A cantilever sheet-pile 8.2m long supports a 5-m high dry sand with dry density of 1.19 g/cc and angle of shearing resistance of 34°. The pile is embedded to a depth of 3.2m. The water table is at the bottom of the sheet pile.
1. What is the maximum active force that can act on the sheet-pile in kN?
A. 158
B. 324
C. 111
D. 211
2. What is the maximum passive resistance that can act on the sheet-pile in kN?
A. 211
B. 111
C. 158
D. 324
3. What passive resistance must be mobilized for stability?
A. 427
B. 262
C. 317
D. 285
Solution:
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A pre-stressed concrete pile, 350mm x 350mm in cross-section and 10m long, is to be driven in a clayey soil. The unconfined compression shear strength, qu of the soil is 110 kPa. Use Nc = 9 and α = 0.76, γ = 16 kN/m3.
1. What is the end bearing capacity of pile in kN.
A. 50.42
B. 78.62
C. 60.64
D. 80.65
2. Compute the skin friction in kN develop along the shaft of the pile.
A. 585.2
B. 635.8
C. 456.2
D. 863.2
3. Compute the capacity of the pile using a factor of safety of 2.
A. 323
B. 358
C. 253
D. 471
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 40 m/day with a porosity of 25%. The piezometric (head) surface in the two observation wells 1375m apart are at elevation 65m and 60m, respectively from the common datum. The aquifer has a 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. 13,221
B. 12,875
C. 15,652
D. 14,546
2. Determine the nearest value to the seepage velocity in m/day.
A. 0.324
B. 0.475
C. 0.582
D. 0.146
3. Determine the nearest value to the time of travel from the head of aquifer to a point 4km downstream, in days.
A. 5427
B. 7624
C. 6875
D. 8725
Solution:
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A soil sample having a volume of 1 x 10-3 m3 has a mass of 1950 grams and moisture content of 10%. The specific gravity of soil is 2.66
1. What is the nearest value of the dry density of the soil in kg/m3?
A. 1714
B. 1773
C. 1824
D. 1597
2. What is the nearest value to the void ratio in percent?
A. 50.1
B. 76.2
C. 42.5
D. 64.2
3. What is the nearest value to the degree of saturation in percent?
A. 74.2
B. 47.2
C. 53.1
D. 63.5
Solution:
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A granular soil sample taken from the field has a density of 1600 kg/m3. In a laboratory test, it was found out that the density of soil solids is 2600 kg/m3, the moisture content is 11.5%, and the void ratios at its densest and loosest states are 0.43 and 0.62, respectively. Determine the following:
1. The dry density in kg/m3.
A. 1532
B. 1814
C. 1704
D. 1652
2. The void ratio.
A. 0.56
B. 0.51
C. 0.36
D. 0.62
3. The relative density of the granular soil in percent.
A. 31
B. 65
C. 87
D. 51
Solution:
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A tri-axial test is conducted on a sand sample. The normal and shearing stresses on failure plane are 475 kPa and 350 kPa, respectively.
1. Determine the angle of shearing resistance.
A. 32.3°
B. 59.1°
C. 61.2°
D. 63.2°
2. Determine the angle that the failure plane makes with the horizontal.
A. 57.3°
B. 59.1°
C. 61.2°
D. 63.2°
3. What is the plunger stress in kPa?
A. 632.4
B. 869.5
C. 798.3
D. 812.7
Solution:
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A vertical tank having a horizontal cross-sectional area of 0.4 square meter has 0.0003m2 orifice at its bottom. The initial head on the orifice is h1 = 1.2m. It takes 312 second for the water level to drop from 1.2m to 0.6m.
1. What is the coefficient of discharge?
A. 0.65
B. 0.62
C. 0.68
D. 0.72
2. If C = 0.6, how long will it take for the water level to drop from 1.2m to 0.8m?
A. 202 s
B. 256 s
C. 185 s
D. 231 s
3. If C = 0.6, what is the head on the orifice after 240?
A. 0.52 m
B. 0.43 m
C. 0.85 m
D. 0.73 m
Solution:
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Water flows at the rate of 0.8 m3/s in a 900-m long pipe with a total head lost of 4m. Solve for the pipe diameter in mm by:
1. Darcy-Weisbach formula using f = 0.018.
A. 735
B. 715
C. 812
D. 793
2. Manning’s formula using n = 0.014.
A. 812
B. 735
C. 715
D. 793
3. Hazen-William’s formula using C1 = 130.
A. 812
B. 793
C. 735
D. 715
Solution:
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The elasticity and dimensions of a pipe leading from a reservoir are such that the celerity of pressure wave is 975m/s. The pipe has a length of 610m and a diameter of 1.2m. The flow is initially 0.85 m3/s.
