A three-hinged arch is shown in the figure.
1. Which of the following most nearly gives the vertical reaction at A in KiloNewtons:
A. 31
B. 36
C. 28
D. 23
2. Which of the following most nearly gives the total reaction at the hinge in KiloNewtons:
A. 45.2
B. 85.6
C. 54.1
D. 32.3
3. Which of the following most nearly gives the total reaction at B in KiloNewtons:
A. 32.3
B. 45.2
C. 85.6
D. 54.1
Solution:
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Concrete beam 8meters long and spaced 4m center-to-center are used to support a concrete slab 115 mm thick. The beams have effective depth of 650 mm measured from the slab surface, bw=300mm, and are reinforced for tension only with six 28-mm-diameter bars. The beams are to be analyzed as T-beams. Steel yield strength fy=350MPa and concrete strength fc=21MPa.
1. Which of the following most nearly give the width of slab effective as T-beam, in millimeters?
A. 2000
B. 2140
C. 4000
D. 3250
2. Which of the following most nearly give the depth of compression block in millimeters?
A. 36.2
B. 45.2
C. 56.3
D. 62.4
3. Which of the following most nearly give the nominal moment capacity of the beam in KiloNewton-Meter.
A. 563
B. 784
C. 952
D. 817
Solution:
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Steel column 3.6m long and hinged at both ends is used to carry an axial load of 800kN. The column is subject to end moments about its strong axis (single curvature) with M1 = 90%M2. The frame is braced against joint translation and is not subjected to any transverse loading. Fy =248MPa, E=200GPa.
The properties of the section are as follows:
A=0.013 m2 rb=94 mm
Sx=0.00099 m2 K=1.0
1. Which of the following most nearly gives the computed (actual) axial stress of the column in MegaPascals.
A. 57
B. 75
C. 62
D. 68
2. Which of the following most nearly gives the allowable axial compressive stress of the column in MegaPascals.
A. 114
B. 120
C. 133
D. 148
3. From a separate calculation with Fb = 149MPa, which of the following most nearly gives the maximum moment that the column can carry, in KiloNewton-Meter.
A. 85.6
B. 75.4
C. 71.4
D. 78.8
Solution:
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The implementing rules of PD 1594 defines an unbalanced bi as a bid containing one or more pay items that are 30% higher than the unit allowable government estimate (AGE) in respect to major items whereas other pay items are priced lower than the unit AGE. AGE is defined as one-half the sum of the AAE and the average of all responsive bids. For purposes of determining the average of all responsive bids, bids higher than 120% of the AAE or lower than 60% of the AAE shall not be considered. Major items are defined as pay items representing at least 20% of the AAE or those indicated or specified in the instruction to bidders. The responsive bids for a government project with 8 bid items are as follows (all cost figures are in thousands of pesos):
| |
Qty |
Total AAE |
Bidder A |
Bidder B |
Bidder C |
| Item 1 |
100 |
1,000 |
1,000 |
1,250 |
750 |
| Item 2 |
100 |
20,000 |
22,000 |
16,000 |
19,000 |
| Item 3 |
500 |
5,000 |
4,000 |
6,100 |
5,100 |
| Item 4 |
60 |
6,000 |
6,000 |
4,800 |
5,600 |
| Item 5 |
1,000 |
3,000 |
2,900 |
3,300 |
2,800 |
| Item 6 |
400 |
1,600 |
1,000 |
1,600 |
2,100 |
| Item 7 |
3,000 |
3,000 |
2,500 |
2,400 |
3,200 |
| Item 8 |
20 |
25,000 |
31,000 |
20,000 |
26,000 |
1. Which of the following most nearly gives the total AAE in thousand pesos:
A. 64,600
B. 54,800
C. 48,000
D. 71,000
2. Which of the following give the complete list of major item?
A. Item 8
B. Items 2,4 & 8
C. Items 2,3,4, & 8
D. Items 2 & 8
3. Which of the following gives the complete list of unbalanced bids?
A. Bidders A, B, C
B. Bidders A, C
C. Bidders A
D. All are balanced bids
Solution:
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The area in the first quadrant is bounded by the curve shown in the figure.
1. Which of the following most nearly gives the area in square units?
A. 2330
B. 2130
C. 2230
D. 2030
2. Which of the following most nearly gives the location of the centroid of the area from the y-axis?
A. 52
B. 48
C. 42
D. 58
3. Which of the following most nearly gives the location of the centroid of the area from the x-axis?
A. 20
B. 10
C. 15
D. 25
Solution:
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Bill of quantity is to be prepared for guardhouse 3.6 m in height with one door opening only and a height of 2.1m as shown. Assume density of steel equal to 7860 kg/m3. CHB is 200 mm x 400 mm and 150 mm thick.
