STRUCTURAL ENGINEERING AND CONSTRUCTION Evaluation Exam
INSTRUCTION: INSTRUCTION: Select the correct answer for each of the following questions. Mark only one answer for each item by shading the box corresponding to the letter of the correct answer. 1.
2.
3.
4.
5.
A 2-N weight is swung in a vertical circle of 1m radius at the end of the cable that will brake if the tension exceeds 500 N. Find the angular velocity of the weight when the cable breaks. a. 254 rpm c. 472 rpm b. 394 rpm d. 502rpm What horizontal force can be applied to a 100-kg block in a level surface with a coefficient of friction of 0.2, which will cause 2 an acceleration of 2.5 m/s ? a. 244.5 N c. 100.8 N b. 446.2 N d. 507.1 N Three forces 20 N, 30 N and 40 N are in equilibrium. Find the angle between the 30 N and 40 N forces. O O a. 28.96 c. 21.65 O O b. 32.72 d. 30.84 A force of 200 lb acts on a block at an angle 0 of 28 with respect to the horizontal. The block is pushed 2 feet horizontally. What is the work done by this force? a. 230 J c. 328 J b. 510 J d. 480 J A metal specimen 36-mm in diameter has a length of 360 mm. A force of 300 kN elongates the length by 1.2 mm. What is the modulus of elasticity? a. 95.35 GPa c. 99.89 GPa b. 88.42 GPa d. 100.23 GPa
13.
What maximum torque can be applied to a solid 115 mm diameter shaft if its allowable torsional shearing stress is 50.23 MPa
14.
a.
20 kN-m
c. 30 kN-m
b.
15 kN-m
d. 25 kN-m
A solid circular steel column is to be design to carry an axial load of 620 kN. If the allowable axial stress is 46 MPa, what diameter of column is required?
15.
a.
151 mm
c. 141 mm
b.
121 mm
d. 131 mm
A cantilever beam 3 m long carries a
SITUATION V A floor opening in a building is to be closed by pouring a concrete slab. The proposed framing is composed of wood joist assumed to be simply supported and given with a total load of 4 kPa. 23. What is the maximum flexural stress in 40 mm x 190 mm wood joist if its span is 3 m and spaced at every 0.30 m on centers? a. 5.61 MPa c. 6.78 MPa b. 7.23 MPa d. 4.65 MPa 24. What is the maximum shearing stress in the said joists? a. 0.40 MPa c. 0.36 MPa b. 0.69 MPa d. 0.54 MPa
distributed load that varies uniformly from 40 kN/m at support to 20 kN/m at the tip. Determine the maximum moment. a.
120 kN-m
c. 150 kN-m
b.
130 kN-m
d. 140 kN-m
SITUATION III The allowable stresses for the splice shown are the following: 150 MPa for shear of rivets, 1.35Fy for bearing, 0.60Fy for tension and Fy = 250 MPa. Note: rivet holes are 2 mm bigger than the rivet diameter and the middle plate is 20 mm thick.
SITUATION VI An elevator weighing 9.8 kN moves upward from rest until it attains a velocity of 20 m/s after it travels a distance of 5 m. 25. Which of the following gives the acceleration of the elevator? 2 2 a. 30 m/s c. 55 m/s 2 2 b. 40 m/s d. 60 m/s 26. Which of the following gives the time which the elevator travels at this instant? a. 0.2 s c. 0.5 s b. 0.7 s d. 1.2 s 27. Which of the following gives the tension in the cable supporting the elevator? a. 49.77 kN c. 76.89 kN b. 97.46 kN d. 64.79 kN SITUATION VII The hanger for each chandelier in the grand ballroom of a five – star hotel is composed of a 2 m diameter ring weighing 2.5 kN/m and is
SITUATION I A rock is thrown at a level ground with an angle of
supported by 6 rods such that said ring will be 3 m below the ceiling support.
O
inclination of 22.78 and initial velocity of 54.23
28.
m/s. 6.
7.
8.
How long will it take to reach the ground? a.
4.28 s
c. 2.86 s
b.