1. What is the water hammer pressure for instantaneous valve closure?
A. 612.52 kPa
B. 731.25 kPa
C. 610.36 kPa
D. 680.74 kPa
2. What is the approximate water hammer pressure at the valve if it is closure in 4 s?
A. 188.8 kPa
B. 209.5 kPa
C. 212.1 kPa
D. 225.3 kPa
3. What pressure is expected when the discharge drops almost instantly from 0.85 m3/s to 0.28 m3/s?
A. 462.8 kPa
B. 550.5 kPa
C. 487.5 kPa
D. 510.2 kPa
Solution:
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A piece of metal weighs 250 N in air and 240 N in water.
1. Determine the volume of the piece of metal in cubic meter.
A. 0.0112
B. 0.0125
C. 0.0136
D. 0.0187
2. What is the unit weight of the metal in kN/m3?
A. 28
B. 25.74
C. 18.72
D. 31.22
3. What is the specific gravity of the metal?
A. 2.85
B. 2.62
C. 3.18
D. 1.91
Solution:
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A plane area is bounded by the curve y2=4x and the line y=x.
1. Find the area bounded by the curves.
A. 3.33
B. 3.67
C. 2.67
D. 2.33
2. How far from the x-axis is the centroid of the curve?
A. 2.5
B. 3.3
C. 2
D. 3
3. Find the volume generated if the area is revolved about the x-axis.
A. 42.8
B. 25.8
C. 38.5
D. 33.5
Solution:
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An equipment have a salvage value of P1 million at the end years. The straight-line depreciation charge is P2million.
1. What is the first cost of the machine?
A. P105 million
B. P101 million
C. P103 million
D. P110 million
2. What is its book value after 25 years?
A. P51 million
B. P55 million
C. P49 million
D. P45 million
3. At what year will its total depreciation be P30 million?
A. 14 years
B. 10 years
C. 18 years
D. 15 years
Solution:
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A projectile is fired upward to the right from the top of a 50-m high building with an initial velocity of 200 m/s and an angle of 60° with the horizontal. A wind of 5 m/s is blowing horizontally to the left.
1. Determine the maximum height above the building that the projectile can reach.
A. 1247 m
B. 1087 m
C. 1632 m
D. 1529 m
2. Compute the time for which the projectile reaches its maximum height.
A. 17.7 sec.
B. 18.2 sec.
C. 12.5 sec.
D. 9.6 sec.
3. Determine the y-component of the velocity with which is hits the ground.
A. 196 m/s
B. 201 m/s
C. 185 m/s
D. 176 m/s
Solution:
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The deflection angle from PC of two points A and B on a simple curve are 3°15’ and 8°15’, respectively. The chord distance between A and B is 40 m.
1. Find the length of curve from PC to A.
A. 32m.
B. 36m
C. 26m
D. 28m
2. Find the length of long chord from PC to B.
A. 62.3m
B. 65.9m
C. 71.4m
D. 76.8m
3. What is the radius of the curve?
A. 247.6m
B. 229.5m
C. 258.7m
D. 187.4m
Solution:
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Determine the derivative of y with respect to x of the following equations:
1. x=y3/3
A. 1/y2
B. y2
C. y-0.5
D. y0.5
2. y=1/(1-u) where u = 1/(1+x)
A. x2
B. –x-2
C. x-2
D. –x2
3. x=y3/3.
A. (3x)3/2`
B. (3x)-3/2
C. (3x)2/3
D. (3x)-2/3
Solution:
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Evaluate the following limits:
1. Limit of (x2-1)/(x-1) as x approaches 1.
A. 4
B. ¼
C. ½
D. 2
2. Limit of sin (1/x) as x approaches zero.
A. -0.99
B. -0.85
C. -0.75
D. -0.65
3. Limit of (x3-2x2+7)/(2x3+x-3) as x approaches infinity.
A. 2
B. 4
C. ½
D. ¼
Solution:
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Given the circle x2 + y2 – 6x + 12y + 9 = 9.
