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MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

SET

A

INSTRUCTIONS: Read the following problems and answer the questions, choosing the best answer among the choices provided. Shade the letter of your choices on the answer sheet provided. Shade letter E if your answer is not among the choices provided. Strictly no erasures. SIT. A: Three cable tensions T1, T2, and T3 act at the top of the flagpole. The resultant force for the three tensions is R = −400 kN.

1. 2. 3.

Find the magnitude of the cable tension T1. A. 79.4 N B. 767.8 N C. 158.85 N Find the magnitude of the cable tension T2. A. 151.6 N B. 621.55 N C. 591.23 N Find the magnitude of the cable tension T3. A. 220.3 N B. 396.61 N C. 440.67 N

D. 529.51 N D. 181.92 N D. 264.41 N

SIT. B: The light boom AB is attached to the vertical wall by a ball-and-socket joint at A and supported by two cables at B. A force P = 12i − 16k kN is applied at B. Note that RA, the reaction at A, acts along the boom because it is a two-force body. 4. Compute the cable tension BC. A. 5.82 kN B. 25.18 kN C. 13.13 kN D. 15.1 kN 5. Compute the cable tension BD. A. 14.95 kN B. 15.2 kN C. 8.31 kN D. 6.65 kN 6. Compute the reaction RA. A. 18.66 kN B. 6.22 kN C. 15.9 kN D. 19.5 kN SIT. C: A truss is loaded as shown in the figure. 7. Compute the forces in member GD given that P = 300 kN and Q = 50 kN. A. 412.5 kN B. 135.2 kN C. 202.81 kN D. 243.74 kN 8. If PCD = 600 kN and PGD = 100 kN (both compression), find P. A. 517 kN B. 37 kN C. 579 kN D. 572.3 kN

1

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

9.

If PCD =600 kN and PGD =100 kN (both compression), find Q. A. 37 kN B. 579 kN C. 5.17 kN

SET

A

D. 572.3 kN

SIT. D: A pin-connected frame is loaded as shown in the figure.

10. 11. 12.

Determine the reaction at B of the pin- connected frame. A. 1014.14 N B. 854.4 N C. 1139.5 N D. 1000 N Determine the reaction at C of the pin- connected frame. A. 711.11 N B. 1070.36 N C. 899.45 N D. 1201.73 N Determine the shear force acting on section 2 (just to the right of the 600-N load) of the pin-connected frame. A. 300 N B. 969 N C. 135 N D. 600 N

SIT. E: The man in the given figure is trying to move a packing crate across the floor by applying a horizontal force P. The center of gravity of the 250-N crate is located at its geometric center. The coefficient of static friction between the crate and the floor is 0.3. 13.

Determine the largest distance h for which the crate will slide without tipping. A. 0.7 m B. 0.8 m C. 0.9 m D. 1 m 2

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION

SET

A

MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

14. 15.

Calculate the force P required to cause tipping of the packing crate. A. 83.3 N B. 75 N C. 107.14 N D. 93.75 N Determine the minimum coefficient of static friction that permits tipping. A. 0.3 B. 0.31 C. 0.2 D. 0.33

SIT. F: Cable AB supports the uniformly distributed load of 2 kN/m. The slope of the cable at A is zero.

16. 17. 18.

Compute the maximum tensile force in the cable. A. 180 B. 90 C. 210 Compute the minimum tensile force in the cable. A. 150 B. 180 C. 90 Compute the length of the cable. A. 62.83 m B. 74.72 m C. 78.54 m

D. 150 D. 30 D. 70.69 m

SIT. G: The 12-kN weight is suspended from a small pulley that is free to roll on the cable. The length of the cable ABC is 18 m.

19.

Determine the horizontal force P that would hold the pulley in equilibrium in the position x = 4 m. A. 1.5 kN B. 1.7 kN C. 1.9 kN D. 2 kN

SIT. H: A circular steel rod of length L and diameter d hangs in a mine shaft and holds an ore bucket of weight W at its lower end. Unit weight of steel is 77 kN/m3. 3

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

20. 21.

SET

A

Calculate the maximum stress in the rod if L = 40 m, d = 8 mm, and W = 1.5 kN. A. 29.84 MPa B. 32.92 MPa C. 31.1 MPa D. 91.12 MPa Calculate the total elongation of the rod. A. 6.28 mm B. 5.97 mm C. 6.57 mm D. 6.12 mm

SIT. I: A plastic bar ACB having two different solid circular cross sections is held between rigid supports as shown in the figure. The diameters in the left- and right-hand parts are 50 mm and 75 mm, respectively. The corresponding lengths are 225 mm and 300 mm. Also, the modulus of elasticity E is 6.0 GPa, and the coefficient of thermal expansion a is 100µ/° C. The bar is subjected to a uniform temperature increase of 30° C. Calculate the following quantities:

22. 23. 24.

the compressive force P in the bar A. 51.8 kN B. 28.92 kN the maximum compressive stress A. 14.73 MPa B. 40.5 MPa the displacement of point C A. 0.403 mm B. 0.178 mm

C. 79.52 kN

D. 35.34 kN

C. 26.4 MPa

D. 18 MPa

C. 0.378 mm

D. 0.314 mm

SIT. J: A steel strut S serving as a brace for a boat hoist transmits a compressive force P = 54 kN to the deck of a pier as shown in the figure. The strut has a hollow square cross section with wall thickness t = 9 mm and the angle θ between the strut and the horizontal is 40°. A pin through the strut transmits the compressive force from the strut to two gussets G that are welded to the base plate B. Four anchor bolts fasten the base plate to the deck. The diameter of the pin is dpin = 18 mm, the thickness of the gussets is tG = 16 mm, the thickness of the base plate is tB = 10

4

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION

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MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

mm, and the diameter of the anchor bolts is dbolt = 12 mm. Determine the following stresses:

25. 26. 27.

the bearing stress between the strut and the pin. A. 53.05 MPa B. 166.67 MPa C. 127.67 MPa the shear stress in the pin. A. 68.2 MPa B. 136.4 MPa C. 106.103 MPa the bearing stress between the pin and the gussets. A. 93.75 MPa B. 71.82 MPa C. 29.84 MPa

D. 106.103 MPa D. 81.28 MPa D. 59.683 MPa

SIT. K: The channel section carries a uniformly distributed load totaling 6W and two concentrated loads of magnitude W.

28. 29.

30.

Determine the moment of inertia about the neutral axis of the channel section. A. 17.25x106 mm4 B. 18.7x106 mm4 C. 19.28x106 mm4 D. 15.96x106 mm4 Determine the maximum allowable value for W if the working stresses are 40 MPa in tension and 80 MPa in compression A. 6.9 kN B. 6.93 kN C. 6.24 kN D. 7.48 kN Determine the maximum allowable value for W if the working stress is 24 MPa in shear. A. 50.4 kN B. 67.2 kN C. 33.6 kN D. 16.8 kN

SIT. L: The force P = 100 kN is applied to the bracket as shown in the figure.

