 mm
Water-cement ratio by weight = 0.49
Specific gravity:
cement = 3.15
coarse aggregate = 2.64
fine aggregate = 2.68

Water (net mixing) = 190 kg/m3

Entrapped air = 1%

CIE 120 – CONCRETE DESIGN

PAST BOARD EXAM PROBLEMS
Unit weight of concrete = 23.3 kN/m3

71. Compute the total solid volume of water, cement, coarse aggregate and entrapped air, if the dry
weight of coarse aggregate is 10.1 kN/m.
A. 0.28 C. 0.71
B. 0.15 D. 0.39

72. For 10 m of concrete, how much cement (kN) is needed?

A. 18.9 C. 10.2
B. 57.6 D. 38.0

73. If the combined solid volume of cement, water, coarse aggregate and entrapped air is 0.55 m what
is the weight (kN) of dry sand is required?
A. 13.2 C. 16.6
B. 11.8 D. 24.3

Situation – The following is submitted for a proposed concrete mix.

Cement:
Specific gravity = 3.15
Weight of one bag = 40 kg

Fine aggregate:
Fineness modulus = 2.65
Specific gravity = 2.48
Absorption = 3%

Coarse aggregate:
Specific gravity = 2.68
Dry bulk density = 1680 kg/m3
Absorption = 0.7%

Concrete:
Slump = 125 mm
Water = 26 liters per bag of cement
Air content = 4%

Cement content = 6.5 bags/ mix

Coarse aggregate = 0.57 bulk

74. What is the dry weight of the coarse aggregate per cu. m of concrete?
A. 6.39 kN/m3 C. 7.39 kN/m3
B. 8.39 kN/m3 D. 9.39 kN/m3

75. What is the absolute volume of the coarse aggregate per cu. m of concrete?
A. 0.36 m3 C. 0.14 m3
B. 0.28 m3 D. 0.57 m3

76. What is the water cement ratio?

A. 0.45 C. 055
B. 0.65 D. 0.75

77. What is the weight of cement per cu. m of fresh concrete?

A. 230 kg/m3 C. 260 kg/m3
B. 240 kg/m 3 D. 250 kg/m3

78. What is the absolute volume of fine aggregate in one cu. m of fresh concrete?
A. 0.0817 m3 C. 0.0834 m3
B. 0.0862 m3 D. 0.0825 m3

79. What is the absolute volume of cement in one cu. m of fresh concrete?
A. 0.0817 m3 C. 0.0834 m3
B. 0.0862 m3 D. 0.0825 m3

80. What is the volume of water designed for use in one cu. m of concrete?
A. 0.1260 m3 C. 0.1420 m3
B. 0.1690 m3 D. 0.1880 m3

81. What is the weight (kg) of sand per cu. m of fresh concrete?
A. 39.75 C. 202.32
B. 46.38 D. 150.21

82. What is the unit weight of the concrete mix in kN/m3?

A. 21.14 C. 19.57
B. 24.20 D. 22.67

83. If the oven-dry weight of the coarse aggregate were 957.6 kg, how much water would it need to
absorb?
A. 5.95 kg C. 6.70 kg

CIE 120 – CONCRETE DESIGN

PAST BOARD EXAM PROBLEMS
B. 6.35 kg D. 7.10 kg

Situation - A 500 mm x 500 mm column by a 3.2 m square footing on 5 piles.

Dimensions:
a = 0.6 m
b = 2.0 m

effective depth = 600 mm

diameter of pile = 400 mm
Concrete compressive strength, fc' = 20.7 MPa
Reinforcing steel yield strength, fy = 415 MPa

Column axial loads:

DL = 430 kN
LL = 380 kN
EL = 220 kN

Column moment due to earthquake 160 kN-m. The rquired strength of the
footing is based on the the following factored load combination:
U = 1.32 DL + 1.1 LL + 1.1 EL

Strength Reduction factors

0.75 for Shear
0.90 for Moment

84. Determine the maximum beam shear strass (MPa) in the pile cap.
A. 0.74 C. 0.31
B. 1.56 D. 0.40

85. Compute the punching shear stress (MPa) in column.

A. 2.08 C. 0.50
B. 0.74 D. 0.61

86. Determine the punching shear stress (MPa) on the most heavily loaded pile.
A. 0.20 C. 0.45
B. 0.18 D. 0.31

87. Determine the required spacing (mm) of 20 mm diameter bars for the critical moment.
A. 255 C. 180
B. 155 D. 120

Situation - A 600 mm square column is centrally located or a pile cap supported by 9 of 350 mm
square precast concrete piles.

