Reinforced Concrete Design7

Name: Engr. Date:

Situation 1 - The archer pulls his bowstrings back 200 mm by exerting a force that
increases uniformly from zero to 540 N at a point A as shown in the figure. In this
problem, a = 200 mm, b = 100 mm, c = 150 mm, d = 150 mm, and e = 400 mm.

1. Findthetension (N) in the chord AB

A. 563.2 C. 517.5
B. 556.3 D. 568.9

2. Findthetension (N) at the bottom chord AD

A. 568.9 C. 563.2
B. 517.5 D. 556.3

3. Whatistheforce (N) exerted by the archer at the front hand C?

A. 500 C. 520
B. 540 D. 530

Situation2 - Thehook shown in the figure is subject to three forces: A, B, and C.

GivenforceA=6kN, force B = 4.5 kN, and angle 𝛼 = 30°,

4. Calculatethe value of angle 𝜃 (degrees) iftheresultantof the three forces is

5.5kNalong the y-axis. A.
30.4 B. 32.8 C. 36.6
D. 34.1

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5. If the resultant force is 12.7 kN and 𝜃 = 80°, find the force C (kN).
A. 7.24 C. 8.12
B. 6.24 D. 6.88

6. If force C = 6.3 kN and 𝜃 = 45°, what is the resultant force (kN)?

A. 9.36 C. 8.81
B. 7.42 D. 8.12

Situation 3 - A student pushes the 600-N ladder horizontally as shown in the figure
in order to prevent it from slipping. Assume B is a frictionless wall.
Given:
a = 1.5 m, b = 4.5 m, 𝜃 = 30°, 𝜇𝐴 = 0.20

7. Determine the vertical reaction at A (N).

A. 800 B. 400 C. 600
D. 550

8. Determine the horizontal reaction at A (N).

A. 110 C. 160
B. 120 D. 80

9. Determine the pushing force (N) exerted by the student.

A. 532.8 C. 487.9
B. 635.7 D. 596.3

Situation 4 - The crane shown in the figure carries the 35 kN load at B. The crane
weighs 8 kN.
Given:
a = 12 m, b = 4 m, c = 9 m

10. What is the tension (kN) in cable AD

A. 30.12 B. 35.69 C. 32.65
D. 26.52

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11. Whatisthetotalreaction (kN) at C?
A. 56 C. 23.11
B. 68 D. 60.58

12. Ifthetensionofcable AD is limited to 42kN,what is the maximum value of the

load W (kN).
A. 52.17 C. 57.77
B. 65.85 D. 55.24

Situation5 - The dam shown in the figure has a height H = 3 m and thickness t =
0.50 m. Unit weight of concrete 𝛾𝑐 = 23.5 kN/m 3 and consider 1 meter length of dam
perpendiculartothefigure. Assume that tensilestress can occur at the base.

13. If the water is level with the top of the dam, compute the maximum compressive
stress (MPa) at the base
A. 1.25 B. 1.13 C. 1.37
D. 0.99

14. If the allowable compressive stress at the base is 1 MPa, compute the depth of
water d (m).
A. 2.914 C. 2.872
B. 2.358 D. 2.563

15. Compute the maximum value of d (m) that willnotproduce any tension at the base.
A. 0.563 C. 0.954
B. 1.216 D. 1.338

Situation 6 - The continuous beam shown is supportedby rollers at B and D and a pin
at C. Assume EI is constant.