5

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

31. 32. 33.

Compute the bending moment on the bracket. A. 11 kN-m B. 20.53 kN-m C. 8.08 kN-m Compute the normal stress developed at point A. A. 29.14 MPa (C) B. 10.08 MPa (C) C. 22 MPa (C) Compute the normal stress developed at point B. A. 55.9 MPa (T) B. 33.92 MPa (T) C. 10.08 MPa (T)

SET

A

D. 49.14 kN-m D. 28.1 MPa (C) D. 44 MPa (T)

SIT. M:A sign of dimensions 2.0 m x 1.2 m is supported by a hollow circular pole having outer diameter 220 mm and inner diameter 180 mm as shown in the figure. The sign is offset 0.5 m from the centerline of the pole and its lower edge is 6.0 m above the ground. The sign is acted by a wind pressure of 2.0 kPa.

34. 35. 36.

Determine the normal stress at point A at the base of the pole. A. 54.91 MPa B. 49.92 MPa C. 47.56 MPa D. 42.31 MPa Determine the resultant shear stress at point B at the base of the pole. A. 7.0 MPa B. 6.24 MPa C. 0.38 MPa D. 0.51 MPa Determine the maximum shear stress at point A at the base of the pole. A. 28.2 MPa B. 28.1 MPa C. 27.46 MPa D. 24.97 MPa 6

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

SET

A

SIT. N: The steel rod fits loosely inside the aluminum sleeve. Both components are attached to a rigid wall at A and joined together by a pin at B. Because of a slight misalignment of the pre-drilled holes, the torque T0 = 750 N∙m was applied to the steel rod before the pin could be inserted into the holes. Use G = 80 GPa for steel and G = 28 GPa for aluminum. 37. Determine the angle of twist on the steel due to the applied T0. A. 6.41° B. 5.91° C. 3.26° D. 4.67° 38. Determine the torque in the steel after T0 was removed. A. 251 N∙m B. 499 N∙m C. 265 N∙m D. 485 N∙m 39. Determine the torque in the aluminum after T0 was removed. A. 251 N∙m B. 499 N∙m C. 265 N∙m D. 485 N∙m

SIT. O: The rigid bars ABC and CD are supported by pins at A and D and by a steel rod at B. There is a roller connection between the bars at C.

40. 41. 42.

Compute the stress in the steel rod. A. 83.33 MPa B. 125 MPa C. 133.33 MPa D. 37.5 MPa Compute the elongation of the steel rod due to the 50-kN load. A. 1.25 mm B. 2 mm C. 1.75 mm D. 1.875 mm Compute the vertical displacement of point C caused by the 50-kN load. A. 3 mm B. 1.875 mm C. 2.63 mm D. 2.813 mm

SIT. P: Cantilever beam AC has a total length of 8m which carries dead load of 10 kN/m, live load of 5 kN/m and a moving wheel load of 15 kN and 10 kN that are 3 meters apart. Using the concept of influence lines, 43. Determine the maximum positive shear at B. A. 100 kN B. 150 kN C. 200 kN D. 250 kN 44. Determine the maximum negative moment at B. A. 292.15 kN∙m B. 282.5 kN∙m C. 325.6 kN∙m D. 266.67 kN∙m 45. Determine the maximum reaction at A. 7

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

A. 115 kN

B. 145 kN

SIT. Q: Given the continuous beam below, 46. Determine the maximum moment. A. 7.16 kN∙m B. 16.93 kN∙m 47. Determine the reaction at A. A. 16.89 kN B. 14.45 kN 48. Determine the reaction at B. A. 16.89 kN B. 14.45 kN

SET

A

C. 125 kN

D. 135 kN

C. 20.54 kN∙m

D. 13.55 kN∙m

C. 17.56 kN

D. 19.77 kN

C. 17.56 kN

D. 19.77 kN

SIT. R: A simply supported beam AD has the following loads indicated in the figure, determine the following in terms of EI. 49. θa E. 120.67/EI F. 525.67/EI G. 326.41/EI H. 156.37/EI 50. Value of x, where x is the location of the maximum deflection of the beam from the left E. 5.836 m F. 4.41 m G. 4.38 m H. 5.66 m 51. Determine the maximum deflection of the beam E. 374/EI F. 167.72/EI G. 486/EI H. 328/EI SIT. S: Given the floor framing below, the floor carries a superimposed dead load of 4kPa and live load of 3kPa on floor BCON, beam EFGH is 300x600 mm and the thickness of the slab is 100mm. 52. Determine the reaction at E. A. 24.96 kN B. 24.32 kN C. 27.84 kN D. 30.06 kN 53. Determine the moment at G. A. 74.8 kN∙m B. 63.7 kN∙m C. 89.18 kN∙m D. 92.4 kN∙m 54. Determine the reaction at F. A. 60.64 kN B. 57.76 kN C. 61.28 kN D. 55.54 kN SIT. T: A rectangular beam 375 mm wide and 500 mm deep is reinforced with 4-28 mm bars with bar centroid 75 mm from the bottom edge of the beam. The beam is acted by a total service moment of 95 kN∙m. Use modular ratio n = 9. 55. Determine the cracking moment for the section shown if f’ c = 28 MPa and if the

56. 57.

modulus of rupture f r =0 .7 √ f ' c . A. 68.5 kN∙m B. 115.76 kN∙m C. 94.72 kN∙m D. 57.88 kN∙m Determine the maximum compressive stress on concrete due to service loading. A. 6.67 MPa B. 7.98 MPa C. 5.56 MPa D. 8.2 MPa Determine the tensile stress in the steel bars. A. 11.66 MPa B. 104.97 MPa C. 92.6 MPa D. 76.74 MPa

SIT. U: A singly reinforced rectangular beam is to be designed, with effective depth approximately 1.5 times the width, to carry a service live load of 21.9 kN/m in addition to 8

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

SET

A

dead load of 3.6 kN/m, on a 7.3 m simple span. Material properties are f y = 415 MPa and f’c = 27.6 MPa. Consider bar centroid of 60 mm from the edge of the beam. 58. Determine the required gross depth of the beam if ρ = 0.6ρmax. A. 510 mm B. 450 mm C. 540 mm D. 500 mm 59. Determine the required width of the beam. A. 290 mm B. 300 mm C. 260 mm D. 320 mm 60. Determine the required area of steel reinforcement. A. 1612.446 mm2 B. 1725.56 mm2 C. 1296.1 mm2 D. 1963.31 mm2 SIT. V: A rectangular beam with width b = 610 mm, total depth h = 355 mm and effective depth to the tensile steel d = 290 mm, is constructed using materials with strengths fy = 415 MPa and f’c = 27.6 MPa. Tensile reinforcement consists of two 36 mm bars plus three 32 mm bars in one row. Compression reinforcement consisting of 32 mm bars is placed at distance 64 mm from the compression face. 61. Determine the depth of the stress block. A. 105.18 mm B. 75.99 mm C. 89.4 mm D. 123.74 mm 62. Determine the nominal moment strength of the beam. A. 357.95 kN∙m B. 441.92 kN∙m C. 397.72 kN∙m D. 404.67 kN∙m 63. Determine the maximum service uniform live load in addition to self-weight of the beam if it spans 6 m on simple supports. A. 48.93 kN/m B. 39.05 kN/m C. 43.73 kN/m D. 37.71 kN/m SIT. W: The section of a monolithic floor system is shown in the figure. The section has a 7.3 m simple span.