1. Which of the following most nearly gives the total length of 12mm bars in meters:
A. 72
B. 65
C. 86
D. 58
2. Which of the following most nearly gives the weight of 12mm bars in Kilogram per meters:
A. 0.89
B. 0.75
C. 0.93
D. 0.63
3. Which of the following most nearly gives the total weight of 12mm bars in Kilograms:
A. 44
B. 58
C. 77
D. 64
Solution:
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A 4-m single span beam having a cross-section of 300mm x 500 mm carries a uniformly distributed load throughout its span. The beam is 80% stress grade Apitong with allowable bending stress of 16.5 MegaPascals, allowable shearing stress of 1.73 MPa and modulus of elasticity of 7.31 GigaPascals. Allowable deflection is 1/240 of the span.
1. Which of the following most nearly gives the value of the uniform load without exceeding the allowable bending stress of the beam, in KiloNewton per Meter.
A. 118
B. 103
C. 132
D. 124
2. Which of the following most nearly gives the value of the uniform load without exceeding the allowable shearing stress of the beam, in KiloNewton per Meter.
A. 63
B. 54
C. 87
D. 75
3. Which of the following most nearly gives the value of the uniform load without exceeding the allowable deflection, in KiloNewton per Meter.
A. 102
B. 98
C. 124
D. 114
Solution:
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A group of friction piles is shown in figure. The total load on the pile less the soil displaced by the footing is 1800kN. The clay is 16m thick. Ground water table is located 2m below the clay surface.
1. Compute for the effective pressure the mid height of the consolidating clay layer, in kPa.
A. 186.4
B. 174.8
C. 147.6
D. 163.5
2. Compute for the compression index of the clay.
A. 0.297
B. 0.245
C. 0.325
D. 0.288
3. What is the approximate settlement of the foundation?
A. 150 mm
B. 168 mm
C. 214 mm
D. 198 mm
Solution:
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A test is set-up as shown. A cylindrical mold 4” in diameter is filled with silt to height H1 = 0.2 ft, whose coefficient of permeability k1 = 6.1 x 10-4 ft/min.
A second coaxial mold is placed on top of the first mold whose inside diameter is d=1.5” and whose height is H2 = 0.30 ft. Its thickness is negligible. The inside of this second mold is filled with the same silt, but the annular ring outside the small tube and outer tube is filled with sand whose coefficient of permeability is k2 = 2.5 x 10-3 ft/min.
The test set-up is a permeameter of constant head. Water is placed in the mold and maintained at a level h=1.4ft. above the level of the outlet. It may be considered that the system consists of a fictitious soil of thickness H=H1 + H2 and coefficient of permeability kf.
The following general equations may be useful:
kv eq = H/[(H1/kv1) + (H2/kv2) + … + (Hn/kvn)]
kv eq = (1/H)[kh1H1 + kh2H2 + … + khnHn]
1. What is the total flow of water in ft3/min?
A. 2.148 x 10-4
B. 3.521 x 10-4
C. 2.554 x 10-4
D. 2.874 x 10-4
2. What is the equivalent coefficient of permeability, kf, in ft/min?
A. 1.045 x 10-3
B. 1.563 x 10-3
C. 1.874 x 10-3
D. 1.245 x 10-3
3. What is the total amount of water that percolated after 30minutes?D. 325.32 cm3
A. 217.12 cm3
B. 187.54 cm3
C. 256.32 cm3
D. 325.32 cm3
Solution:
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A cut slope was excavated in a saturated clay. The slope made an angle of 60° with the horizontal. When slope failure occurs, distance BC is 8m. Given: Stability number, m=0.185: γ=17 kN/m3; cu = 20kPa.
1. What is the stability factor?
A. 6.32
B. 5.41
C. 4.57
D. 9.36
2. Determine the critical depth of cut in meters.
A. 7.52
B. 6.36
C. 6.87
D. 5.21
3. What is the angle of failure plane in degrees?
A. 19.5
B. 25.4
C. 22.5
D. 28.6
Solution:
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A 4-meter thick sand layer is overlying a very thick dense clay layer. The water table is 2.5m below the ground (sand) surface. The sand have void ratio of 52% and the degree of saturation above water table is 37%. The clay has moisture content of 42%. Assume specific gravity of solids for both sand and clay equal to 2.65.