1. What is the radius of the circle?
A. 7.21
B. 6.71
C. 6.28
D. 8.63
2. Where is the center of the circle?
A. (3,-6)
B. (-3,-6)
C. (-3,6)
D. (3,6)
3. Find the shortest distance from the line y = 2x + 10 to the center of the circle.
A. 6.87
B. 10.24
C. 8.49
D. 9.84
Solution:
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Given an ellipse 16x2 + 25y2 + 128x – 150y + 38 = 0.
1. Determine the distance between the foci.
A. 4
B. 2.5
C. 3
D. 3.5
2. Determine the distance between the directrices.
A. 8.67
B. 9.67
C. 12.44
D. 8.33
3. Determine the center of the ellipse.
A. (-4,3)
B. (-4,-3)
C. (4,3)
D. (4,-3)
Solution:
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Given the Matrix A and its inverse matrix B:
1. Determine the value of x.
A. -2
B. 5
C. 1
D. -7
2. Determine the value of y.
A. 1
B. 5
C. -7
D. -2
3. Determine the value of.z.
A. -2
B. -7
C. 5
D. 1
Solution:
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A steel frame is braced against joint translation (sideway). The girders are W21 x 402 with I = 0.0051m4. The columns are W 21 x 93 with I = 0.00086 m4. It is required to determine the effective length of column KL using the alignment chart given. The subscripts A and B in the chart refer to the joints at the two ends of the column section being considered. The factor G is defined as
In which ∑ indicates a summation of all members rigidly connected to that joint. Ic is the moment of inertia and Lc the unsupported length of a column section, and Ig is the moment of inertia and Lg the unsupported length of a girder or other restraining member. In calculating G, only rigidly attached girders or columns are included.
For column ends supported by but not rigidly connected to a footing or foundation, G is theoretically infinity, but, unless actually designed as a true friction free pin, may be taken as “10” for practical designs. If the column end is rigidly attached to a properly designed footing, G may be taken as 1.0.
1. Which of the following most nearly gives the factor G for the top end of member KL.
A. 2.14
B. 1.54
C. 2.87
D. 1.77
2. Which of the following most nearly gives the factor G for the bottom end of member KL.
A. 2.57
B. 1.73
C. 1.54
D. 3.21
3. Which of the following most nearly gives the effective length of column KL in meters.
A. 2.95
B. 3.25
C. 2.64
D. 3.87
Solution:
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A spiral column 500-mm in diameter is reinforced with 8-28mm diameter bars as shown. The interaction diagram for the column is also given.
1. Which of the following most nearly gives the reinforcement ratio in percent.
A. 0.025
B. 0.032
C. 0.016
D. 0.041
2. Which of the following most nearly gives the ratio of eccentricity to column dimension in the direction of bending.
A. 0.40
B. 0.30
C. 0.25
D. 0.35
3. Which of the following most nearly gives the nominal load capacity of the column.
A. 2800
B. 2600
C. 2700
D. 2500
Solution:
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A 200mm wide and 260mm deep Apitong is used as a beam simply supported over a span of 4m and to carry a uniformly distributed load of 10KiloNewton per meter including its own weight. The beam dimension was reduced by 10mm after being planned. The properties of Philippine woods at 80% stress grade is given.
1. Which of the following most nearly gives the maximum bending stress on the beam is MegaPascals.
A. 14
B. 16
C. 12
D. 10
2. Which of the following most nearly gives the maximum shearing stress on the beam in MegaPascals.
A. 0.63
B. 0.25
C. 0.95
D. 0.87
3. Which of the following most nearly gives the maximum deflection in mm.
A. 15.2
B. 18.4
C. 21.3
D. 12.4
Solution:
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Rectangular beams 300mm wide 600mm effective deep and 5.8m long are spaced 3m on centers. These beams are used to support a 90-mm thick concrete slab poured monolithically with the beam, thus the beams may be considered as T-beams. The beams are reinforced for tension only with eight 28-mm diameter bars. Concrete strength fc = 27MPa and steel strength fy = 345 MPa. The provisions of the 1992 Structrural Code of the Philippines regarding T-Beams is given.