64.

65. 66.

Determine the depth of the stress block for one of the T-beams when the beam collapses if fy = 415 MPa and f’c = 34.5 MPa A. 18.46 mm B. 13.9 m C. 15.23 mm D. 16.39 mm Determine the nominal moment strength of one of the T-beams. A. 491.4 kN∙m B. 489.46 kN∙m C. 498.38 kN∙m D. 490.86 kN∙m Determine the maximum floor factored load the T-beams can sustain. A. 73.48 kN/m B. 66.39 kN/m C. 66.13 kN/m D. 66.32 kN/m 9

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

SET

A

SIT. X: A tied column 450 mm square is reinforced with 8-ϕ25 mm equally distributed on its sides. The unsupported length of the column is 2.6 m and is prevented to sidesway by shear walls. K 1.0, f’c = 20.7 MPa and fy = 415 MPa. Use 40 mm covering of tie reinforcement with diameter 12 mm. Es = 200 GPa. 67. Determine the location of the plastic centroid from the right face. A. 250 B. 200 C. 225 D. 275 68. Determine the nominal axial load in kN when concrete strain is 0.003 and yield strain of steel is y = fy/Es. A. 1684 B. 1541 C. 1178 D. 1098 69. Determine the nominal moment in kN·m to this nominal axial load. A. 482 B. 405 C. 434 D. 440 SIT. Y: A beam of 280 mm width and effective depth of 410 mm carries a factored uniformly distributed load of 77.4 kN/m, including its own weight, in addition to a concentrated factored load of 53.4 kN at midspan. Clear span is 5.5 m on simple supports. 70. Calculate the factored shear force at critical section for shear. A. 207.816 kN B. 290.94 kN C. 239.55 kN D. 247.3 kN 71. Calculate the required spacing of 10-mm stirrups with fy = 275 MPa. Consider the nominal shear stress on concrete is fv = 0.88 MPa.

A. 120 m B. 130 mm C. 100 mm D. 140 mm 72. Through what part of the beam from the face of the left support is web reinforcement theoretically required? A. 50 mm B. 2640 mm C. 2750 mm D. 2540 mm SIT. Z: A rectangular footing 2.4 m x 3 m x 0.45 m thick supports a rectangular column 300mm x 400 mm at its center, with short dimensions parallel with each other. Column loads are service conditions: DL = 680 kN LL = 400 kN f’c = 20.7 MPa fy = 275 MPa Concrete cover to the centroid of steel reinforcement = 100 mm 73. Calculate the nominal beam-shear stress acting at the critical section of the footing slab in MPa. A.) 0.724 MPa B.) 0.619 MPa C.) 0.546 MPa D.) 0.526 MPa 74. Calculate the ultimate punching-shear stress acting at the critical section of the footing slab in MPa. A.) 1.83 MPa B.) 1.55 MPa C.) 1.413 MPa D.) 1.242 MPa 75. Calculate the maximum factored bending moment on the footing slab in kN∙m. A.) 459.68 B.) 374.85 C.) 245.48 D.) 166.6 SIT. AA: A 6 m long cantilever T-beam, with properties shown in the figure, carries a concentrated live load of “F” at the free end. To prevent excessive deflection of the beam it 10

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION

SET

A

MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

is pre-tensioned with 12-mm-diameter strands causing an initial pre-stressing force of 740 kN.

A = 180,000 mm2 217 mm

INA = 4150x106 mm4

283 mm

76.

77.

78.

Determine the resulting stress due to initial pre-stressing force and self-weight of the beam at the bottom fiber at the fixed end if the strands are placed at the centroid of the section. A. 8.18 MPa (C) B. 9.41 MPa (C) C. 1.19 MPa (T) D. 2.40 MPa (T) Determine the resulting stress due to pre-stressing force and total dead load at the top fiber at the fixed end if the strands are placed 140 mm above the neutral axis of the beam and pre-stress loss is15%. A. 2.35 MPa (C) B. 5.46 MPa (C) C. 4.03 MPa (C) D. 2.79 MPa (T) Determine the live load “F” that will make the stress at the top fiber at the fixed end zero. A. 12.85 kN B. 6.83 kN C. 10.26 kN D. 9.35 kN

SIT. BB: The connection shown in the figure uses 20 mm diameter A325 bolts. The tension member is A36 steel (Fy = 248 MPa, Fu = 400 MPa) and the gusset plate is A572 steel (Fy = 290 MPa, Fu = 415 MPa). Determine the strength of the connection considering the following modes of failure: 9 mm gusset plate 37.5 mm P

75 mm 37.5 mm

12 mm x 150 mm 37.5 mm 75 mm 79.

Net section fracture with allowable stress 0.5Fu. A. 168 kN

80.

B. 264 kN

C. 248 kN

D. 267 kN

Bearing on plate holes with allowable stress 1.2Fu. A. 358.60 kN

81.

37.5 mm

B. 362.88 kN

C. 460.80 kN

D. 483.84 kN

Block shear with Ft = 0.5Fu and Fv = 0.3Fu. 11

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION

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MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

A. 184.68 kN

B. 270.86 kN

C. 294.84 kN

D. 348.09 kN

SIT. CC: A W12x79 of A573 Grade 60 (Fy = 415 MPa) steel is used as a compression member. It is 8.5 m long, fixed at the top and bottom, and has additional support in the weak direction at the midpoint. Properties of the section are as follows: A = 14,500 mm2 82.

Calculate the effective slenderness ratio with respect to strong axis buckling. A. 31.82

83.

B. 44.55

C. 55.71

D. 111.43

Calculate the effective slenderness ratio with respect to weak axis buckling. A. 22.28

84.