16. Determine the distribution factor of span BC.

A. 1 C. 1/2
B. 2/3 D. 0

17. Determine the distribution factor of span CD.

A. 0 C. 1
B. 1/2 D. 2/3

18. If an additional fixed support is provided at E, determine the distribution

factor of span ED.
A. 2/3 C. 1/2
B. 0 D. 1

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Situation7 - Thedouble angle shown in the figurecarries a tensile force of P.
Given:
Allowableshearing stress of bolt = 150MPa
Allowabletensile stress of bolt = 195MPa
Boltdiameter,D1 = D2 = 25mm
H=2,V= 1

19. Find the maximum safe load P (kN) based ontensileandshearing strength of bolt
D2.
A. 632 C. 329
B. 856 D. 587

20. Find the P (kN) based on shear strength ofboltD. 1

A. 587 C. 441
B. 365 D. 220

21. If P = 400kN, what is the required diameter(mm)ofbolt D2?

A. 22 C. 25
B. 32 D. 28

Situation 8 - A precast concrete slab is liftedbyfourcables as shown in the figure.

Unit weight of concrete is 23.5 kN/m3

22. Determine the tensile force (kN) in each cable

A. 3.85 C. 6.01
B. 8.09 D. 6.94

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23. What is the tensile stress (MPa) in each cable if its diameter is 16 mm?
A. 34.5 C. 40.3
B. 19.2 D. 29.9

24. If the cable deforms by 1.5 mm, what is the vertical deflection (mm) of the
concrete?
A. 0.863 C. 0.524
B. 2.186 D. 1.458

Situation 9 - A truss is loaded as shown in the figure.

Given:
F1 = 14 kN, F2 = 7 kN, F3 = 7 kN, s = 3 m, and h = 2.4 m.

25. Findtheaxialforce(kN)in member BF A.

7(C) B. 14(T) C. 14(C)
D. 7(T)
Findtheaxialforce(kN)in member AF
26. A. 25.8(T)
B. 37(T) C. 37(C)
D. 25.8(C)
Findtheaxialforce(kN)in member DE
27. A. 25.8(C)
B. 25.8(T) C. 37(T)
D. 37(C)

Situation10 - A pressure vessel 360 mm in diameter is to be fabricated from steel

plates.Thevesselistocarryan internalpressureof6MPa.

28. What is the required thickness (mm) of the plate if the vessel is to be cylin-
dricalandtheallowablesteel stressis120MPa?
A. 10mm C. 9mm
B. 11mm D. 13mm

29. Whatistherequiredthickness (mm) of theplateifthevesselistobespherical

andthe allowablesteelstress is 120 MPa?
A. 5.5 C. 6.5
B. 5 D. 4.5

30. If the vessel to be fabricated is cylindrical using 12 mm thick steel plate,

what is the maximum internal pressure (MPa) that the vessel can carry if the
allowablesteelstressis 60 MPa?
A. 2 C. 5
B. 4 D. 3

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Situation 11 - The trusses are pin connected and suspended from the parabolic cable.
Given:
a = 4 m, b = 3 m, c = 5 m, d = 4 m, P1 = 15.8 kN, P2 = 14.6 kN

31. Determine the horizontal force acting on the cable (kN)

A. 48 C. 71
B. 37.7 D. 55

32. Determine the equivalent horizontal distributed load supported by the cable
(kN/m)
A. 0.30 C. 0.60
B. 1.30 D. 1.178

33. Determine the maximum tension in the cable (kN)

A. 31.60 C. 42.15
B. 28.43 D. 59.33

Situation 12 - The shaft ABCD shown below has a 60mm diameter and is subjected to
multiple torques, 1200 N-m at B and 1060 N-m at C, both in the same direction.
Supports A and D are unyielding (no twisting can happen) and G = 80,000 MPa.