1. Compute for the value of the unit weight of sand above water table.
A. 18.8 kN/m3
B. 18.3 kN/m3
C. 19.3 kN/m3
D. 17.5 kN/m3
2. Compute for the value of the total stress at a depth of 10m from the ground surface, in kPa.
A. 174.5
B. 181.4
C. 196.3
D. 186.7
3. Compute for the value of the effective stress at a depth of 10m from the ground surface, in kPa.
A. 98.6
B. 132.4
C. 124.5
D. 107.8
Solution:
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A triaxial test was conducted on a cohesionless soil. At failure plane, the normal stress is 500kPa and the shearing stress is 300kPa.
1. What is the nearest value to the angle of internal friction of the soil?
A. 31°
B. 33°
C. 29°
D. 27°
2. What is the nearest value to the angle of failure plane?
A. 60.5°
B. 62.5°
C. 58.5°
D. 59.5°
3. What is the nearest value to the maximum principal stress in kPa?
A. 1280
B. 1240
C. 1030
D. 1150
Solution:
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Water flows on a straight 150m pipe, 600mm in diameter. The velocity of flow is 2.5m/s. Pipe thickness is 20mm. Bulk modulus of elasticity of water is 2.2 x 109 Pa. Modulus of elasticity of pipe material is 1.4 x 1011 Pa.
1. What is the composite modulus of elasticity of water?
A. 5.24 x 109 Pa
B. 4.67 x 109 Pa
C. 1.85 x 109 Pa
D. 1.49 x 109 Pa
2. Determine the celerity of pressure wave of water.
A. 1,365 m/s
B. 1,458 m/s
C. 1,056 m/s
D. 1,223 m/s
3. Determine the water hammer pressure assuming instantaneous closure.
A. 3,425 kPa
B. 3,057 kPa
C. 2,875 kPa
D. 3,254 kPa
Solution:
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A parallel pipe system is shown in the figure. The pressure head at A is 76m and the pressure head at B is 52m. Hazen Williams coefficient for all pipes C1 = 120.
1. Determine the nearest value to the flow in Line 1 in m3/s.
A. 0.103
B. 0.056
C. 0.214
D. 0.038
2. Determine the nearest value to the flow in Line 2 in m3/s.
A. 0.214
B. 0.038
C. 0.056
D. 0.103
3. Determine the nearest value to the total flow in m3/s.
A. 0.181
B. 0.164
C. 0.197
D. 0.214
Solution:
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Two pressurized tanks A & B are connected at the bottom by 140mm-diameter short pipe as shown in figure. The coefficients of velocity and contraction of the short pipe are 0.92 and 0.86, respectively.
1. What is the flow through the pipe in m3/s?
A. 0.214
B. 0.115
C. 0.187
D. 0.231
2. What is the head lost in meters?
A. 0.85
B. 0.53
C. 1.71
D. 1.32
3. What is the power lost in horsepower?
A. 2.59
B. 1.93
C. 2.98
D. 1.45
Solution:
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An open-top cylindrical tank 1 meter in diameter is 2.80m tall. The tank floats in water with a draft of 2.30 meters. Unit weight of lead is 110 kN/m3.
1. What is the weight of tank in KiloNewtons?
A. 19.54
B. 21.57
C. 15.24
D. 17.72
2. How much lead (in KiloNewtons) must be fastened to the outside bottom of the tank in order make it completely submerged in water?
A. 100m
B. 120m
C. 150m
D. 80m
3. How much lead (in KiloNewtons) must be place inside the tank in order make it completely submerged in water?
A. 4.87
B. 4.21
C. 3.85
D. 3.24
Solution:
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The implementing rules of PD 1594 defines an unbalanced bi as a bid containing one or more pay items that are 30% higher than the unit allowable government estimate (AGE) in respect to major items whereas other pay items are priced lower than the unit AGE. AGE is defined as one-half the sum of the AAE and the average of all responsive bids. For purposes of determining the average of all responsive bids, bids higher than 120% of the AAE or lower than 60% of the AAE shall not be considered. Major items are defined as pay items representing at least 20% of the AAE or those indicated or specified in the instruction to bidders. The responsive bids for a government project with 8 bid items are as follows (all cost figures are in thousands of pesos):