Ix = 258.6 x 106 mm4 Iy = 84.375 x 106 mm4

B. 27.86

C. 39.00

D. 55.71

Calculate the axial load capacity of the column. A. 1,709 kN

B. 2 905 kN

C. 2 523 kN

D. 2 444 kN

SIT. DD: A W356x383 is designed to carry a compressive force due to dead load and live load P = 1,900 kN with a bending moment of 285 kN∙m about the strong axis. The unbraced length is 4.5 m with K = 1.25 for bending about the strong axis and K = 1.10 for bending about the weak axis. Use Cm = 0.85 for both directions. Allowable stresses are F bx = 0.66Fy, Fby = 0.75Fy and Fa = 128 MPa where Fy = 248 MPa. Section properties are A = 48,774 mm2, Sx = 6.8x106 mm3, Sy = 2.638x106 mm3, rx = 170.40 mm, ry = 104.90 mm. 85.

Calculate the ratio of the actual to the allowable axial stress. A. 0.228

86.

C. 0.304

D. 0.389

Calculate the value of the moment magnification factor for bending about the strong axis. A. 0.89

87.

B. 0.261

B. 0.85

C. 1.05

D. 0.94

Calculate the value of the interaction formula using fa C mx f bx Cmy f by + + ≤1 Fa fa fa 1− F 1− F F ' ex bx F ' ey by

(

) (

)

12 π 2 E F ' e= 23 ( kL/r )2 Where A. 0.532

B. 0.560

C. 0.545

D. 0.574

SIT. EE: In the connection shown in the figure FIG. F, A 502−I bearing type bolts with threads in shear are used with 12 mm diameter. Allowable shear stress is Fv=120 MPa. Allowable bearing stress is 480 MPa and allowable tensile stress is 150 MPa. Assume the service load passes through the centroid of the rivet group.

12

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

88. 89. 90.

Determine the shear stress in the bolt if P=200 kN . A. 98.01 MPa B. 153.14 MPa C. 88.41 MPa Calculate the bearing stress if P=200 kN . A. 160.38 MPa B. 127.52 MPa C. 185.19 MPa Find the maximum value of P by tension on bolts. A. 153.71 kN B. 169.65 kN C. 195.89 kN

SET

A

D. 176.84 MPa D. 119.47 MPa D. 339.29 kN

SIT. FF: An angle 75 mm x 75 mm x 9 mm is welded to a plate to resist a load P = 500 kN acting through its centroid. The side welds have a nominal thickness of 8 mm.

91.

Calculate the direct shear load on the welds in N/mm. A. 2500 B. 1818.2 C. 2857.14 D. 1428.57 92. Calculate the maximum shear load on the welds in N/mm due to torsion produced by the eccentricity of the load to the center of the welds. A. 924.81 B. 1011.63 C. 863.41 D. 772.3 93. Calculate the maximum resultant shear load on the welds in N/mm. A. 3511.63 B. 2696.92 C. 3210.65 D. 3143.19 SIT. GG: A W600x110 beam is supported by a bearing plate 300 mm x 200 mm x 25 mm centered on a wall with a thickness of 300 mm. Properties of W600x110 beam are as follows: d = 600 mm, bf = 225 mm, tf = 18 mm, tw = 12 mm, K = 36 mm, fc’ = 24 MPa, fy = 248 MPa. The allowable bearing stress is 0.35 fc’, allowable bending stress is 0.75Fy and allowable web yielding stress is 0.66Fy. Determine the maximum reaction at the beam for the following conditions: 94. Considering the bearing of concrete wall. 13

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION

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MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

95. 96.

A. 1440 kN B. 712 kN C. 1224 kN D. 360 kN Considering bending of plates at a distance K if Fy = 345 MPa. A. 333.6 kN B. 248.9 kN C. 168.2 kN D. 193.5 kN Due to allowable web yielding stress at a distance (N + 2.5K). A. 569.61 kN B. 792.3 kN C. 436.6 kN D. 839.21 kN

SIT. HH: A timber purlin, 50 mm x 125 mm, is supported on rafters 2.4 m on center. The angle of the roof slope is 30° and the purlin are spaced 80 cm on centers. The total gravity load, including an estimated purlin weight, is 358.75 Pa of roof surface and a wind pressure of 250 Pa acting normal to the roof. The allowable bending stress used is 8 MPa. 97. Calculate the maximum bending moment about the strong axis acting on the purlin. A. 351 N-m B. 323 N-m C. 207 N-m D. 103 N-m 98. Calculate the bending stress due to maximum moment about the weak axis acting on the purlin. A. 0.79 MPa B. 0.92 MPa C. 1.36 MPa D. 1.98 MPa 99. Calculate the total bending stress on the purlin. A. 5.1 MPa B. 4.5 MPa C. 3.8 MPa D. 3.3 MPa SIT. II: A 50 mm by 100 mm timber is used as a column with fixed ends. 2

π EI P= ( KL )2 can be used 100. Determine the minimum length at which Euler’s formula, if E = 10 GPa and the proportional limit is 30 MPa. A. 1.18 m B. 1.66 m C. 2.36 m

D. 3.32 m

NSCP: SHEAR IN CONCRETE BEAMS Shear Strength Provided by Concrete Shear strength Vc , provided by concrete for non-prestressed member shall be computed as follows: SIMPLIFIED CALCULATION 1. For members subject to shear and flexure only,

V c=

1 f' b d 6√ c w

2. For members subject to axial compression,

V c=

N 1 1+ u 6 14 A g

(

)√

f ' c bw d

Quantity Nu/Ag shall be expressed in MPa Design Of Shear Reinforcement 14

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

SET

A

Where factored shear force Vu exceeds shear strength ϕVc, shear reinforcement shall be

φV n≥V u and V n =V c +V s where

provided to satisfy

Av f y d S Where Av is the area of shear reinforcement within spacing S. Minimum Shear Reinforcement A minimum area of shear reinforcement shall be provided in all reinforced concrete flexural members where factored shear force exceeds one half the shear strength provided by concrete φV c except for slabs and footings, concrete joint construction and beams V s=

with total depth not greater than 250 mm, two and one half times thickness of flange or one half the width of the web, whichever is greater. Where shear reinforcement is required the minimum area of the shear reinforcement shall be computed by bS Av= s 3f y Spacing Limits for Shear Reinforcement Spacing of shear reinforcement shall not exceed d/2 in non-prestressed members and (3/4)h in prestressed members or 600 mm. When Vs exceeds (1/3) half.

√ f 'c

bwd maximum spacing given above shall be reduced by one

NSCP: ALLOWABLE AXIAL COMPRESSIVE STRESS IN STEEL COMPRESSION MEMBERS

2π 2 E C c= Fy Limiting Slenderness Ratio,

√

Le r

If

[

F a= 1− Le r

If

intermediate column

2 ( Le / r ) F y

2C

c

≥C c 2

F a=

→

2

]

→

FS

where

3 5 3 ( L e / r ) ( Le / r ) FS= + − 3 8 Cc 8C 3 c

long column

12 π E 23 ( Le /r )2

15

SET

A

INSTRUCTIONS: Read the following problems and answer the questions, choosing the best answer among the choices provided. Shade the letter of your choices on the answer sheet provided. Shade letter E if your answer is not among the choices provided. Strictly no erasures. SIT. A: Three cable tensions T1, T2, and T3 act at the top of the flagpole. The resultant force for the three tensions is R = −400 kN.