1. Which of the following most nearly gives the effective flange width according to the 1992 NSCP, in millimeters.
A. 1450
B. 1740
C. 3000
D. 1250
2. Which of the following most nearly gives the depth of compression block measured from the top of the beam, in millimeters.
A. 68
B. 72
C. 60
D. 51
3. Which of the following most nearly gives the nominal capacity of the beam in KiloNewton-Meter.
A. 854
B. 976
C. 753
D. 1104
Solution:
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The uniform 50-kg plank is resting on rough surfaces at A and B. The coefficients of static friction are shown in the figure. A 100-kg woman starts walking form A toward B. It is required to determine the distance x when the plank starts to slide.
1. Which of the following most nearly gives the total reaction at B in Newtons.
A. 758
B. 742
C. 817
D. 863
2. Which of the following most nearly gives the total reaction at B in Newtons.
A. 680
B. 690
C. 700
D. 670
3. Which of the following most nearly gives the value of x in meters.
A. 1.73
B. 1.85
C. 1.62
D. 1.54
Solution:
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A non-prismatic beam AB is shown. The beam is fixed at B and hinged at A. The beam is loaded with a concentrated moment at A causing a 1-radian rotation at A.
1. Which of the following gives the value of the moments at A.
A. 530EI/1101
B. 532EI/1201
C. 520EI/1301
D. 540EI/1111
2. Which of the following gives the vertical reaction at A.
A. 73EI/1301
B. 96EI/1101
C. 75EI/1111
D. 87EI/1201
3. Which of the following gives the ratio of the moment at B and moment at A.
A. 169/266
B. 185/456
C. 184/385
D. 132/541
Solution:
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For the cable shown
1. Which of the following most nearly gives the tension in segment CD, in KiloNewton:
A. 7.3
B. 6.8
C. 5.2
D. 6.9
2. Which of the following most nearly gives the tension in segment AB, in KiloNewton:
A. 6.8
B. 5.2
C. 6.9
D. 7.3
3. Which of the following most nearly gives the value of h in meters:
A. 2.74
B. 2.57
C. 2.32
D. 3.12
Solution:
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The coplanar force system shown consists of two forces and a couple. All coordinates are in meters.
1. Which of the following most nearly gives the resultant of the force system in Newtons.
A. 16.8
B.14.3
C. 12.2
D. 13.1
2. Which of the following most nearly gives the angle that the resultant forces make with the horizontal axis in degrees (positive counterclockwise)?
A. 72.4
B. 55.2
C. 68.9
D. 65.2
3. Which of the following most nearly gives the y-intercept of the resultant force in meters.
A. 3.14
B. 6.38
C. 2.46
D. 5.34
Solution:
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A sheet pile 10.5 m in length is to retain a 7.3 m deep of soil with friction angle of 31°and unit weight of 17.5kN/m3. It is anchored to a depth of 1.2m below the top of the pile. The anchors are spaced 3m.
1. Find the total active force on the wall per meter width.
A. 279.9 kN
B. 308.8 kN
C. 358.4 kN
D. 421.2 kN
2. What percentage of the total passive resistance is utilized by the wall?
A. 77.7%
B. 65.3%
C. 95.5%
D. 84.5%
3. Determine the tension on the anchor.
A. 321.4 kN
B. 187.5 kN
C. 273.8 kN
D. 91.3 kN
Solution:
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Two footings rest in a layer of sand 2.7m thick. The bottoms of the footings are 0.90m below the ground surface. Beneath the sand layer is a 1.8m thick clay layer. Underneath the clay layer is solid surface. Beneath the sand layer is at a depth of 1.8m below the ground surface.
1. Compute the stress increase in kPa below footing A (1.5m x 1.5m) at the center of the clay layer. Assume that the settlement in the clay layer is the same beneath footings A and B.
