a force system is shown.
1. Which of the following most nearly gives the resultant of the force system in Newtons?
A. 72
B. 96
C. 84
D. 77
2. Which of the following most gives the angles that ht eresultant force make with the horizontal (positive counterclockwise)
A. 58.4°
B. 63.4°
C. 45.6°
D. 52.2°
3. Which of the following most nearly gives the distance from the origin where the resultant force crosses the X-axis.
A. 6m
B. 6.5m
C. 5.5m
D. 5m
Solution:
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Dry soil is mixed with 17% by weight with water and then compacted. The moist soil has a volume of 1 x 10-3 m3 and a mass of 1.6kg. The soil solids have specific gravity of 2.70.
Determine the following:
1. What is the dry unit weight of the soil in kN/m3?
A. 14.25
B. 13.42
C. 12.54
D. 15.63
2. What is the void ratio of the soil?
A. 97.4%
B. 86.35%
C. 95.85%
D. 92.54%
3. What is the degree of saturation of the soil?
A. 32.21%
B. 25.87%
C. 47.12%
D. 52.32%
Solution:
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A 600-mm non-rigid pipe takes water from a large reservoir. The velocity of flow in the pipe is 2.5 m/s. The flow is suddenly stopped by a quick-closing valve situated 400 m from the reservoir. The pipe is 20mm thick and modulus of elasticity of pipe material is 1.4 x 1011Pa. Bulk modulus of elasticity of water is 2.2 x 109Pa.
1. Compute for the value of the celerity of pressure wave in m/s.
A. 1532
B. 1223
C. 1142
D. 1358
2. Compute for the time for the pressure wave to travel round trip along the pipe.
A. 0.74sec
B. 0.96sec
C. 0.85sec
D. 0.65sec
3. What is the maximum water hammer pressure developed on the pipe due to instantaneous closure of the valve?
A. 3057 kPa
B. 3185 kPa
C. 3263 kPa
D. 3321 kPa
Solution:
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A pump draws 20 liters per second of water from reservoir C and lifts it to reservoir D as shown. The head lost from C to 1 is three times the velocity head in the 150-mm suction line and the head lost from 2 to D is fifteen times the velocity head in the 100-mm discharge line.
1. What is the power delivered by the pump to the system?
A. 62.6 horsepower
B. 64.5 horsepower
C. 75.6 horsepower
D. 87.4 horsepower
2. What is the pressure head at point 1 in meters of water?
A. 32.56m
B. 48.57m
C. 19.74m
D. 15.23m
3. What is the pressure head at point 2 in meters of water?
A. 187.56m
B. 264.63m
C. 321.27m
D. 242.33m
Solution:
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A closed conical tank, upright is position, has a bottom radius of 30cm and a height of 65cm.
1. What is the total volume of the tank in cubic meter?
A. 0.0541
B. 0.0963
C. 0.0852
D. 0.0613
2. If the tank contains 0.022m3 of water, how much water is required to fill the tank?
A. 0.0236m3
B. 0.0147m3
C. 0.0586m3
D. 0.0393m3
3. If the tank contains 0.022m3 of water, what is the depth of water in the tank?
A. 0.09m
B. 0.05m
C. 0.08m
D. 0.12m
Solution:
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A 10-m wide rectangular channel have a flow of 17.6 m3/s when the depth of flow is 1.20m. Use n= 0.014.
1. Compute for the value of the minimum specific energy in meter.
A. 1.32m
B. 1.02m
C. 0.85m
D. 1.63m
2. What is the normal slope?
A. 0.00055
B. 0.00022
C. 0.00044
D. 0.00033
3. What is the average boundary shearing stress in Pa?
A. 4.18Pa
B. 6.85Pa
C. 25.87Pa
D. 102.45Pa
Solution:
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Three sides of a triangle measure 16cm, 24cm, and 20cm, respectively. What is the median to the 20-cm side?
A. 17.78cm
B. 18.32cm
C. 16.92cm
D. 20.59cm
Solution:
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The upper base of a frustum of a rectangular pyramid is 2.5m x 4m and its altitude is 5m. If its volume is 116.67 m3 what is the area of the lower base?