6.25 s
d. 5.54 s
16.
joint capacity due to shear approximately approximately
How far would it reach horizontally? a.
210 m
c. 214 m
b.
222 m
d. 219
How high will it reach at it reaches zero
17.
21.89 m
c. 24.87 m
b.
22.63 m
d. 22.48 m
b.
1234.67 N
d. 1432.67 N
SITUATION II A mild steel column is hollow and circular in cross
What is the minimum required diameter of
25.4 mm
c. 28.65 mm
stress 124 MPa.
b.
30.79 mm
d. 36.97 mm
a.
5.32 mm
c. 6.70 mm
b.
4.41 mm
d. 3.09 mm
Find the maximum safe value of P without 773.6 kN 878.1 kN
c. 938.3 kN
30.
A square tied column 400 mm on each side is reinforced with 8 – 25 mm bars with fy = 275
d. 848.2 kN
Find the maximum safe value of P without
MPa. Assuming fc’ = 22 MPa, determine the
exceeding the allowable tensile stress.
ultimate axial load capacity of this column.
b.
What is the frictional resistance? c. 1243.76 N
d. 2.62 kN
a.
a.
O
inclined at angle of 25 with the horizontal. 2341.76 N
c. 2.76 kN
3.38 kN
each rod without exceeding the allowable
b.
A 300 kg box impends to slide down a ramp
a.
1.72 kN
equal to the bearing capacity.
a. 18.
9.
29.
a. b.
exceeding the allowable shearing stress
velocity? a.
Find the diameter of the rivets so that the
Find the tension in each rod.
579.3 kN 495.5 kN
c. 716.1 kN
a.
2250 kN
c. 2243 kN
d. 692.5 kN
b.
2239 kN
d. 2356 kN
31.
A reinforced concrete spiral column having a
SITUATION IV A rocket was fired at 350 m/s from a level ground
diameter of 500 mm carries an ultimate load
at an angle to reach a maximum range.
find the number of 28 mm diameter bars.
of 5000 kN. If fc’ = 25 MPa and fy = 400 MPa,
Compute the total time of flight.
a.
16
c. 17
section with an external 350 mm and internal
a.
15.75 s
c. 46.38 s
b.
18
d. 19
diameter of 300 mm. It carries a compressive axial
b.
50.46 s
d. 37.91 s
20.
load of 2000 kN. 10.
a.
12,487.26 m
c. 9,174.21 m
direct shear stress in the column?
b.
11,876.90 m
d. 14,294.55 m
b.
12.
Find the range.
Which of the following most nearly gives the a.
11.
19.
79.3 MPa 77.5 MPa
c. 76.8 MPa
21.
Find the maximum height reached by the rocket.
d. 78.4 MPa
Which of the following gives the shortening
a.
4197.25 m
c. 3121.82 m
of the column if its initial height is 5 m?
b.
1876.90 m
d. 2294.11 m
a.
1.69 mm
c. 1.96 mm
b.
1.73 mm
d. 1.85 mm
a.
15.72 MPa
c. 24..23 MPa
A simply supported wooden beam 120 mm x 180 mm and 6 m long carries a uniformly distributed load of 4 kN/m. Determine the horizontal shearing stress developed at layer 30 mm from the top for a section 1 m from the left support. a. 350 kPa c. 246 kPa
b.
17.92 MPa
d. 18.97 MPa
b.
A 150 mm x 250 mm timber beam is subjected to a maximum moment of 28 kNm. What is the maximum bending stress?
22.
309 kPa
d. 450 kPa
SITUATION VIII A rectangular footing, 0.70 m thick, 2.5 m wide along the y-axis and 3 m long along x-axis, supports concentrically a column 0.40 m square subjected to the following loads: Axial load = 1200 kN Moment about the y-axis = 360 kN-m 32. Determine the maximum soil pressure. a. 256 kPa c. 188 kPa b. 268 kPa d. 215 kPa 33. Determine the minimum soil pressure. a. 64 kPa c. 56 kPa b. 49 kPa d. 72 kPa SITUATION IX A rectangular beam has a width of 300 mm and an effective depth of 500 mm. The beam has a span of 6 m. If fy =280 MPa and fc’ = 28 MPa:
34.