1. 2. 3.

Find the magnitude of the cable tension T1. A. 79.4 N B. 767.8 N C. 158.85 N Find the magnitude of the cable tension T2. A. 151.6 N B. 621.55 N C. 591.23 N Find the magnitude of the cable tension T3. A. 220.3 N B. 396.61 N C. 440.67 N

D. 529.51 N D. 181.92 N D. 264.41 N

SIT. B: The light boom AB is attached to the vertical wall by a ball-and-socket joint at A and supported by two cables at B. A force P = 12i − 16k kN is applied at B. Note that RA, the reaction at A, acts along the boom because it is a two-force body. 4. Compute the cable tension BC. A. 5.82 kN B. 25.18 kN C. 13.13 kN D. 15.1 kN 5. Compute the cable tension BD. A. 14.95 kN B. 15.2 kN C. 8.31 kN D. 6.65 kN 6. Compute the reaction RA. A. 18.66 kN B. 6.22 kN C. 15.9 kN D. 19.5 kN SIT. C: A truss is loaded as shown in the figure. 7. Compute the forces in member GD given that P = 300 kN and Q = 50 kN. A. 412.5 kN B. 135.2 kN C. 202.81 kN D. 243.74 kN 8. If PCD = 600 kN and PGD = 100 kN (both compression), find P. A. 517 kN B. 37 kN C. 579 kN D. 572.3 kN

1

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

9.

If PCD =600 kN and PGD =100 kN (both compression), find Q. A. 37 kN B. 579 kN C. 5.17 kN

SET

A

D. 572.3 kN

SIT. D: A pin-connected frame is loaded as shown in the figure.

10. 11. 12.

Determine the reaction at B of the pin- connected frame. A. 1014.14 N B. 854.4 N C. 1139.5 N D. 1000 N Determine the reaction at C of the pin- connected frame. A. 711.11 N B. 1070.36 N C. 899.45 N D. 1201.73 N Determine the shear force acting on section 2 (just to the right of the 600-N load) of the pin-connected frame. A. 300 N B. 969 N C. 135 N D. 600 N

SIT. E: The man in the given figure is trying to move a packing crate across the floor by applying a horizontal force P. The center of gravity of the 250-N crate is located at its geometric center. The coefficient of static friction between the crate and the floor is 0.3. 13.

Determine the largest distance h for which the crate will slide without tipping. A. 0.7 m B. 0.8 m C. 0.9 m D. 1 m 2

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION

SET

A

MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

14. 15.

Calculate the force P required to cause tipping of the packing crate. A. 83.3 N B. 75 N C. 107.14 N D. 93.75 N Determine the minimum coefficient of static friction that permits tipping. A. 0.3 B. 0.31 C. 0.2 D. 0.33

SIT. F: Cable AB supports the uniformly distributed load of 2 kN/m. The slope of the cable at A is zero.

16. 17. 18.

Compute the maximum tensile force in the cable. A. 180 B. 90 C. 210 Compute the minimum tensile force in the cable. A. 150 B. 180 C. 90 Compute the length of the cable. A. 62.83 m B. 74.72 m C. 78.54 m

D. 150 D. 30 D. 70.69 m

SIT. G: The 12-kN weight is suspended from a small pulley that is free to roll on the cable. The length of the cable ABC is 18 m.

19.

Determine the horizontal force P that would hold the pulley in equilibrium in the position x = 4 m. A. 1.5 kN B. 1.7 kN C. 1.9 kN D. 2 kN

SIT. H: A circular steel rod of length L and diameter d hangs in a mine shaft and holds an ore bucket of weight W at its lower end. Unit weight of steel is 77 kN/m3. 3

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

20. 21.

SET

A

Calculate the maximum stress in the rod if L = 40 m, d = 8 mm, and W = 1.5 kN. A. 29.84 MPa B. 32.92 MPa C. 31.1 MPa D. 91.12 MPa Calculate the total elongation of the rod. A. 6.28 mm B. 5.97 mm C. 6.57 mm D. 6.12 mm

SIT. I: A plastic bar ACB having two different solid circular cross sections is held between rigid supports as shown in the figure. The diameters in the left- and right-hand parts are 50 mm and 75 mm, respectively. The corresponding lengths are 225 mm and 300 mm. Also, the modulus of elasticity E is 6.0 GPa, and the coefficient of thermal expansion a is 100µ/° C. The bar is subjected to a uniform temperature increase of 30° C. Calculate the following quantities:

22. 23. 24.

the compressive force P in the bar A. 51.8 kN B. 28.92 kN the maximum compressive stress A. 14.73 MPa B. 40.5 MPa the displacement of point C A. 0.403 mm B. 0.178 mm

C. 79.52 kN

D. 35.34 kN

C. 26.4 MPa

D. 18 MPa

C. 0.378 mm

D. 0.314 mm

SIT. J: A steel strut S serving as a brace for a boat hoist transmits a compressive force P = 54 kN to the deck of a pier as shown in the figure. The strut has a hollow square cross section with wall thickness t = 9 mm and the angle θ between the strut and the horizontal is 40°. A pin through the strut transmits the compressive force from the strut to two gussets G that are welded to the base plate B. Four anchor bolts fasten the base plate to the deck. The diameter of the pin is dpin = 18 mm, the thickness of the gussets is tG = 16 mm, the thickness of the base plate is tB = 10

4

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION

SET

A

MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

mm, and the diameter of the anchor bolts is dbolt = 12 mm. Determine the following stresses:

25. 26. 27.

the bearing stress between the strut and the pin. A. 53.05 MPa B. 166.67 MPa C. 127.67 MPa the shear stress in the pin. A. 68.2 MPa B. 136.4 MPa C. 106.103 MPa the bearing stress between the pin and the gussets. A. 93.75 MPa B. 71.82 MPa C. 29.84 MPa

D. 106.103 MPa D. 81.28 MPa D. 59.683 MPa

SIT. K: The channel section carries a uniformly distributed load totaling 6W and two concentrated loads of magnitude W.

28. 29.

30.

Determine the moment of inertia about the neutral axis of the channel section. A. 17.25x106 mm4 B. 18.7x106 mm4 C. 19.28x106 mm4 D. 15.96x106 mm4 Determine the maximum allowable value for W if the working stresses are 40 MPa in tension and 80 MPa in compression A. 6.9 kN B. 6.93 kN C. 6.24 kN D. 7.48 kN Determine the maximum allowable value for W if the working stress is 24 MPa in shear. A. 50.4 kN B. 67.2 kN C. 33.6 kN D. 16.8 kN

SIT. L: The force P = 100 kN is applied to the bracket as shown in the figure.