A. 38m2
B. 40m2
C. 44m2
D. 64m2
Solution:
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Solve for y from the following complex equation:
2x + 5y + 3yi + 15 – 3i = 0.
A. 2
B. -5
C. -10
D. 1
Solution:
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When f(x) = x4 + ax3 + 7x2 + bx + 6 is divided by (x-2) the remainder is 16 and when divided by (x+1) the remainder is 10. What is the value of a?
A. -7
B. 11
C. -5
D. 3
Solution:
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What is the arithmetic mean of the following set of numbers?
-14, -4, -10, 5, -1, -12
A. -6
B. 6
C. 5
D. -5
Solution:
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The upper base diameter of the frustum of a right circular cone is 2m and the lower base diameter is 4m. if its altitude is 5m find its lateral area.
A. 55.21 m2
B. 43.98 m2
C. 48.06 m2
D. 32.87 m2
Solution:
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Two sides of a triangle are measuring 20cm and 28cm, respectively. If the area of the triangle is 227.125 cm2, what is the measure of the third sides in cm?
A. 22
B. 23
C. 24
D. 25
Solution:
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A polygon has twenty-four sides. How many are its diagonals?
A. 222
B. 212
C 232
D. 252
Solution:
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The steel frame is braced against joint translation (sideways). The girders have moment of inertia I=0.0003107 m4 and the columns have I=0.0000457m4. The columns are properly attached to footings. Use the alignment chart
Multipliers for Rigidly Attached Members
| Condition at far-end of girder |
Sideways Inhibited |
Sideways Uninhibited |
| Pinned |
1.5 |
0.5 |
| Fixed against rotation 2 |
2 |
0.67 |
1. Which of the following most nearly gives the stiffness of column C5?
A. 2.12 x 10-5
B.1.24 x 10-5
C. 1.58 x 10-5
D. 3.21 x 10-5
2. Which of the following most nearly gives the G on top of column C3?
A. 0.48
B. 0.69
C. 0.12
D. 0.32
3. Which of the following most nearly gives the effective length of column C3?
A. 2.44m
B. 2.68m
C. 3.21m
D. 2.87m
Solution:
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Samples for strength tests of each class of concrete placed each day shall be taken not less than once a day, or not less than once for every 120cubic meters of concrete, or not less than once for each 500 square meters of surface area for slabs or walls.
The first paragraph states the provision for the frequency of testing for concrete. It is required to determine the required number of test sample per day for the following item.
Column : 1m x 1m x 3.5m 12pcs
Beam : 1m x 1.7m x 6m 17pcs
Slab : 6m x 3m x 0.3m 8pcs
Shear wall : 6m x 3m x 0.3m 4pcs
1. Which of the following gives the volume of concrete in columns in cubic meter?
A. 58
B. 42
C. 22
D. 174
2. Which of the following gives the total area of shear wall in square meter?
A. 160
B. 124
C. 72
D. 288
3. Which of the following gives the required number of test per day according to NSCP?
A. 3
B. 2
C. 4
D. 1
Solution:
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The implementing rules and regulations of P.D. 1594 states that for a unit price contract, quantity overruns or underruns of not more than 15% of the estimates per major pay item and 25% er minor item need not be covered by a Change Order provided that the same is authorized by the approving authority of the contract. Major items are defined as pay items representing at least 20% of the AAE or the first two items having the highest percentage of the AAE, or those indicated/ specified in the instruction to bidders.
