MATHEMATICS, SURVEYING, AND TRANSPORTATION ENGINEERING
INSTRUCTION: Select the best answer for each of the following questions. Mark only one answer for
each item by shading the box corresponding to the letter of your choice on the answer sheet
provided. STRICTLY NO ERASURES ALLOWED. Use pencil no. 2 only.
1.
Light bulbs having a mean life of 2400 hours and standard deviation of 62 hours are used
for a consignment of 4000 bulbs. Determine the percentage of bulbs with a life between
2300 and 2500 hours.
a. 87.44%
b. 89.23 %
c. 88.18%
d. 84.25%
2.
At elevation 2402 m., the distance BC is 18 658.2 m. Find the sea level distance if the
average radius of curvature is 25,184 m.
a. 16,878.62 m.
b. 16,854.49
c. 16,881.19
d. 16,820.56
3.
Messages when painted on pavement should be limited to how many words only?
a. Five
b. Four
c. Three
d. Six
4.
Evaluate the integral of 3^x / e^x dx as approaches from 0 to 1.
a. 1.090
b. 1.051
c. 2.193
d. 2.110
5.
At what time will the hands of the clock be in a straight line between 7 o clock and 8 o
clock in the morning ?
a. 7:5 5/11
b. 7:38 2/11
c. Both A and B
d. None
6.
Compute the eccentricity of the curve 9x^2 + 25y^2 + 54x – 250y + 481 = 0 .
a. 0.80
b. 0.75
c. 0.50
d. 0.64
7.
A businessman buys a property which is worth P 2,000,000. He paid a downpayment of P
500,000 at the end of the first year he paid another P 1,000,000 and the remaining
balance he paid at the end of third year. How much is the balance to be paid on the third
year if money is worth 24% compounded semi annually?
a. P 1.224 M
b. P 1.399 M
c. P 1.576 M
d. P 1.387 M
8.
A rectangular sheet of paper measures 16 cm x 24 cm. Circles are to be cut from the paper
each with a radius of 4 cm. How much area is thrown away?
a. 115.59 cm^2
b. 82.40
c. 77.25
d. 96.13
9.
A machine costing P 720000 is estimated to have a life of 10 years. If the annual rate of
depreciation is 25%, determine the total depreciation using a constant percentage of the
declining balance method.
a. P 674,112.90
b. P 679,454.27
c. P 670,207.15
d. P 677,212.56
10. Find the minor of 5 in the following matrices:
[
a. 10
b. 8
]
[
c. 4
]
d. 12
11. A highway curve has a super elevation of 7°. Find the radius of the curve so that there
will be no lateral pressure between the tires and the roadway at a speed of 40 mph?
a. 265.71 m
b. 227.48
c. 256.80
d. 292.20
12. Find the length of the curve of the polar equation r = 4(1 – sin A).
a. 32
b. 16
c. 20
d. 8
13. The expression (xt – x) is defined to be absolute error x, where xt is the true value of a
quantity and x is measured value in a computer. If the true value of a quantity is 3.5,
and the absolute error is ± 0.05, determine the acceptable values.
a. 3.45 < x < 3.55
b. 3.45 > x > 3.55
c. 3.45 < x > 3.55
d. 3.45 > x < 3.55
14. A parabolic curve having a forward tangent of -3% intersects a back tangent of 6.5% at
station 10 + 800 whose elevation is 5260 m. If the length of the curve is 400 m.,
determine the distance of the summit (highest point) from PC .
a. 228.20 m.
b. 252.86
c. 273.68
d. 290.17
15. Two runners A and B compete for stretched of 1000 m long. It took 130 secs for A to reach
the finish line and B 138 secs to reach the finish line. How far was B behind A when A
reaches the finish line?
a. 55.16 m
b. 53.18
c. 54.26
d. 58.02
16. The first cost of an equipment is P 150,000 with salvage value of P 20,000 at the end of
its life of 10 years. Using Declining Balance method, compute the book value at the end
of 6 years.
a. P 48,124.93
b. P 41,215.89
c. P 44,776.95
d. P 43,212.85
17. Find the acute angle in radians between the plane 2x – 4y – z + 5 = 0 and 3x + 4y + 5z +
6 = 0.
a. 1.77 rad
b. 1.09
c. 1.26
d. 1.02
18. The configuration and roughness of the ground is referred to as:
a. contour
b. relief
c. hachure
d. topography
19. Find the differential equations of the family of lines passing through the origin.
a. x dx + y dy = 0
b. x dx – y dy = 0
c. x dy + y dx = 0
d. x dy – y dx = 0
20. What is the latus rectum of the curve x^2 = 16y?
a. 8
b. 16
d. 2
d. 4
21. In which kind of polygon does the sum of the measurements of the interior angles equals
the sum of the measurements of the exterior angles?