5

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

31. 32. 33.

Compute the bending moment on the bracket. A. 11 kN-m B. 20.53 kN-m C. 8.08 kN-m Compute the normal stress developed at point A. A. 29.14 MPa (C) B. 10.08 MPa (C) C. 22 MPa (C) Compute the normal stress developed at point B. A. 55.9 MPa (T) B. 33.92 MPa (T) C. 10.08 MPa (T)

SET

A

D. 49.14 kN-m D. 28.1 MPa (C) D. 44 MPa (T)

SIT. M:A sign of dimensions 2.0 m x 1.2 m is supported by a hollow circular pole having outer diameter 220 mm and inner diameter 180 mm as shown in the figure. The sign is offset 0.5 m from the centerline of the pole and its lower edge is 6.0 m above the ground. The sign is acted by a wind pressure of 2.0 kPa.

34. 35. 36.

Determine the normal stress at point A at the base of the pole. A. 54.91 MPa B. 49.92 MPa C. 47.56 MPa D. 42.31 MPa Determine the resultant shear stress at point B at the base of the pole. A. 7.0 MPa B. 6.24 MPa C. 0.38 MPa D. 0.51 MPa Determine the maximum shear stress at point A at the base of the pole. A. 28.2 MPa B. 28.1 MPa C. 27.46 MPa D. 24.97 MPa 6

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

SET

A

SIT. N: The steel rod fits loosely inside the aluminum sleeve. Both components are attached to a rigid wall at A and joined together by a pin at B. Because of a slight misalignment of the pre-drilled holes, the torque T0 = 750 N∙m was applied to the steel rod before the pin could be inserted into the holes. Use G = 80 GPa for steel and G = 28 GPa for aluminum. 37. Determine the angle of twist on the steel due to the applied T0. A. 6.41° B. 5.91° C. 3.26° D. 4.67° 38. Determine the torque in the steel after T0 was removed. A. 251 N∙m B. 499 N∙m C. 265 N∙m D. 485 N∙m 39. Determine the torque in the aluminum after T0 was removed. A. 251 N∙m B. 499 N∙m C. 265 N∙m D. 485 N∙m

SIT. O: The rigid bars ABC and CD are supported by pins at A and D and by a steel rod at B. There is a roller connection between the bars at C.

40. 41. 42.

Compute the stress in the steel rod. A. 83.33 MPa B. 125 MPa C. 133.33 MPa D. 37.5 MPa Compute the elongation of the steel rod due to the 50-kN load. A. 1.25 mm B. 2 mm C. 1.75 mm D. 1.875 mm Compute the vertical displacement of point C caused by the 50-kN load. A. 3 mm B. 1.875 mm C. 2.63 mm D. 2.813 mm

SIT. P: Cantilever beam AC has a total length of 8m which carries dead load of 10 kN/m, live load of 5 kN/m and a moving wheel load of 15 kN and 10 kN that are 3 meters apart. Using the concept of influence lines, 43. Determine the maximum positive shear at B. A. 100 kN B. 150 kN C. 200 kN D. 250 kN 44. Determine the maximum negative moment at B. A. 292.15 kN∙m B. 282.5 kN∙m C. 325.6 kN∙m D. 266.67 kN∙m 45. Determine the maximum reaction at A. 7

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

A. 115 kN

B. 145 kN

SIT. Q: Given the continuous beam below, 46. Determine the maximum moment. A. 7.16 kN∙m B. 16.93 kN∙m 47. Determine the reaction at A. A. 16.89 kN B. 14.45 kN 48. Determine the reaction at B. A. 16.89 kN B. 14.45 kN

SET

A

C. 125 kN

D. 135 kN

C. 20.54 kN∙m

D. 13.55 kN∙m

C. 17.56 kN

D. 19.77 kN

C. 17.56 kN

D. 19.77 kN

SIT. R: A simply supported beam AD has the following loads indicated in the figure, determine the following in terms of EI. 49. θa E. 120.67/EI F. 525.67/EI G. 326.41/EI H. 156.37/EI 50. Value of x, where x is the location of the maximum deflection of the beam from the left E. 5.836 m F. 4.41 m G. 4.38 m H. 5.66 m 51. Determine the maximum deflection of the beam E. 374/EI F. 167.72/EI G. 486/EI H. 328/EI SIT. S: Given the floor framing below, the floor carries a superimposed dead load of 4kPa and live load of 3kPa on floor BCON, beam EFGH is 300x600 mm and the thickness of the slab is 100mm. 52. Determine the reaction at E. A. 24.96 kN B. 24.32 kN C. 27.84 kN D. 30.06 kN 53. Determine the moment at G. A. 74.8 kN∙m B. 63.7 kN∙m C. 89.18 kN∙m D. 92.4 kN∙m 54. Determine the reaction at F. A. 60.64 kN B. 57.76 kN C. 61.28 kN D. 55.54 kN SIT. T: A rectangular beam 375 mm wide and 500 mm deep is reinforced with 4-28 mm bars with bar centroid 75 mm from the bottom edge of the beam. The beam is acted by a total service moment of 95 kN∙m. Use modular ratio n = 9. 55. Determine the cracking moment for the section shown if f’ c = 28 MPa and if the

56. 57.

modulus of rupture f r =0 .7 √ f ' c . A. 68.5 kN∙m B. 115.76 kN∙m C. 94.72 kN∙m D. 57.88 kN∙m Determine the maximum compressive stress on concrete due to service loading. A. 6.67 MPa B. 7.98 MPa C. 5.56 MPa D. 8.2 MPa Determine the tensile stress in the steel bars. A. 11.66 MPa B. 104.97 MPa C. 92.6 MPa D. 76.74 MPa

SIT. U: A singly reinforced rectangular beam is to be designed, with effective depth approximately 1.5 times the width, to carry a service live load of 21.9 kN/m in addition to 8

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

SET

A

dead load of 3.6 kN/m, on a 7.3 m simple span. Material properties are f y = 415 MPa and f’c = 27.6 MPa. Consider bar centroid of 60 mm from the edge of the beam. 58. Determine the required gross depth of the beam if ρ = 0.6ρmax. A. 510 mm B. 450 mm C. 540 mm D. 500 mm 59. Determine the required width of the beam. A. 290 mm B. 300 mm C. 260 mm D. 320 mm 60. Determine the required area of steel reinforcement. A. 1612.446 mm2 B. 1725.56 mm2 C. 1296.1 mm2 D. 1963.31 mm2 SIT. V: A rectangular beam with width b = 610 mm, total depth h = 355 mm and effective depth to the tensile steel d = 290 mm, is constructed using materials with strengths fy = 415 MPa and f’c = 27.6 MPa. Tensile reinforcement consists of two 36 mm bars plus three 32 mm bars in one row. Compression reinforcement consisting of 32 mm bars is placed at distance 64 mm from the compression face. 61. Determine the depth of the stress block. A. 105.18 mm B. 75.99 mm C. 89.4 mm D. 123.74 mm 62. Determine the nominal moment strength of the beam. A. 357.95 kN∙m B. 441.92 kN∙m C. 397.72 kN∙m D. 404.67 kN∙m 63. Determine the maximum service uniform live load in addition to self-weight of the beam if it spans 6 m on simple supports. A. 48.93 kN/m B. 39.05 kN/m C. 43.73 kN/m D. 37.71 kN/m SIT. W: The section of a monolithic floor system is shown in the figure. The section has a 7.3 m simple span.