The quantities and contract prices of a project are as follows:
| |
Quantity |
Unit AAE |
Unit Contract Price |
| Item 1 |
100 |
7000 |
8000 |
| Item 2 |
200 |
5500 |
6000 |
| Item 3 |
500 |
5000 |
6000 |
| Item 4 |
200 |
4000 |
3500 |
| Item 5 |
500 |
4800 |
5000 |
| Item 6 |
320 |
6000 |
5000 |
| Item 7 |
440 |
3500 |
4000 |
| Item 8 |
600 |
6000 |
10000 |
1. Which of the following most nearly gives the cost of labor and equipment per kilogram?
A. P4.3
B. P6.3
C. P7.9
D. P5.2
2. Which of the following most nearly gives the cost of materials per kilogram?
A. P14.11
B. P10.47
C. P18.21
D. P15.52
3. Which of the following most nearly gives the unit cost of the project per kilogram?
A. P30.21
B. P38.65
C. P20.14
D. P25.47
Solution:
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A project has been bid out by the Department of Public Works and Highways. The approved agency estimate (AAE) is P1000M. The results of four bids are as follows:
Bidder A ………………….. P1300
Bidder B ………………….. P700
Bidder C ………………….. P500
Bidder D ………………….. P900
Note: All units are in thousand of pesos.
The implementing rules and regulations of P.D. 1594 states that no award of contract shall be made to a bidder whose bid price is higher than the allowable government estimate (AGE) or the Approved Agency Estimate (AAE), whichever is higher, or lower than 70% of the AGE. The allowable government estimate (AGE) is defined as one half the sum of the AAE and the average of all responsive bids, for the purposes of determining the average of responsive bids, bids higher than 120% of the AAE or lower than 60% of the AAE shall not be considered. No. negotiation will be allowed to bring down the bid to the level of the AAE/AGE.
1. Which of the following gives the maximum bid to be considered is responsive bid, in millions of pesos:
A. P1300
B. P1100
C. P1200
D. P900
2. Which of the following gives the minimum bid to be considered as responsive bid, in millions of pesos:
A. P900
B. P1200
C. P600
D. P800
3. Which of the following gives the complete list of responsive bidders:
A. Bidders B & D
B. Bidders A & C
C. Bidders B, C, & D
D. Bidders A, B, & D
Solution:
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A rectangular reinforced concrete beam has a width of 300mm and an effective depth of 450mm to tension bars. The beam is reinforced with six 32-mm-diameter tension bars and two 28-mm-diameter compression bars with centroid 65mm from extreme concrete fiber. Concrete strength fc=34.5MPa and steel strength fy=345MPa. Assume that the contribution of the compression steel cannot be neglected and that compression steel yields.
1. Which of the following most nearly gives the balanced steel ratio if the beam were singly reinforced:
A. 0.044
B.0.033
C. 0.055
D. 0.022
2. Which of the following most nearly gives the balanced steel ratio for doubly reinforced considering the effect of the compression steel:
A. 0.048
B. 0.059
C. 0.062
D. 0.053
3. Which of the following most nearly gives the ultimate moment capacity of the beam in KiloNewton-Meter.
A. 632
B. 724
C. 517
D. 571
Solution:
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The beam shown is 50mm wide and 200mm deep. The 100-kN load acts at the centroid of the beam. Include the shearing stress caused by the load.
1. Which of the following most nearly gives the shearing stress at B in the x-axis in MegaPascals:
A. 80
B. 85
C. 75
D. 70
2. Which of the following most nearly gives the shearing stress at B in xy-plane in MegaPascals:
A. 8.54
B. 9.74
C. 10.98
D. 12.32
3. Which of the following most nearly gives the direction (angle) of the principal stress in the xy-plane in degrees.
A. 7.8
B. 8.2
C. 9.6
D. 12.4
Solution:
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Rotation of the radically slotted arm shown is governed by θ = 0.2t + 0.02t3, where θ is in radians and t is in seconds. Simultaneously, the power screw in the arm engages the slider B and controls its distance from O according to r = 0.2 + 0.04t2, where r is in meters and t is in seconds.
1. Which of the following most nearly gives the x-coordinate of the slider after 3 seconds:
A. 0.234m
B.0.453m
C. 0.167m
D. 0.56m
2. Which of the following most nearly gives the velocity of the slider after 3 seconds in m/s:
A. 0.48
B. 0.67
C. 0.54
D. 0.89
3. Which of the following most nearly gives the acceleration of the slider after 3 seconds in m/s2:
A. 0.723
B. 0.678
C. 0.601
D. 0.622
Solution:
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A particle with a mass of 0.75 kg has an initial velocity of u=6m/s in the direction shown. Forces F1 and F2 act on the particle, and their magnitudes change with time according to the graphical schedule shown.