Which of the following most nearly gives the
SITUATION XIII A structural member 2 m long, found to be 1.5 mm short when positioned in a framework. To enable the member to be fitted, it is heated uniformly along its length. E = 200 GPa, coefficient O of thermal expansion a= 0.000012 / C.
maximum steel area allowed by the code?
46.
Which of the following most nearly gives the balanced steel ratio?
35.
a.
0.0532
c. 0.0576
b.
0.0493
d. 0.0345
a.
4571 mm
2
b.
8659 mm
2
2
c. 7645 mm
d. 5546 mm
2
SITUATION X A 6 m simply supported reinforced concrete rectangular beam is 250 mm wide. The total depth is 600 mm and the effective depth is 500 mm. It is reinforced for tension only with 4 – 20 mm diameter bars. It carries a 120 mm thick slab and 6 3 m wide. The weight of concrete is 24 kN/m . fy = 280 MPa and fc’ = 30 MPa. The beam is to be analyzed using the strength design method. 36. Which of the following nearly gives the total uniform unfactored service dead load? a. 15.36 kN/m c. 20.88 kN/m b. 17.69 kN/m d. 19.67 kN/m 37. Which of the following most nearly gives the nominal capacity of the beam? a. 166.22 kN-m c. 156.7 kN-m b. 173.69 kN-m d. 149.6 kN-m 38. Which of the following most nearly gives the unfactored uniform live load capacity of the beam? a. 6.57 kN/m c. 8.57 kN/m b. 7.56 kN/m d. 5.12 kN/m SITUATION XI An 8 m simply supported footbridge consists of logs of constant diameters. Each log must be capable of carrying a uniform load of 12 kN/m. Allowable stresses are 8.5 MPa for bending and 0.82 MPa for shear and maximum allowable deflection is L/240. Neglect the log weight. Use E w = 12000 MPa. 39. What is the required log diameter not to exceed the allowable flexural stress? a. 435 mm c. 390 mm b. 460 mm d. 490 mm 40. Which of the following most nearly gives the diameter not to exceed the allowable shearing stress? a. 300 mm c. 310 mm b. 320 mm d. 290 mm 41. Which of the following gives the diameter of the log not to exceed the maximum deflection? a. 420 mm c. 425 mm b. 320 mm d. 300 mm 42. Which of the following is the most suitable diameter of log to be used in the footbridge? a. 460 mm c. 490 mm b. 425 mm d. 320 mm SITUATION XII The following are design data for a column footing: Column size = 450 mm x 450 mm Column load: DL = 1000 kN LL = 780 kN Soil bearing capacity = 240 kPa Depth of footing = 1.5 m 3 Concrete unit weight = 24 kN/m 3 Soil unit weight = 18 kN/m Thickness of the footing slab = 600 mm Steel covering = 100 mm 43. Find the effective soil pressure. a. 230.1 kPa c. 227.5 kPa b. 221.3 kPa d. 209.4 kPa 44. Find the minimum safe dimension of the isolated square footing. a. 3.86 m c. 2.92 m b. 2.81 m d. 2.78 m 45. Find the ultimate soil pressure at the bottom of the footing. a. 420.12 kPa c. 189.54 kPa b. 287.11 kPa d. 332.19 kPa
Which of the following gives the necessary temperature rise to enable the member to be fitted? O O a. 59.5 C c. 38.6 C O O b. 72.8 C d. 62.5 C 47. Which of the following gives the strain of the member? a. 0.075 c. 0.75 b. 0.0075 d. 0.00075 48. Which of the following gives the residual stress in the member when it cools to its original temperature? a. 100 MPa c. 150 MPa b. 200 MPa d. 250 MPa SITUATION XIV Steel railroad rail 10 m long are laid with a O clearance of 3 mm at a temperature of 15 C. -6 Coefficient of thermal expansion a= 11.7 x 10 O / C, E = 200 GPa. 49. Which of the following gives the temperature when the rails will just touch? o O a. 35.46 C c. 25.64 C O O b. 40.64 C d. 50.62 C 50. Which of the following gives the stress that will be induced in the rails at that temperature if there were no initial clearance? a. 54 MPa c. 48 MPa b. 80 MPa d. 60 MPa 51. Which of the following gives the gap O between rails at a temperature of 30 C? a. 1.245 mm c. 1.755 mm b. 2.215 mm d. 1.435 mm SITUATION XV For the given frame shown, analyze using cantilever method:
56.