64.

65. 66.

Determine the depth of the stress block for one of the T-beams when the beam collapses if fy = 415 MPa and f’c = 34.5 MPa A. 18.46 mm B. 13.9 m C. 15.23 mm D. 16.39 mm Determine the nominal moment strength of one of the T-beams. A. 491.4 kN∙m B. 489.46 kN∙m C. 498.38 kN∙m D. 490.86 kN∙m Determine the maximum floor factored load the T-beams can sustain. A. 73.48 kN/m B. 66.39 kN/m C. 66.13 kN/m D. 66.32 kN/m 9

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

SET

A

SIT. X: A tied column 450 mm square is reinforced with 8-ϕ25 mm equally distributed on its sides. The unsupported length of the column is 2.6 m and is prevented to sidesway by shear walls. K 1.0, f’c = 20.7 MPa and fy = 415 MPa. Use 40 mm covering of tie reinforcement with diameter 12 mm. Es = 200 GPa. 67. Determine the location of the plastic centroid from the right face. A. 250 B. 200 C. 225 D. 275 68. Determine the nominal axial load in kN when concrete strain is 0.003 and yield strain of steel is y = fy/Es. A. 1684 B. 1541 C. 1178 D. 1098 69. Determine the nominal moment in kN·m to this nominal axial load. A. 482 B. 405 C. 434 D. 440 SIT. Y: A beam of 280 mm width and effective depth of 410 mm carries a factored uniformly distributed load of 77.4 kN/m, including its own weight, in addition to a concentrated factored load of 53.4 kN at midspan. Clear span is 5.5 m on simple supports. 70. Calculate the factored shear force at critical section for shear. A. 207.816 kN B. 290.94 kN C. 239.55 kN D. 247.3 kN 71. Calculate the required spacing of 10-mm stirrups with fy = 275 MPa. Consider the nominal shear stress on concrete is fv = 0.88 MPa.

A. 120 m B. 130 mm C. 100 mm D. 140 mm 72. Through what part of the beam from the face of the left support is web reinforcement theoretically required? A. 50 mm B. 2640 mm C. 2750 mm D. 2540 mm SIT. Z: A rectangular footing 2.4 m x 3 m x 0.45 m thick supports a rectangular column 300mm x 400 mm at its center, with short dimensions parallel with each other. Column loads are service conditions: DL = 680 kN LL = 400 kN f’c = 20.7 MPa fy = 275 MPa Concrete cover to the centroid of steel reinforcement = 100 mm 73. Calculate the nominal beam-shear stress acting at the critical section of the footing slab in MPa. A.) 0.724 MPa B.) 0.619 MPa C.) 0.546 MPa D.) 0.526 MPa 74. Calculate the ultimate punching-shear stress acting at the critical section of the footing slab in MPa. A.) 1.83 MPa B.) 1.55 MPa C.) 1.413 MPa D.) 1.242 MPa 75. Calculate the maximum factored bending moment on the footing slab in kN∙m. A.) 459.68 B.) 374.85 C.) 245.48 D.) 166.6 SIT. AA: A 6 m long cantilever T-beam, with properties shown in the figure, carries a concentrated live load of “F” at the free end. To prevent excessive deflection of the beam it 10

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION

SET

A

MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

is pre-tensioned with 12-mm-diameter strands causing an initial pre-stressing force of 740 kN.

A = 180,000 mm2 217 mm

INA = 4150x106 mm4

283 mm

76.

77.

78.

Determine the resulting stress due to initial pre-stressing force and self-weight of the beam at the bottom fiber at the fixed end if the strands are placed at the centroid of the section. A. 8.18 MPa (C) B. 9.41 MPa (C) C. 1.19 MPa (T) D. 2.40 MPa (T) Determine the resulting stress due to pre-stressing force and total dead load at the top fiber at the fixed end if the strands are placed 140 mm above the neutral axis of the beam and pre-stress loss is15%. A. 2.35 MPa (C) B. 5.46 MPa (C) C. 4.03 MPa (C) D. 2.79 MPa (T) Determine the live load “F” that will make the stress at the top fiber at the fixed end zero. A. 12.85 kN B. 6.83 kN C. 10.26 kN D. 9.35 kN

SIT. BB: The connection shown in the figure uses 20 mm diameter A325 bolts. The tension member is A36 steel (Fy = 248 MPa, Fu = 400 MPa) and the gusset plate is A572 steel (Fy = 290 MPa, Fu = 415 MPa). Determine the strength of the connection considering the following modes of failure: 9 mm gusset plate 37.5 mm P

75 mm 37.5 mm

12 mm x 150 mm 37.5 mm 75 mm 79.

Net section fracture with allowable stress 0.5Fu. A. 168 kN

80.

B. 264 kN

C. 248 kN

D. 267 kN

Bearing on plate holes with allowable stress 1.2Fu. A. 358.60 kN

81.

37.5 mm

B. 362.88 kN

C. 460.80 kN

D. 483.84 kN

Block shear with Ft = 0.5Fu and Fv = 0.3Fu. 11

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION

SET

A

MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

A. 184.68 kN

B. 270.86 kN

C. 294.84 kN

D. 348.09 kN

SIT. CC: A W12x79 of A573 Grade 60 (Fy = 415 MPa) steel is used as a compression member. It is 8.5 m long, fixed at the top and bottom, and has additional support in the weak direction at the midpoint. Properties of the section are as follows: A = 14,500 mm2 82.

Calculate the effective slenderness ratio with respect to strong axis buckling. A. 31.82

83.

B. 44.55

C. 55.71

D. 111.43

Calculate the effective slenderness ratio with respect to weak axis buckling. A. 22.28

84.