34. Findthe reaction (torque) at A.

A. 1020 N-m C. 1250 N-m
B. 1100 N-m D. 1310 N-m

35. Whatis the maximum shearing stress in theshaft?

A. 22.73 MPa C. 27.11 MPa
B. 25.49 MPa D. 29.24 MPa

36. Calculate the rotation between A and C in degrees.

A. 1.20° C. 2.09°
B. 1.76° D. 2.54°

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Situation13 - AcantileverbeamBDrests on a simple beam AC as shown in the figure.
Bothbeamsareofthesamematerialand are 100 mm x 200 mm. If they jointly carried
a triangular loadW=10kN/mdetermine the following:
Given:
L1 = 3.6 m, L2 = 2.4 m, L3 = 1.2 m

37. The load carried by beam AC (kN)

A. 1.585 C. 3.431
B. 1.247 D. 2.052

38. The maximum deflection (mm) of beam AC if E = 180 MPa

A. 0.144 C. 0.369
B. 0.239 D. 0.524

39. Determine the maximum flexural stress (MPa) developed in beam AC

A. 2.463 C. 1.241
B. 2.754 D. 4.117

Situation14 - Abuilt-upsectionconsistingofW350x90withtwo12-mmplateswelded
to form a box section as shown in the figure. The section is used as a column 10
meters long. The column is fixed at both ends, and braced at midheight about the weak
axis (y-axis). Use Fy = 248 MPa.
Properties of W350x90:
bf = 250 mm Ix = 266x106 mm4
tf = 16.4 mm Iy = 44.54x106 mm4
d = 350 mm A = 11,550 mm2
tw = 9.5 mm

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40. Determine the effective slenderness ratio of the column with respect to lateral
buckling about the x-axis.
A. 42.76 B. 34.89 C. 37.66
D. 35.98

41. Determine the effective slenderness ratio of the column with respect to lateral
buckling about the y-axis.
A. 34.89 C. 37.66
B. 35.98 D. 42.76

42. Determine the axial load capacity of the column in kN

A. 2435 C. 3210
B. 2895 D. 2750

Situation 15 - The 12-mm-thick plate shown in the figure is bolted to the web of a
beam. In this problem, P = 200 kN, e = 200 mm, x1 = 50 mm, x2 = 40 mm, x3 = 75 mm,
x4 = 40 mm, x5 = 65 mm, x6 = 60 mm

43. Determinethedirectshearload(kN) on the critical bolt.

A. 12.5 C. 50
B. 37.5 D. 25

44. Determinethetorsionalload(kN)on the critical bolt.

A. 72.4 C. 66.6
B. 20.1 D. 89.6

45. Determine the total shear stress (MPa) on the critical bolt if the diameter of
the bolt is 20 mm.
A. 244 C. 230
B. 264 D. 637

Situation16 - Light-gradechannelsection is used as a purlin of a truss.

Given the following data:
Properties of channel section:
W=79N/m,Sx=6.19x104mm3,Sy=1.61x104 mm3
Simple span = 6 m
Angle of inclination of truss = 15°
Spacing of purlins = 1 m
Totalgravityload(appliedattopofpurlin) = 950 Pa
Wind Load:
Windward side = 288 Pa (pressure)
Leeward side = 864 Pa (suction)

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Allowable stresses:
Fbx = Fby = 195 MPa
46. How much is the critical bending stress, fbx, (MPa) due to gravity loads and wind
loads.
A. 143.2 C. 93.2
B. 110.5 D. 126.3

47. How much is the critical bending stress, fby, (MPa) due to gravity loads and wind
loads.
A. 126.3 C. 110.5
B. 143.2 D. 93.2

48. What is the maximum spacing (m) of purlins to prevent overstressing?

A. 0.80 C. 0.90
B. 0.70 D. 1.10

Situation 17 - Given the following data of a rectangular tied column:

Kn = 0.60; Rn = 0.28, ρ = 0.04; f’c = 20.7 MPa, fy = 414 MPa
Reduction factor, Φ = 0.65

49. Ifthecolumn dimension is 600 mm x 600 mm,determine the designaxial strength

(kN)ofthe column.
A. 3260 C. 2900
B. 2640 D. 4470
If
50. the column dimension is 600 mm x 600 mm, determine the design moment (kN-m)
ofthecolumn.
A. 810 C. 856
B. 1320 D. 1250

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51. Using a steel ratio of 0.03, and Kn – 0.60, what is the required column depth
“h” in mm with the same gross area?
A. 775 B. 700 C. 625
D. 675

Situation 18 - For the spiral column shown in the figure.