A. 28.32
B. 20.14
C. 25.87
D. 22.68
2. Determine the size of footing B so that the settlement in the clay layer is the same beneath footings A and B.
A. 3.2m x 3.2m
B. 2.4m x 2.4m
C. 3.6m x 3.6m
D. 3.8m x 3.8m
3. Determine the settlement in mm beneath footing A.
A. 42.3mm
B. 34.2mm
C. 69.8mm
D. 57.4mm
Solution:
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A pre-stressed concrete pile, 300mm x 300 mm in cross-section, is to be driven in a clayey soil (γ = 18.5 kN/m3) as shown. The design pile has a design capacity of 450 kN. Use factor of safety of 2. The unconfined compression shear strength, qu, of the soil is 110 kPa. Use Nc = 9.
1. What is the end bearing capacity of pile in kN.
A. 44.6
B. 58.6
C. 62.7
D. 75.4
2. Compute the skin friction in kN expected to develop along the shaft of the pile.
A. 855.5
B. 963.2
C. 754.2
D. 689.1
3. Compute the length of the pile if frictional constant α = 0.6.
A. 14.5 m
B. 28.4 m
C. 21.6 m
D. 18.5 m
Solution:
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A 5-m thick sand layer overlies a very thick layer of clay. The sand has void ratio of 0.52 and specific gravity of solids of 2.62. The clay has moisture content of 42% and specific gravity of solids of 2.65. The water table is 3m below the sand (ground) surface. The sand above water table is 30% saturated.
1. Find the total active force on the wall per meter width.
A. 16.85 kN/m3
B. 18.21 kN/m3
C. 17.47 kN/m3
D. 17.04 kN/m3
2. Determine the total stress 10m below the ground surface.
A. 214.5 kPa
B. 154.8 kPa
C. 181.6 kPa
D. 112.9 kPa
3. Determine the effective stress 10m below the ground surface.
A. 112.9 kPa
B. 181.6 kPa
C. 154.8 kPa
D. 214.5 kPa
Solution:
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Water flows at the rate of 2m/s in a 2.5-km long 600-mm pipe that is 20mm thick. Bulk modulus of elasticity of water, EB = 2.2 x 109 Pa. Modulus of elasticity of pipe material is E = 1.4 x 1011 Pa. Density of water is 998 kg/m3.
1. Calculate the nearest value to the velocity of pressure (sound) wave in m/s.
A. 1087
B. 975
C. 1563
D. 1224
2. If a valve at the end of the pipe is closed, determine the maximum time of closure that can be considered as instantaneous closure.
A. 2.1 s
B. 4.1 s
C. 3.2 s
D. 5.2 s
3. Calculate the rise in pressure near the valve due to instantaneous closure of the valve.
A. 2145 kPa
B. 3254 kPa
C. 2443 kPa
D. 2864 kPa
Solution:
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The solid steel ball shown is submerged between the interface of two liquids. The ball has a diameter of 225mm and specific gravity of 7.4.
1. Determine the weight of the ball in Newtons.
A. 485
B. 433
C. 402
D. 387
2. Determine the buoyant force acting on the ball in Newtons.
A. 44
B. 87
C. 79
D. 35
3. Determine the tension in the rope in Newtons.
A. 354
B. 398
C. 315
D. 371
Solution:
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The tank shown is 3m wide into the paper. Neglect atmospheric pressure. Unit weight of water is 9.79 kN.m3.
1. Determine the nearest value to the vertical component of the total hydrostatic force on the quarter-circle panel AB, in kilo Newton.
A. 1485
B. 1365
C. 1658
D. 1505
2. Determine the nearest value to the resultant hydrostatic force acting on the quarter-circle panel AB, in kilo Newton.
A. 1164
B. 955
C. 1234
D. 1321
3. Calculate the nearest value to the angle that the resultant hydrostatic force makes with the horizontal, in degrees.
A. 39.7
B. 56.3
C. 48.1
D. 50.6
Solution:
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Water flow at the rate of 1.2 m3/s at a depth of 1.5m in a 10-m wide irrigation canal. Assume uniform flow and use n = 0.035.
1. Calculate the nearest value to the specific energy in Joule/Newton.
A. 1.5124
B. 1.5087
C. 1.5003
D. 1.5024
2. Determine the slope of the channel bed in meter per kilometer.
A. 0.0064785
B. 0.000064785
C. 0.0000064785
D. 0.064785
3. Determine the boundary shearing stress at the walls in Pa.
A. 0.00733
B. 0.0733
C. 0.0007333
D. 0.733
Solution:
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