Ix = 258.6 x 106 mm4 Iy = 84.375 x 106 mm4

B. 27.86

C. 39.00

D. 55.71

Calculate the axial load capacity of the column. A. 1,709 kN

B. 2 905 kN

C. 2 523 kN

D. 2 444 kN

SIT. DD: A W356x383 is designed to carry a compressive force due to dead load and live load P = 1,900 kN with a bending moment of 285 kN∙m about the strong axis. The unbraced length is 4.5 m with K = 1.25 for bending about the strong axis and K = 1.10 for bending about the weak axis. Use Cm = 0.85 for both directions. Allowable stresses are F bx = 0.66Fy, Fby = 0.75Fy and Fa = 128 MPa where Fy = 248 MPa. Section properties are A = 48,774 mm2, Sx = 6.8x106 mm3, Sy = 2.638x106 mm3, rx = 170.40 mm, ry = 104.90 mm. 85.

Calculate the ratio of the actual to the allowable axial stress. A. 0.228

86.

C. 0.304

D. 0.389

Calculate the value of the moment magnification factor for bending about the strong axis. A. 0.89

87.

B. 0.261

B. 0.85

C. 1.05

D. 0.94

Calculate the value of the interaction formula using fa C mx f bx Cmy f by + + ≤1 Fa fa fa 1− F 1− F F ' ex bx F ' ey by

(

) (

)

12 π 2 E F ' e= 23 ( kL/r )2 Where A. 0.532

B. 0.560

C. 0.545

D. 0.574

SIT. EE: In the connection shown in the figure FIG. F, A 502−I bearing type bolts with threads in shear are used with 12 mm diameter. Allowable shear stress is Fv=120 MPa. Allowable bearing stress is 480 MPa and allowable tensile stress is 150 MPa. Assume the service load passes through the centroid of the rivet group.

12

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

88. 89. 90.

Determine the shear stress in the bolt if P=200 kN . A. 98.01 MPa B. 153.14 MPa C. 88.41 MPa Calculate the bearing stress if P=200 kN . A. 160.38 MPa B. 127.52 MPa C. 185.19 MPa Find the maximum value of P by tension on bolts. A. 153.71 kN B. 169.65 kN C. 195.89 kN

SET

A

D. 176.84 MPa D. 119.47 MPa D. 339.29 kN

SIT. FF: An angle 75 mm x 75 mm x 9 mm is welded to a plate to resist a load P = 500 kN acting through its centroid. The side welds have a nominal thickness of 8 mm.

91.

Calculate the direct shear load on the welds in N/mm. A. 2500 B. 1818.2 C. 2857.14 D. 1428.57 92. Calculate the maximum shear load on the welds in N/mm due to torsion produced by the eccentricity of the load to the center of the welds. A. 924.81 B. 1011.63 C. 863.41 D. 772.3 93. Calculate the maximum resultant shear load on the welds in N/mm. A. 3511.63 B. 2696.92 C. 3210.65 D. 3143.19 SIT. GG: A W600x110 beam is supported by a bearing plate 300 mm x 200 mm x 25 mm centered on a wall with a thickness of 300 mm. Properties of W600x110 beam are as follows: d = 600 mm, bf = 225 mm, tf = 18 mm, tw = 12 mm, K = 36 mm, fc’ = 24 MPa, fy = 248 MPa. The allowable bearing stress is 0.35 fc’, allowable bending stress is 0.75Fy and allowable web yielding stress is 0.66Fy. Determine the maximum reaction at the beam for the following conditions: 94. Considering the bearing of concrete wall. 13

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION

SET

A

MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

95. 96.

A. 1440 kN B. 712 kN C. 1224 kN D. 360 kN Considering bending of plates at a distance K if Fy = 345 MPa. A. 333.6 kN B. 248.9 kN C. 168.2 kN D. 193.5 kN Due to allowable web yielding stress at a distance (N + 2.5K). A. 569.61 kN B. 792.3 kN C. 436.6 kN D. 839.21 kN

SIT. HH: A timber purlin, 50 mm x 125 mm, is supported on rafters 2.4 m on center. The angle of the roof slope is 30° and the purlin are spaced 80 cm on centers. The total gravity load, including an estimated purlin weight, is 358.75 Pa of roof surface and a wind pressure of 250 Pa acting normal to the roof. The allowable bending stress used is 8 MPa. 97. Calculate the maximum bending moment about the strong axis acting on the purlin. A. 351 N-m B. 323 N-m C. 207 N-m D. 103 N-m 98. Calculate the bending stress due to maximum moment about the weak axis acting on the purlin. A. 0.79 MPa B. 0.92 MPa C. 1.36 MPa D. 1.98 MPa 99. Calculate the total bending stress on the purlin. A. 5.1 MPa B. 4.5 MPa C. 3.8 MPa D. 3.3 MPa SIT. II: A 50 mm by 100 mm timber is used as a column with fixed ends. 2

π EI P= ( KL )2 can be used 100. Determine the minimum length at which Euler’s formula, if E = 10 GPa and the proportional limit is 30 MPa. A. 1.18 m B. 1.66 m C. 2.36 m

D. 3.32 m

NSCP: SHEAR IN CONCRETE BEAMS Shear Strength Provided by Concrete Shear strength Vc , provided by concrete for non-prestressed member shall be computed as follows: SIMPLIFIED CALCULATION 1. For members subject to shear and flexure only,

V c=

1 f' b d 6√ c w

2. For members subject to axial compression,

V c=

N 1 1+ u 6 14 A g

(

)√

f ' c bw d

Quantity Nu/Ag shall be expressed in MPa Design Of Shear Reinforcement 14

MOCK BOARD EXAMINATION: DESIGN AND CONSTRUCTION MAPUA INSTITUTE OF TECHNOLOGY DEPARTMENT OF CEGE

SET

A

Where factored shear force Vu exceeds shear strength ϕVc, shear reinforcement shall be

φV n≥V u and V n =V c +V s where

provided to satisfy

Av f y d S Where Av is the area of shear reinforcement within spacing S. Minimum Shear Reinforcement A minimum area of shear reinforcement shall be provided in all reinforced concrete flexural members where factored shear force exceeds one half the shear strength provided by concrete φV c except for slabs and footings, concrete joint construction and beams V s=

with total depth not greater than 250 mm, two and one half times thickness of flange or one half the width of the web, whichever is greater. Where shear reinforcement is required the minimum area of the shear reinforcement shall be computed by bS Av= s 3f y Spacing Limits for Shear Reinforcement Spacing of shear reinforcement shall not exceed d/2 in non-prestressed members and (3/4)h in prestressed members or 600 mm. When Vs exceeds (1/3) half.

√ f 'c

bwd maximum spacing given above shall be reduced by one

NSCP: ALLOWABLE AXIAL COMPRESSIVE STRESS IN STEEL COMPRESSION MEMBERS

2π 2 E C c= Fy Limiting Slenderness Ratio,

√

Le r

If

[

F a= 1− Le r

If

intermediate column

2 ( Le / r ) F y

2C

c

≥C c 2

F a=

→

2

]

→

FS

where

3 5 3 ( L e / r ) ( Le / r ) FS= + − 3 8 Cc 8C 3 c

long column

12 π E 23 ( Le /r )2

15