Dimensions:
a = 0.6 m
b = 1.2 m
c = 0.6 m
d = 1.0 m

Effective depth of pile cap = 400 mm

Net ultimate axial Load = 2100 kN
Net ultimate moment about the y-axis = 300 kN-m
Concrete compressive strength, fc' = 20.7 MPa
Reinforcing steel yield strength, fy = 413 MPa

Strength Reduction factors

0.75 for Shear
0.90 for Moment

88. Compute the maximum pile reaction (kN) at ultimate

loads.
A. 320.00 C. 233.33
B. 191.67 D. 275.00

89. Compute the minimum pile reaction (kN) at ultimate

loads.
A. 257.00 C. 233.33
B. 191.67 D. 275.00

90. Determine the maximum beam shear strass (MPa) in the pile cap.
A. 0.86 C. 0.38
B. 1.14 D. 1.06

91. Compute the punching shear stress (MPa) in column.

A. 3.61 C. 2.41
B. 1.56 D. 1.22

CIE 120 – CONCRETE DESIGN

PAST BOARD EXAM PROBLEMS
92. Determine the punching shear stress (MPa) on the most heavily loaded pile.
A. 0.20 C. 0.40
B. 0.38 D. 0.31

93. Find the critical design moment (kN-m).

A. 490.0 C. 940.0
B. 742.5 D. 724.5

94. Determine the required spacing (mm) of 20 mm diameter bars for the critical moment.
A. 255 C. 190
B. 263 D. 114

Situation – A footing 2 m wide by 2 m long carries a square column 0.40 m by 0.40 m on its center.

Concrete compressive strength, fc' = 28 MPa

Reinforcing steel yield strength, fy = 415 MPa

Allowable stresses at ultimate loads:

For wide beam shear = 0.85 MPa
For two-way action shear = 1.85 MPa

Reduction factors:
Shear = 0.85
Moment = 0.90

95. Given:
Effective depth of pile cap = 350 mm
Calculate the allowable axial load (kN) for the two-way action shear at ultimate condition.
A. 1490.0 C. 1940.0
B. 1921.3 D. 1724.5

96. Given:
Effective depth of pile cap = 350 mm
Calculate the allowable axial load (kN) for the wide beam shear at ultimate condition.
A. 2490.0 C. 1940.0
B. 1742.5 D. 2247.8

97. The design moment at ultimate loads at the face of the column is 450 kN-m. How many 20 mm bars
are required?
A. 7 C. 12
B. 9 D. 11

98. Given:
DL = 200 kN
LL = 410 kN
U = 1.2DL + 1.6LL
Minimum concrete cover to the centroid of reinforcement bar = 250 mm
Calculate the required footing thickness (mm) for punching shear stress at ultimate loads.
A. 680 C. 425
B. 550 D. 750

99. Given:
DL = 820 kN
LL = 410 kN
U = 1.2DL + 1.6LL
Minimum concrete cover to the centroid of reinforcement bar = 250 mm
Calculate the required footing thickness (mm) for the critical wide beam shear stress at ultimate
loads.
A. 350 C. 600
B. 370 D. 300

PRESTRESSED CONCRETE

Situation - The figure shows a prestressed hallow core slab used for flooring of a library.
Given the following properties of the slab:
A = 1.4 x 105 mm2
a = 1.20 m
b = 200 mm
St = Sb = 6.8 x 106 mm3
Slab weight = 2.7 kPa
Superimposed dead load = 2 kPa
Live load = 2.9 kPa
Prestressing force = 820 kN at e = 63 mm below N.A.