A simply supported beam carries a uniform load of 24 kN/m. Use E = 200 GPa and I = 240 6
4
x 10 mm . Determine the deflection at a point 4 m from the left support.
57.
a.
78 mm
c. 62 mm
b.
58 mm
d. 45 mm
A reinforced concrete T- beam is to be designed for tension reinforcement only. The beam width is 250 mm and effective depth is 400 mm. The flange thickness is 100 mm and its effective flange width is 900 mm. The applied moment is 300 kN-m. Determine the area of tension steel reinforcement required. Use fc’ = 20.7 MPa and fy =414 MPa.
a. b.
4094 mm
2
c. 5105 mm
2166 mm
2
2
d. 3983 mm
2
SITUATION XVI A certain area is found to have the following properties: 6 4 Ix = 100 x 10 mm 6 4 Iy = 60 x 10 mm 6 4 Ixy = 15 x 10 mm 58. Find the minimum moment of inertia. a. b. 59.
60.
65 x 10
6
c. 40 x 10
55 x 10
6
6
d. 30 x 10
6
Determine the maximum moment of inertia. a.
105 x 10
6
c. 130 x 10
6
b.
120 x 10
6
d. 115 x 10
6
Find the angle that weakest axis makes with the x-axis. a.
10.35
O
c. 21.84
O
b.
15.34
O
d. 18.44
O
SITUATION XVII A s piral column has a diameter of 600 mm. If fc’ = 21 MPa and fy = 275 MPa: 61.
Which of the following gives the minimum diameter of spiral reinforcement?
62.
a.
10 mm
c. 12 mm
b.
16 mm
d. 20 mm
Which of the following gives the minimum number of longitudinal bars?
63.
a.
5
c. 8
b.
4
d. 6
Which of the following gives the percentage of spiral ratio?
52.
a.
22.5 kN
c. 82.5 kN
b.
62.5 kN
d. 45 kN
Which of the following gives the shear at column DF?
c. 1.246%
1.346%
d. 1.742%
a.
45 kN
c. 30 kN
b.
95 kN
d. 50 kN
SITUATION XVIII A projectile is fired upward to the right at an initial slope of 4 vertical and 3 horizontal and hits the ground at a point 2 m higher than the origin. The maximum height is attained 8 m away from the origin. 64. What is the initial velocity in kph?
54. Which of the following gives the moment at
support B?
65.
a.
12.79
c. 54.35
b.
37.65
d. 46.04
Determine the range of the projectile.
a.
160 kN-m
c. 140 kN-m
a.
12.46 m
c. 14.33 m
b.
150 kN-m
d. 120 kN-m
b.
18.76 m
d. 20.82 m
66. 55.
1.139%
b. Which of the following gives the axial load for column BD?
53.
a.
Find the total time of flight.
A 100 x 300 mm rectangular beam carries a
a.
2.27 s
c. 1.56 s
uniformly distributed load of
b.
1.87 s
d. 2.80 s
kN/m over
its entire simple span. If the maximum allowable bending stress is 8.27 MPa and maximum allowable shearing stress is 0.70
SITUATION XIX A prismatic beam is loaded as shown;
MPa, determine the safe span of the beam. a.
3.544 m
c. 2.554 m
b.
3.854 m
d. 3.124 m
67.
Which of the following gives the deviation at A, tA/C, from the tangent drawn at C? a.
4700/3EI
c. 2670/EI
b.
367/3EI
d. 467/EI
68.
a. b.