1. Which of the following most nearly gives the y-component of particles velocity after 3 seconds, in m/s.
A. 9.8
B.12.4
C. 6.1
D. 14.5
2. Which of the following most nearly gives the particle’s velocity after 3 seconds, in m/s?
A. 14.3
B. 12.5
C. 15.8
D. 16.2
3. Which of the following most nearly gives the direction of the particle from the x-axis after 3 seconds (positive counterclockwise):
A. 113°
B. 125°
C. 136°
D. 102°
Solution:
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The cantilever beam shown is loaded with a counterclockwise couple of 60 kN-m 1 m from the fixed end and a uniformly distributed load of 5 kN/m over 3m from the free end.
1. Which of the following give the moment at A in KiloNewton-Meter.
A. -9
B.-7.5
C. -6
D. -8.5
2. Which of the following gives the shear at C in KiloNewton-Meter.
A. 15
B. 20
C. 10
D. 25
3. Which of the following give the moment at C in KiloNewton-Meter.
A. -20.5
B. -18.5
C. -25
D. -22.5
Solution:
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A triaxial test is conducted on a clay specimen and the following results were obtained: cohesion = 32kPa, angle of internal friction = 28°, shearing stress at failure plane = 61 kPa.
1. What is the maximum normal stress in kPa?
A. 114
B. 69
C. 147
D. 156
2. What is the confining stress in kPa?
A. 23.6
B. 17.8
C. 11.2
D. 32.7
3. What is the normal stress at failure plane?
A. 60.2
B. 54.5
C. 45.3
D. 72.8
Solution:
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A 4.2m thick layer of sand is underlain by a layer of clay. The water table is 2m below the ground (sand) surface. For sand, Gs = 2.65 and the average void ratio is 0.52. The sand above water table has a degree of saturation of 0.37. The saturated nit weight of the clay layer is 20.2 kN/m3.
1. Determine the unit weight of sand above water table in kN/m3
A. 17.86
B. 20.46
C. 10.65
D. 18.35
2. Determine the total stress at a point 10m below the ground.
A. 199 kPa
B. 123 kPa
C. 232 kPa
D. 167 kPa
3. Determine the effective stress at a point 10m below the ground.
A. 134.5 kPa
B. 120.4 kPa
C. 156.9 kPa
D. 111.1 kPa
Solution:
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A confined aquifer is shown. This aquifer has a source of recharge located as shown. The hydraulic conductivity of the aquifer is 40m/day with porosity of 25%. The piezometric (head) surface in the two observation wells 1250m apart are at elevation 65m and 60m, respectively from the common datum. The aquifer has an average thickness of 25m and an average width of 4km.
1. Determine the nearest value to the rate of flow of water through the aquifer, in cubic meters per day.
A. 14,000
B. 16,000
C. 18,000
D. 15,000
2. Determine the nearest value to the seepage velocity in m/day.
A. 0.76
B. 0.42
C. 0.54
D. 0.64
3. Determine the nearest value to the time of travel from the head of aquifer to a point 3.4km downstream, in days.
A. 4876
B. 6325
C. 5313
D. 5874
Solution:
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A soil sample taken from subgrade have a density of 1900 kg/m3 with moisture content of 11%. Laboratory tests reveals that the soil solids have density of 2660 kg/m3 and the maximum and minimum void ratios of the soil mass are 0.63 and 0.44, repectively.
1. Determine the nearest value to the dry unit weight of the soil in kN/m3.
A. 17.4
B. 16.8
C. 16.1
D. 18.3
2. Determine the relative density of the sample.
A. 0.554
B. 0.654
C. 0.425
D. 0.722
3. Determine the relative density of the sample.
A. 0.63
B. 0.54
C. 0.40
D. 0.48
Solution:
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An examination has two types of questions as follows:
Type A: 10 points at 3 minutes each
Type B: 15 point at 6 minutes each
There are 16 questions in the exam for a total time of 60 minutes.