Given:
f'c = 27.5 MPa Kn = 0.80
fy = 414 MPa Rn = 0.18
Reinforcement steel ratio, ρg = 0.03
Diameter of spiral column = 400 mm
Strength reduction factor = 0.75

52. What is the diameter (mm) of 12 pcs longitudinal bars?

A. 18 B. 20 C. 25
D. 28
WhatisthemaximumaxialloadPu(kN)
53. A. 2563 thatthespiralcolumncould support?
B. 3254 C. 3748
D. 2811

54. Compute the factored moment, Mu (kN-m) acting on the column.

A. 163 C. 186
B. 514 D. 249

- A monolithic floor framing plan is shown in the

figure. The columns
Situation19
are300mmsquare,girdersare250mmwideby500mmdeepandslabsare 100 mm thick.
Thefloorloadsincludefloorfinishof1.5kPa,ceilingsystemof0.75 kPa, partition
loadof1.0kPa,andliveloadof4.8kPa.Barcentroidfromtheedge of the beam is
70 mm. Use f’c = 21 MPa and fy = 280 MPa.

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55. Calculate the ultimate bending moment at face of column G for member FG inkNm
A. 115.36 C. 111.27
B. 117.41 D. 115.28

56. Calculate the factored shear force in kN at face of column F for girder EF
A. 118.85 C. 101.48
B. 103.35 D. 116.70

57. Calculate the ultimate bending moment at face of girder MN for slab IJMN in kNm
A. 16.47 C. 19.76
B. 7.32 D. 6.10

Situation 20 - The reinforcement for negative moment of a continuous beam consists

ofthe following:
Topbars = 8-20 mm diameter bars
Bottom bars = 4-20 mm diameter bars
Stirrups = 12 mm diameter bars
Material strength:
Concrete: f’c = 28 MPa 𝜌𝑚𝑎𝑥 = 0.023

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Reinforcing steel: fy = 413 MPa (Main reinforcement)
Reinforcing steel: fy = 275 MPa (Stirrups)
Dimensions: h1 = 100 mm h2 = 400 mm
b = 350 mm
a = 50 mm
Clear concrete cover to stirrups = 50 mm
Shear strength provided by concrete:
′
𝑉𝑐 = 0.17√𝑓 𝑐𝑏𝑑
Shear strength provided by shear reinforcement:
𝐴𝑣𝑓𝑦𝑣𝑑
𝑉𝑠=
𝑠

58. Compute for the nominal shear capacity of the beam Vn (kN) if the stirrups are
spaced at 110 mm center-to-center. C.
A. 580 D. 520
B. 340 270

59. Findthenominalmomentcapacity(kNm)ofthebeamatthesupports.
A. 350 C. 410
B. 250 D. 290

60. Where shear is minimum the stirrups are spaced at 200 mm center-to-center.
Determine the shear strength (kN) provided by the stirrups.
A. 250 C. 237
B. 186 D. 214

Situation21 - A 400-mm-thick footing supports a 300-mm-thick concrete wall. The

allowable soil bearing pressure is 192 kPa. Concrete strength f’c = 27.5 MPa and
steel yield strength fy = 415 MPa.

61. The footing is subjected to a moment of 180 kN-m and a total vertical load of
300 kN. Compute the minimum width (m) of the footing to prevent uplift.
A. 3.0 C. 2.7
B. 2.3 D. 3.6

62. The footing is subjected to the following forces:

Resisting moment = 465 kNm
Overturning moment = 255 kNm
Total vertical load = 290 kN
Compute the maximum width (m) of the footing to prevent uplift.
A. 2.90 C. 5.80
B. 4.34 D. 2.17

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63. Given: Width of footing = 3 m Resisting moment =
530 kNm Overturning moment = 285 kNm Total
vertical load = 350 kN Determine the maximum soil
bearing pressure in kPa

A. 303.3 C. 570
B. 750 D. 333.3

Situation 22 - Refer to the combined footing shown.