| |
Qty |
Total AAE |
Bidder A |
Bidder B |
Bidder C |
| Item 1 |
100 |
1,000 |
1,000 |
1,250 |
750 |
| Item 2 |
100 |
20,000 |
22,000 |
16,000 |
19,000 |
| Item 3 |
500 |
5,000 |
4,000 |
6,100 |
5,100 |
| Item 4 |
60 |
6,000 |
6,000 |
4,800 |
5,600 |
| Item 5 |
1,000 |
3,000 |
2,900 |
3,300 |
2,800 |
| Item 6 |
400 |
1,600 |
1,000 |
1,600 |
2,100 |
| Item 7 |
3,000 |
3,000 |
2,500 |
2,400 |
3,200 |
| Item 8 |
20 |
25,000 |
31,000 |
20,000 |
26,000 |
1. Which of the following most nearly gives the total AAE in thousand pesos:
A. 64,600
B. 54,800
C. 48,000
D. 71,000
2. Which of the following give the complete list of major item?
A. Item 8
B. Items 2,4 & 8
C. Items 2,3,4, & 8
D. Items 2 & 8
3. Which of the following gives the complete list of unbalanced bids?
A. Bidders A, B, C
B. Bidders A, C
C. Bidders A
D. All are balanced bids
Solution:
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Given the following road cross-section notes in cut:
Station 1000+100
2.75 1.00 0.50
9.45 0.00 4.50
Station 1000+220
2.50 1.25 0.80
8.50 0.00 6.00
Width of roadway is 8m.
1. Determine the area of cut at Station 1000+100 in square meter.
A. 13.475
B. 12.586
C. 15.663
D. 10.685
2. Determine the area of cut at Station 1000+220 square meter.
A. 12.586
B. 10.685
C. 13.475
D. 15.663
3. Determine the volume of cut using the end-area method in cubic meter.
A. 1,856.36
B. 1,748.25
C. 1,625.36
D. 1,997.58
Solution:
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A closed traverse ABCD has the following data:
| Line |
Length |
Bearing |
| AB |
122.00 |
N 30° E |
| BC |
149.00 |
N 60° E |
| CD |
241.00 |
S 10° E |
| DA |
159.00 |
N 70° W |
1. Determine the corrected bearing of side BC using compass rule.
A. N 59° 11’E
B. N 59° 11’E
C. N 60° 12’E
D. N 60° 49’E
2. Determine the corrected bearing of side CD using the compass rule.
A. 149.632 m
B. 148.368 m
C. 149.547 m
D. 148.453 m
3. Determine the corrected length of side BC using the compass rule.
A. 242.067 m
B. 241.852 m
C. 240.148 m
D. 239.933 m
Solution:
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A telephone company have a production capacity of 500,000 units per month. At its present capacity of 350,000 units per month, the company have a total monthly income of P350,000,000. The company has a fixed cost of P100,000,000 per month and a variable cost of P200 per unit.
1. What is the present profit or loss in millions of pesos?
A. 200
B. 210
C. 180
D. 190
2. What is the break-even quantity?
A. 135,000
B. 125,000
C. 155,000
D. 165,000
3. If the production is increased to 80% of its capacity, what is the profit or loss in millions of pesos?
A. 220
B. 250
C. 200
D. 190
Solution:
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The following data of road accident versus driver’s age form a quadratic equation:
Age of Driver Accident per year
20 250
40 150
60 200
1. Find the coefficient a of x2.
A. 0.1875
B. 0.1575
C. 0.2125
D. 0.1765
2. Find the coefficient b of x.
A. -14.75
B. -15.25
C. -17.75
D. -16.25
3. Find the number of accidents per year for an age of 30.
A. 154.75
B. 254.25
C. 189.65
D. 181.25
Solution:
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A 50-kg block is being pushed horizontally with a constant force F such that its acceleration is 1 m/s2. The coefficient of friction between the block and the surface is 0.40. The block has an initial velocity of 5 m/s.
1. What is the magnitude of the constant force F in Newtons?
A. 265.8
B. 246.2
C. 212.2
D. 302.7
2. What is the distance travelled by the block after 10 seconds?
A. 100m
B. 120m
C. 150m
D. 80m
3. What is the velocity by the block after 5 seconds?
A. 12 m/s
B. 15 m/s
C. 8 m/s
D. 10 m/s
Solution:
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Evaluate the following integrals:
Solution:
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Line A has a slope of 04 and passes through (-25, – 10). Line B has x-intercept of 10 and y-intercept of 25.