a. Pentagon
b. Triangle
c. Quadrilateral
d. None
22. Given the following descriptions of a four sided lot:
LINE
AB
BC
CD
DA
BEARING
N 30° 30’ E
N 75° 30’ W
S 45° 30’ W
___________
What is the bearing of the line DA?
a. N 78° 02’ E
b. S 75° 15’ W
DISTANCE
56.5 m
46.5 m
87.5 m
___________
c. N 77° 15’ E
d. S 79° 8’ E
23. If 8 men can chop 28 trees in one day, how many trees can 20 men chop down in one day?
a. 70
b. 50
c. 75
d. 45
24. A deposit of P 110,000 was made for 31 days. The net interest after deducting 20%
withholding tax is P 890.36. Find the rate of return annually.
a. 12.36%
b. 11.75%
c. 15.33%
d. 10.61%
25. A structure used to prevent scouring and erosion and the carrying away of river banks.
a. revetments
b. jetty
c. levee
d. dikes
26. A horizontal force of 250 N pushes a flat bottomed 600 N block on a horizontal surface
from rest to a velocity of 22 m/s after travelling 120 m. What is the coefficient of
friction between the block and the surface?
a. 0.16
b. 0.35
c. 0.21
d. 0.44
27. What is the equivalent value of 405 degrees into mils?
a. 6400
b. 7000
c. 7200
d. 8000
28. A bag contains 3 white and 5 black balls. If two balls area drawn in succession without
replacement, what is the probability that both balls are in the same color?
a. 5/14
b. 13/28
c. 10/14
d. 3/7
29. Evaluate log_6 845 = x .
a. 4.11
b. 4.79
c. 3.88
30. Evaluate the expression (tan x)(cos x) / sin x
a. cot x
b. tan^2 x
c. 0
d. 3.76u
d. 1
31. A conic has an equation of an asymptote equal to 3x = 4y. Find the equation of the conic
having its center at (0,0) and its transverse axis equal to y = 0.
a. 9x^2 – 16y^2 = 144 b. 9x – 16y = 12
c. 9x^2 – 16y = 144
d. 9x – 16y^2 = 12
32. A at certain point on the ground , the tower at the top of a 20 m high building subtends
at an angle of 45° . At another point on the ground 25 m closer the building, the tower
subtends an angle of 45° . Find the height of the tower.
a. 124.75 m
b. 87.45
c. 154.32
d. 101.85
33. Evaluate the following subject to the functional relation x = t^3 and y = t^2.
a. 99
b. 100
c. 150
d. 96
34. The MRT system runs from North Ave to Taft Ave for a total distance of 15 km. The cost of
electric energy consumed by a train per hour is directly proportional to the cube of its
speed and is P 250 per hour at 50 kph. Other expenses such as salaries, depreciations,
damages to technical glitches, etc… amounts to P 1687.50 per hour. Find the most
economical speed of the train in kph.
a. 75
b. 80
c. 65
d. 60
35. Determine the length of the line in meters if there were 3 tallies, 8 pins and the last
pin is 9 m from the end of the line. The tape used is 50 m long.
a. 1879
b. 1509
c. 1909
d. 2009
36. The _____ refers to the highest derivative of the differential equation.
a. Degree
b. Exponent
c. Variable
d. Order
37. A balloon is rising vertically over a point A on the ground at the rate of 15 ft/sec. A
point B on the ground is level with and 30 ft from A. When the balloon is 40 ft from A,
at what rate is its distance from B changing?
a. 15 ft/s
b. 20
c. 12
d. 10
38. The rational expression 130x/(100 – x) describes the cost, in millions of dollars, to
inoculate x percent of the population against a particular strain of flu. For what value
of x is the expression undefined?
a. 100
b. -100
c. 0
d. 130
39. The capacity of the roads can be affected by the following EXCEPT:
a. Number of lanes
b. Lane and shoulder width
c. Traffic situation
d. Intersection capacity
40. A base line AB was measured accurately using a subtense bar 1 m long. From a point C near
the centre of the base, the lengths AC and CB were measured as 9.375 m and 9.493 m,
respectively. If the standard error in the angular mesurement was ± 1″, determine the
error in the length of the line.
a. ± 0.75 mm
b. ±0.61
c. 0.84
d. 0.90
41. A tin pan 2 ft high , with a spherical bottom, has its sides flared out 60° from the
vertical. The bottom measures 4 ft across. How much tin does it take to make it?
a. 77.211 ft^2
b. 90.579
c. 73.592
d. 84.777
42. A feasibility study shows that a fixed capital investment of P10,000,000 is required for
a proposed construction firm and an estimated working capital of P2,000,000. Annual
depreciation is estimated to be10% of the fixed capital investment. Determine the rate of
return on the total investment if the annual profit is P3,500,000.