Which of the following gives the deviation at D, tD/C, from the tangent drawn at C?
69.
a.
-100/3EI
c. -1600/3EI
b.
-200/3EI
d. -2560/3EI
82.
Which of the following gives the deflection at D? a.
97/3EI
c. 89/3EI
b.
280/3EI
d. 366/3EI
SITUATION XX A concurrent force system in space is composed of three forces that act through the origin and the following points. P 1 = 126 kN (-1, 5, -3), P 2 = 93 kN (5, -4, 6), and P 3 = 38 kN(4, 1, -3). 70. Which of the following most nearly gives the x-component of the resultant force? a. 48.0 kN c. 32.9 kN b. 57.4 kn d. 61.5 kN 71. Which of the following most nearly gives the y – component of the resultant force? a. 84.52 kN c. 65.60 kN b. 71.55 kN d. 93.20 kN 72. Which of the following most nearly gives the magnitude of the resultant force? a. 82.5 kN c. 73.4 kN b. 97.0 kN d. 61.8 kN The properties of a given steel section are as 2 6 4 follows; A = 6000 mm , Ix = 50 x 10 mm , Iy = 6 4 6 4 120 x 10 mm , I xy = 75 x 10 mm . Compute the minimum radius of gyration. a. 19.32 mm c. 21.36 mm b. 22.43 mm d. 15.48 mm 74. What is the angle of twist for a solid aluminum rod 100 mm in diameter subjected to a twisting moment of 10 kN-m. The rod is 3 m long. G = 80 GPa. O O a. 2.93 c. 3.29 O O b. 2.19 d. 1.35
83.
81.
A triangular wooden beam width of 150 mm base and 300 mm height carries two concentrated loads of 20 kN at third points. If the simple span of the beam is 6 m, compute the maximum shearing stress of the beam.
A truck has wheel loads of 10 kN, 20 kN and 30 kN, separated at a distance 3 m and 5 m respectively. The truck crosses a bridge having a simple span of 15 m. What is the maximum shear on the beam of the bridge due to moving loads? a. 32 kN c. 52 kN b. 48 kN d. 36 kN
Which of the following most nearly gives the
84.
a.
600 N
c. 300 N
b.
200 N
d. 250 N
Which of the following most nearly gives the value of
85.
?
a.
52.452
O
c. 78.632
b.
61.045
O
d. 43.256
O O
Which of the following most nearly gives the value of a? a. b.
O
c. 49.53
O
d. 35.21
43.43 54.78
Find its nominal moment capacity. a. 174 kN-m c. 194 kN-m b. 276 kN-m d. 356 kN-m 92. Find the ultimate uniform load it can carry throughout its length. a. 18.78 kN/m c. 48.78 kN/m b. 38.78 kN/m d. 58.78 kN/m 91.
resultant of the 200-N and 400-N forces?
86.
SITUATION XXII A solid shaft in a rolling mill transmits 20 kW at 2 revolutions per second. The length of the shaft is 3 m and modulus of rigidity is 83,000 MPa. 78. Which of the following gives the torque carried by the shaft? a. 1.59 kN-m c. 2.69 kN-m b. 3.45 kN-m d. 4.81 kN-m 79. Which of the following gives the minimum diameter so that the allowable torsional shearing of 40 MPa will not be exceeded? a. 88 mm c. 59 mm b. 45 mm d. 76 mm 80. Which of the following gives the minimum diameter so that the allowable angle of twist O of 6 will not be exceeded? a. 29 mm c. 35 mm b. 49 mm d. 55 mm
c. 1.33 MPa d. 0.86 MPa
SITUATION XXII The concurrent forces shown are in equilibrium.
73.
SITUATION XXI A steel rod having a cross sectional area of 300 2 mm and a length of 150 m is suspended vertically from one end. It supports a tensile load of 20 kN at the lower end. The unit mass of steel is 7850 3 kg/m and E = 200 GPa. 75. Which of the following gives the elongation of the rod due to its weight? a. 8.7 mm c. 4.3 mm b. 6.3 mm d. 5.4 mm 76. Which of the following gives the elongation of the rod due to the tensile load? a. 60 mm c. 40 mm b. 45 mm d. 50 mm 77. Which of the following gives the total elongation of the rod? a. 58.7 mm c. 54.3 mm b. 56.3 mm d. 55.4 mm
0.58 MPa 0.48 MPa
93.