The slab is simply supported on a span of 8 m. Allowable

stresses at service loads are 2.0 MPa in tension and 15.5 MPa
in compression. Consider 15% loss of prestress at service loads.

CIE 120 – CONCRETE DESIGN

PAST BOARD EXAM PROBLEMS
100.
Calculate the stress (MPa) at the top fiber of the slab at the ends due to initial prestress
force.
A. 5.29 C C. 1.74 T
B. 13.45 C D. 7.32 C

101.
Calculate the stress (MPa) at the top fiber of the slab at midspan due to loads and prestress
force.
A. 9.25 C C. 13.4 T
B. 10.8 T D. 7.5 C

102.
The maximum total load (kN/m) including its own weight, that the slab can be subjected to if the
allowable stresses at service loads are not to be exceeded.
A. 14.4 C. 10.2
B. 12.2 D. 11.4

Situation - A 6-m long cantilever beam 250 mm x 600 mm carries a uniformly distributed dead load of
5 kN/m (including beam weight) and a concentrated live load of 18 kN at the free end. To prevent
excessive deflection of the beam it is prestressed with 12 mm diameter strands causing a final
prestress of 640 kN.

103.
Determine the resulting stress (MPa) at the bottom fiber at the free end if the center of
gravity of the strands coincides with the centroid of the section.
A. 5.36 C C. 4.27 C
B. 4.27 T D. 5.36 T

104.
Determine the resulting stress (MPa) at the top fiber at the fixed end if the center of gravity
of the strands is 100 mm above the neutral axis of the beam.
A. 4.67 T C. 4.67 C
B. 3.87 T D. 3.87 C

105.
Determine the eccentricity (mm) of the prestressing force at the fixed end such that the
resulting stress at the top fiber of the beam at the fixed end is zero.
A. 195.4 C. 200.6
B. 209.2 D. 221.7

Situation - A prestressed concrete beam is 250 mm wide by 450 mm deep. The initial prestressing
force is 600 kN. Assume that there is a loss of prestress of 15% at service loads.

106.
What is the final compressive stress in the beam if the prestressing force is applied at the
centroid of the beam?
A. -5.33 MPa C. -4.8 MPa
B. -4.53 MPa D. -5.65 MPa

107.
What is the final compressive stress in the beam if the prestressing force is applied at 100 mm
below the centroid of the beam?
A. -1.51 MPa C. -11.2 MPa
B. -12.44 MPa D. -10.58 MPa

108.
What is the maximum eccentricity at which the prestressing force can be applied without
producing tensile stress in the beam?
A. 100 mm C. 150 mm
B. 125 mm D. 75 mm

Situation - The section of a double tee (DT) prestress concrete joist is shown in the figure. The
joists are simply supported on a span of 7.5 m and are pre-tensioned with total initial force of
1100 kN from low-relaxation strands. The joist supports a total dead load of 2.3 kPa (including
beam weight) and live load of 6.2 kPa. There is a loss of prestress of 20% at service loads. Unit
weight of concrete is 24 kN/m3 .
Properties of the sections:
A = 200,000 mm2
INA = 1.88 x 109 mm4

CIE 120 – CONCRETE DESIGN

PAST BOARD EXAM PROBLEMS

2.40 m
88 mm N.A
.

267 mm

75 mm

109. C
alculate the stress at the top fibers of the DT at end span due to initial prestressing only.
A. – 5.21 MPa C. 4.39 MPa
B. 3.65 MPa D. – 2.85 MPa

110. C
alculate the compressive stress at the bottom fibers of the DT at midspan due to initial
prestressing force only.
A. –35.49 MPa C. 38.65 MPa
B. 8.04 MPa D. –28.65 MPa

111. C
alculate the additional load in kPa such that the stress at the bottom fibers of the DT at
midspan (due to service loads and prestress force) will be zero.
A. 8.04 C. 3.35
B. 5.65 D. 4.86

CIE 120 – CONCRETE DESIGN