a. 28.33%
b. 29.17%
c. 30.12%
d. 30.78%
43. Find the distance from the line x = 3y – 12 to the point (5,-1).
a. 5.078
b. 5.299
c. 5.945
d. 6.324
44. Determine the standard error for the following group of six measurements: 11,249.71 ft;
11,250.06 ft; 11,249.86 ft; 11,249.99 ft; 11,250.01 ft; 11,249.98 ft.
a. ±0.13 ft
b. 0.12
c. 0.10
d. 0.08
45. A solid wooden cube 30 cm on each edge, can be totally submerged in water if it is pushed
downward with a force of 54 N. What is the density of the wood?
a. 800 kg/m^3
b. 500
c. 540
d. 1000
46. In how many ways can three people be seated in a room that consists of 7 seats?
a. 450
b. 900
c. 210
d. 350
47. Find the area inside one loop of the lemniscate r^2 = cos 2x.
a. 1/2
b. 1
c. 1/3
d. √3 / 2
48. For parking facilities , it refers to the use of a single parking space for 1 hour.
a. Turnover
b. Load
c. Duration
d. Space hour
49. Hugo plays a game: he places a chess piece on the top left square of a 20 x 20 chessboard
and makes 10 moves with it. On each of these 10 moves, he moves the piece either one
square horizontally (left or right) or one square vertically (up or down). After the last
move, he draws an X on the square that the piece occupies. When Hugo plays this game over
and over again, what is the largest possible number of squares that could eventually be
marked with an X?
a. 55
b. 36
c. 45
d. 90
50. A manufacturer has been shipping his product (moderately heavy machines), mounted only on
skids without comlete crating. To avoid crating he must ship in freight cars which
contain only his machines. To do this he must pay freight on a car capacity load of 42
tons regardless of whether or not the car is completely full. In the past he actually has
shied only 30 tons in each car. The car load freight rate is P4.10 per hundred pounds. If
the machines are crated so that they can be shied in mixed car lots, along with other
merchandise, they can be shied at a rate of P4.20 per hundred pounds with the freight
bill computed only on the actual weight shied. The cost of crating would be P25.00 per
machine and would increase the shipping weight from 1,200- 1220 pounds per machine. How
much the shipping without using cranes is cheaper?
a. P 507.48
b. P 456.20
c. P 404.80
d. P 516.94
---END OF EXAMINATION IN MATHEMATICS, SURVEYING, AND TRANSPORTATION ENGINEERING---
WATER RESOURCES ENGINEERING AND GEOTECHNICAL ENGINEERING
INSTRUCTION: Select the best answer for each of the following questions. Mark only one answer for
each item by shading the box corresponding to the letter of your choice on the answer sheet
provided. STRICTLY NO ERASURES ALLOWED. Use pencil no. 2 only.
Notes: For the tables and other charts, kindly refer to your handouts given from your respective
review centers.
1.
The maximum stresses that causes a failure of a cohesive soil specimen in a tri axial
test is equal to 220 kPa. The angle of friction is equal to 25°. If the deviator stress
at failure is equal to 140 kPa. Compute the cohesion of the soil.
a. 8.54 kPa
b. 7.29
c. 5.64
d. 10.02
2.
A conical having a radius of base equal to 35 cm and a height of 65 cm. has its base at
the bottom. Find the height of free surface if 0.025 m^3 of water is poured into a
conical tank.
a. 0.577 m
b. 0.610
c. 0.814
d. 0.477
3.
A sample of dry soil is uniformly mixed with 17% by mass of water and compacted in a
cylindrical mold. The volume of the wet soil is 1 x 10^-3 m^3 and its mass is 1.6 kg. If
the specific gravity of the soil particles is 2.70 and using unit weight of water = 9.81
kN/m^3. Find the void ratio.
a. 0.84
b. 0.90
c. 0.56
d. 0.97
4.
Water is flowing at 2.2 m/sec in a cast iron with diameter of 600 mm and wall thickness
of 20 mm at 350 m long length and bulk modulus of water is 2.2 x 10^9 N/m^2 and modulus
of elasticity of steel is 1.4 x 10^11 N/m^2. Of what length of time should be allowed for
closing the valve to avoid water hammer pressure?
a. 0.57 sec
`
b. 0.68
c. 0.95
d. 1.12
5.
A rectangular channel 6 m wide has a constant specific energy of 2.2 m. Calculate the
critical depth.
a. 1.11 m
b. 1.23
c. 1.47
d. 1.85
6.
A 300 mm diameter well penetrates 27 m below the static water table. After 24 hours of
pumping at 69 L/s. The water level in an observation well at a distance of 95 m from the
test well is lowered 0.55 m and the other observation well at a distance of 1.10 m.