A steel pipe 1.5 m in diameter is required to carry an internal pressure of 750 kPa. If the allowable tensile stress is 140 MPa, determine the required thickness of the pipe. a. 4.56 mm c. 4.25 mm b. 5.12 mm d. 4.02 mm
SITUATION XXV A beam has a T – section built up by two plates as follows: 200 mm x 40 mm plate as flange and 100 mm x 20 mm plate as web. The maximum shear force acting on the beam is 60 kN. 94. Which of the following most nearly gives the moment of inertia of the section about the 4 neutral axis in mm a. 10,600,000 b. 39,000,000 c. 8,700,000 d. 24,500,000 95. Which of the following most nearly gives the shear stress at the neutral axis? a. 4.63 MPa c. 1.94 MPa b. 3.28 MPa d. 2.71 MPa 96. Which of the following most nearly gives the shear stress on the web at the junction of the web and the flange? a. 19.6 MPa c. 31.8 MPa b. 48.2 MPa d. 52.2 MPa
O O
Determine the ultimate moment capacity of a doubly reinforced rectangular concrete beam having the following properties: b = 350 mm
fy =345 MPa
d = 600 mm
As = 3265 mm
d’ = 63 mm
As’ = 775 mm
2
2
fc’ = 27.5 MPa
a.
501.4 kN-m
c. 551.2 kN-m
b.
587.7 kN-m
d. 606.3 kN-m
SITUATION XXIII A reinforced concrete T-beam has a slab thickness of 100 mm which is supported by 6.5 m span length beams casts monolithically with the slab. Spacing of beams is 2.4 m on centers and has a web width of 300 mm and effective depth of 485 mm. The beam carries a live load moment of 163 kN-m and a dead load moment of 84 kN- m. fc’ = 20.7 MPa and fy = 414 MPa. 87. Which of the following gives the effective width of the flange? a. 1750 mm c. 2400 mm b. 1900 mm d. 1625 mm 88. Which of the following gives the area of steel bars needed? 2 2 a. 3424.5 mm c. 1890.4 mm 2 2 b. 2064.3 mm d. 3212.6 mm 89. Which of the following gives the number of 28 mm diameter bars needed? a. 4 c. 5 b. 6 d. 8 SITUATION XXIV A 300 mm x 500 mm reinforced concrete beam (fy = 248 MPa and fc’ = 30 MPa) that is 12 m long is supported by hinge/roller at ends and mid span. It is reinforced by 4 – 25 mm diameter bars in tension and 2 – 25 mm diameter bars in compression. Effective concrete cover is 70 mm. 90. Find the depth of the rectangular stress block. a. 57.3 mm c. 26.1 mm b. 76.2 mm d. 63.7 mm
SITUATION XXV A block initially at rest slides down an inclined O plane at angle of 30 with the horizontal. The block is placed at a vertical distance of 6 m above the bottom of the inclined plane. The coefficient of kinetic friction between the block and the plane is 0.25. 97. Which of the following most nearly gives the acceleration of the block? 2 2 a. 2.45 m/s c. 2.36 m/s 2 2 b. 2.31 m/s d. 2.78 m/s 98. Which of the following gives the velocity of the block after it has traveled 3 m? a. 3.98 m/s c. 3.84 m/s b. 4.08 m/s d. 4.15 m/s 99. How long will it takes for the block to reach the bottom of the inclined plane? a. 3.02 s c. 2.89 s b. 2.94 s d. 3.09 s 100. A
400 N block slides on a horizontal plane by applying a horizontal force of 200 N and reaches a velocity of 10 m/s in a distance of 30 m from rest. Determine the coefficient of friction between the floor and the block. a. 0.66 c. 0.33 b. 0.45 d. 0.56