1. Determine the distance of line A to point (8, -3).
A. 35.85
B. 33.71
C. 30.21
D. 28.54
2. Determine the point of intersection of lines A and B.
A. (-90, 240)
B. (-90, 250)
C. (-80, 250)
D. (-80, 240)
3. Determine the equation of a line perpendicular to line B and passing through (-20, 10).
A. 2x – 5y – 90 = 0
B. 2x + 5y + 90 = 0
C. 2x + 5y – 90 = 0
D. 2x – 5y + 90 = 0
Solution:
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Answer the following problems:
1. Find the equation of the line parallel to 2x + y = 3 and normal to the curve y = x4
A. 8x + 4y + 9 = 0
B. 8x – 4y + 9 = 0
C. 32x + 16y – 17 = 0
D. 16x – 32y – 17 = 0
2. Find the angle of intersection of the curve x + xy = 1 and y3 = (x + 1)2.
A. 100m
B. 120m
C. 150m
D. 80m
3. Find the value of the second derivative of the curve y = x2 ex at x = -1.
A. -0.368
B. -0.421
C. -0.587
D. -0.699
Solution:
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The perimeter of a triangle is 102 cm and its area is 431.1554 square centimeters. Find the maximum diameter of a circle that can be inscribed in this triangle.
A. 7.63 cm
B. 12.45 cm
C. 9.54 cm
D. 8.45 cm
Solution:
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If a = 4 cos x + 6 sin x and b = 6 sin x – 4 cos x, what is the value of a2 + b2?
A. 32+40 sin2x
B. 16+2- sin2x
C. 40+32 sin2x
D. 20+16 sin2x
Solution:
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Two interior angles of a triangle measure 48° and 62°. If the perimeter of this triangle is 84cm, find the longest side of the triangle.
A. 28.91cm
B. 34.56cm
C. 30.76cm
D. 24.33cm
Solution:
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Salt is poured into a conical tank 100cm in diameter on top and 70cm high. If the volume of salt is 30,000 cm3, what is the depth of salt in the tank?
A. 45.21cm
B. 38.29cm
C. 31.25cm
D. 52.45cm
Solution:
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The lower and upper bases of a frustum of a pyramid measure 18cm x 18cm and 10cm x 10cm, respectively. If its lateral surface area is 448cm2, find the altitude of the pyramid.
A. 9.36cm
B. 8cm
C. 6.72cm
D. 6.93cm
Solution:
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What is the surface area of a sphere having a volume of 1904 cubic meters?
A. 856.3 m2
B. 742 m2
C. 624.7 m2
D. 1056.2 m2
Solution:
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A load of 6 KiloNewtons is supported as shown. They pulley weighs 2 KiloNewtons.
1. Which of the following most nearly gives the reaction at C in KiloNewtons:
A. 8
B. 10
C. 9
D. 11
2. Which of the following most nearly gives the reaction at B in KiloNewtons:
A. 30
B. 32
C. 41
D. 36
3. Which of the following most nearly gives the angle that the reaction at B make with the horizontal:
A. 21.5°
B. 29.6°
C. 24.8°
D. 22.4°
Solution:
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A three-span continuous beam is shown. The provisions of the 1992 National Structural Code of the Philippine relevant to this problem are also given in the second figure.
1. Which of the following most nearly gives the factored uniform load, in kiloNewtons per meter:
A. 6.32
B. 5.65
C. 7.45
D. 4.58
2. Which of the following most nearly gives the ultimate (factored) bending moment at G, in kiloNewton-meters:
A. 24.8
B. 21.9
C. 27.7
D. 32.2
3. Which of the following most nearly gives the ultimate (factored) bending moment at I, in kiloNewton-meters:
A. 16.5
B. 14.9
C. 12.4
D. 18.7
Solution:
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It is required to analyze the indeterminate truss shown. By superposition. The product AE = 10,000 where A is the cross-sectional area in m2 and E is the modulus of elasticity in Pascals.
1. Which of the following most nearly gives the relative displacement of joints B and D if member BD is removed, in meters?
A. 0.012
B. 0.004
C. 0.005
D. 0.008
2. Which of the following most nearly gives the relative displacement of joints B and D due to two unit loads (1 N) acting at joints B and D acting towards each other, if member BD is removed.
A. 0.001m
B. 0.003m
C. 0.004m
D. 0.002m
3. Which of the following most nearly gives the value of the force on member BD in Newtons?
A. 6.4
B. 7.3
C. 9.5
D. 7.9
Solution:
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It is required to construct the influence line for the beam shown.
1. Which of the following most nearly gives the ordinate of the influence line for the vertical reaction at A at a point 4m from A:
A. 0.33
B. 0.67
C. -0.33
D. -0.67
2. Which of the following most nearly gives the ordinate of the influence line for the shear at D at a point 4m from A:
A. 0.67
B. -0.33
C. -0.67
D. 0.33
3. Which of the following most nearly gives the ordinate of the influence line for the moment at D at a point 4m from A:
A. -0.67
B. 0.67
C. 0.33
D. -0.33
Solution:
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