1. How many Type A questions are there in the examination?
A. 4
B. 12
C. 10
D. 6
2. How many Type B questions are there in the examination?
A. 12
B. 10
C. 4
D. 6
3. What is the maximum score of this exam?
A. 160 points
B. 180 points
C. 190 points
D. 170 points
Solution:
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A 3-m square plate is immersed in water in a vertical position such that the two edges of the square are horizontal. The immersion is such that the center of pressure on the plate is 10cm from its center of gravity.
1. Determine the distance from the water surface to the center of pressure.
A. 6.5m
B. 6.75m
C. 7.5m
D. 6m
2. Determine the distance from the water surface to the center of pressure.
A. 7.6m
B. 7.5m
C. 6.6m
D. 6.5m
3. Determine the distance from the water surface to the center of pressure.
A. 662 kN
B. 612 kN
C. 856 kN
D. 587 kN
Solution:
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A conical tank with lower base radius of 35cm and 65cm tall contains 0.025m3 of water.
1. What is the total volume of the tank in m3?
A. 0.0912
B. 0.0732
C. 0.0834
D. 0.0891
2. What is the depth of water in the tank in meters?
A. 0.0672
B. 0.0789
C. 0.0728
D. 0.0842
3. How much water must be added to fill the tank in m3?
A. 0.0482
B. 0.0583
C. 0.0641
D. 0.06621
Solution:
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A calibration test of a 0.00785-m2 circular sharp-edged orifice in a vertical side of a large tank showed a discharge of 22,300 N of water in 1minute & 40 seconds at a constant head of 1.20m. Measurement of the jet showed that it traveled 1.92m horizontally while dropping 0.8m.
1. Determine the coefficient of discharge.
A. 0.621
B. 0.597
C. 0.649
D. 0.721
2. Determine the coefficient of velocity.
A. 0.84
B. 0.93
C. 0.74
D. 0.98
3. Determine the coefficient of contraction.
A. 0.77
B. 0.97
C. 0.61
D. 0.67
Solution:
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A 1.6kg soil specimen have a volume of 1 x 10-3 m3 and moisture content of 12%. Specific gravity of soil solids is 2.5.
1. What is the dry density of this soil in kg/m3?
A. 1356
B. 1567
C. 1429
D. 1632
2. What is the void ratio of this soil?
A. 85%
B. 78%
C. 75%
D. 72%
3. What is the degree of saturation?
A. 40%
B. 35%
C. 30%
D. 45%
Solution:
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Water is flowing in a 200-mm diameter rigid pipe that is 650m long. The increase in pressure caused by instantaneous closure of the valve near the exit is 700kPa. Bulk modulus of elasticity of water is 2.07 x 109 Pa.
1. What is the celerity of pressure wave in m/s?
A. 1439
B. 1621
C. 1256
D. 1176
2. What is the maximum discharge in m3/s?
A. 0.0188
B. 0.0279
C. 0.0232
D. 0.0153
3. What water hammer pressure is expected if the valve is closed in 3 seconds?
A. 289kPa
B. 187kPa
C. 342kPa
D. 211kPa
Solution:
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An area is bounded by the curve y = sin x and the x-axis from x = 0 to x=π.
1. What is the area bounded by the curve?
A. 2.4
B. 4.1
C. 2.0
D. 3.2
2. How far above the x-axis is the centroid of the area?
A. 0.452
B. 0.276
C. 0.393
D. 0.321
3. Find the volume generated by revolving the area about the x-axis.
A. 5.446
B. 6.773
C. 4.453
D. 4.935
Solution:
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A vertical sag parabolic curve is to connect a -2% grade to a +3% grade. The change in grade per meter station must be 0.2%. The PT of the curve is at Station 25 + 325 and elevation 25.42m.
1. What is the elevation of the PC of the curve?
A. 21.12 m
B. 26.44 m
C. 23.45 m
D. 22.92 m
2. What is the length of the curve?
A. 450 m
B. 550 m
C. 500 m
D. 600 m
3. What is the stationing of the PC of curve?
A. 24+750
B. 24+865
C. 24+825
D. 24+625
Solution:
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