Given:
a=0.4m,b=3.5m,c=0.4 m,W=4m
Effective depth = 600 mm
f’c = 27.5 MPa, fy = 413 MPa
Net soil pressure at factored loads = 98 kPa
Shear due to factored loads:
e=156.8kN,f=610.4kN,g=761.6kN,h=509.6 kN
Reduction factors:
Shear = 0.75
Moment = 0.90

64. How much is the punching shear stress (MPa) at column B?

A. 0.85 C. 0.64
B. 0.74 D. 0.55

65. How much is the critical wide beam shear stress (MPa)?
A. 0.45 C. 0.29
B. 0.36 D. 0.22

66. Compute the number of 25-mm bars within the length “d” from column B.
A. 12 C. 22
B. 15 D. 17

Situation 23 - Refer to the cantilever beam shown:

Given:
db = 25mm h = 600mm
f’c = 41.3 Mpa L = 2.5m

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 fy = 413 MPa a = 60mm
Apply factors for normal weight concrete uncoated reinforcement Cb = 50mm, Ktr=0.
The minimum development length is 300mm for bars in tension and 200mm for barsin
compression.

67. Howmuch is the total length L (mm) of bar"A"?

A. 3389 C. 2920
B. 3142 D. 1288

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68. How much is the total length L (mm) of bar "B"?
A. 2883 C. 2544
B. 2612 D. 2465

69. How much is the total length L (mm) of bar "A" if 20mm diameter is used?
A. 2926 C. 3124
B. 2828 D. 3273

Situation 24 - The basic data for proportioning trial batches for normal weight
concrete with an average compressive strength of 35 MPa at 28 days are as follows:
slump = 70 mm to 100 mm
water-cement ratio by weight = 0.62
specific gravity of cement = 3.15
specific gravity of fine aggregate = 2.64
specific gravity of coarse aggregate = 2.68
water (net mixing) = 180 kg/m3
weight of coarse aggregate = 10.65 kN/m3
entrapped air = 1%
concrete unit weight = 23.4 kN/m3

70. What is the required volume of cement (m3) per cubic meter of concrete?
A. 0.125 C. 0.065
B. 0.073 D. 0.092

71. Compute the volume of coarse aggregate (m3) per cubic meter of concrete.
A. 0.587 C. 0.632
B. 0.487 D. 0.405

72. If the combined solid volume of cement, water, coarse aggregate and entrapped
air is 0.58 m3 what is the weight (kN) of dry sand is required?
A. 10.88 C. 9.12
B. 12.54 D. 8.54

Situation 25 - The section of a prestressed hollow core slab is shown in the figure.
The slab is simply supported over a span of 7.5 m and carries a superimposed dead
load of 1.5 kPa and live load of 2.1 kPa. The total prestressing force is 550 kN at
eccentricity of 38 mm. Assume loss of prestress of 20% at service loads. Use b = 1200
mm and h = 150 mm.
Properties of the cross-section are as follows:
Cross-sectional area, A = 120x103 mm2
Moment of inertia, I = 312x106 mm4
Weight of beam, W = 2.30 kPa

73. Determine the stress (MPa) at the bottom fibersat L/4 due to total load.
A. -6.32 C. 1.29
B. -8.62 D. 12.58

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74. Determinethestress (MPa) at the topfibersatmidspandue to total load.
A. -10.22 C. 4.28
B. -9.87 D. -11.61

75. What maximum uniform load (kN/m) can the slab carry if the maximum allowable
tensile stress in concrete is 3.2 MPa and the maximum allowable compressive
stressis18.5MPa? A.
6.44 B. 6.87 C. 5.63
D. 7.12

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