Compute the transmissibility of the aquifer in m^2/day.
a. 1977.5 m^2/day
b. 2156.7
c. 2105.4
d. 2256.8
7.
An open can of water is subjected to an upward acceleration of 4.5 m/s^2. What is the
pressure at a depth of 1.5 meters?
a. 24.6 kPa
b. 26.3
c. 21.5
d. 25
8.
The weight of water expressed as a percentage of the total dry weight of a soil material.
a. dry density
b. natural moisture content
c. degree of saturation
d. void ratio
9.
From the given data, shows the sieve analysis of soil sample:
SIEVE NO
4
8
10
20
40
60
100
200
DIAMETER
4.760
2.380
2.000
0.840
0.420
0.250
0.149
0.074
Classify the soil using AASHTO Soil Classification.
a. A-1-a
b. A-1-b
c. A-3(0)
PCT PASSING
100
97
94
77
58
44
24
8
d. A-2
10. A stone weighs 468 N in air. When submerged in water if weighs 298 N. Find the volume of
the stone.
a. 0.0173 m^3
b. 0.0215
c. 0.0188
d. 0.0236
11. For a certain soil the cohesion c is 50 kPa, the unit weight is 19.2 kN/m^3. Assuming
local shear failure and the angle of friction is ϕ = 10°. Calculate the ultimate bearing
capacity for a strip footing of width = 1.25 m at a depth of 4.5 m using Terzaghi’s
ultimate bearing capacity.
a. 456.75 kPa
b. 490.81
c. 477.25
d. 411.28
12. A square plate having one of its sides equal to 3 m is immerse in a water surface in a
vertical position such that two edges of the square would be horizontal in order that the
center of pressure shall be 8 cm from the center of gravity. What is the distance of the
center of pressure from water surface?
a. 9.207 m
b. 9.315
c. 9.455
d. 9.176
13. A small orifice 0.0003 m^2 in area is in the vertical side of a rectangular tank. The
horizontal sectional area of the tank is 0.40 m^2. At a given instant the head of the
orifice is 1.2 m and 312 later it is 0.6 m. Using the coefficient of discharge of 0.60,
how long will it take to lower the water surface from 1.2 m to 0.8 m?
a. 201.70 sec
b. 222.59
c. 237.54
d. 256.19
14. A jet of water 250 mm in diameter impinges normally on a steel plate. If the discharge is
0.491 m^3/s. Find the fore exerted by the jet on the stationary plate.
a. 2.79 kN
b. 4.07
c. 3.56
d. 4.91
15. A thick layer of clay underlies a sand formation having a thickness of 5 m. The
groundwater is located 2 m below the ground surface. Specific gravity of sand and clay is
2.65 with sand having an average void ratio of 0.52. The clay has a water content of 42%.
Compute the effective stress at a depth of 10 m below the ground surface.
a. 177.9 kPa
b. 153.5
c. 181.6
d. 190.5
SITUATION 1: A vertical circular gate in a tunnel 8 m in diameter has oil (s = 0.80) on one side
and air on the other side as shown in Figure FS - 001. If oil is 12 m above the the invert and
the air pressure is 40 kPa,
16. Compute distance the center of pressure from the top of the gate.
a. 4.7 m
b. 4.9
c. 4.5
d. 5.3
17. Compute the force exerted by the air.
a. 2011 kN
b. 2370
d. 2818
c. 2513
18. Where will a single support be located to hold the gate in position (above the invert of
the gate) ?
a. 1.36 m
b. 1.84
c. 3.24
d. 2.62
SITUATION 2: From the Figure SM – 001,
19. Determine the total flow in ft^3/min
a. 2.755 x 10^-4
b. 2.964 x 10^-4
c. 2.823 x 10^-4
d. 2.429 x 10^-4
20. Find the equivalent value of the K1 for both sand and silt.
a. 1.36 x 10^-3 ft/min b. 1.77 x 10^-3
c. 1.36 x 10^-3
d. 1.29 x 10^-3
21. Find the volume of water which percolate after 30 mins in cm^3.
a. 229
b. 282
c. 218
d. 252
SITUATION 3: The soil under a dam has four layers of soil with different coefficients of
permeability.
LAYER
1
2
3
4
DEPTH
4 m
8 m
12 m
3 m
COEFFICIENT OF PERMEABILITY
5 cm/hr
3 cm/hr
2 cm/hr
1 cm/hr
22. Compute the average vertical coefficient of permeability in meters/day.
a. 0.68
b. 0.52
c. 0.48
d. 0.40
23. Compute the transmissibility of the soil when the water surface is at the ground surface
in m^2/day.
a. 14.04
b. 13.93
c. 12.76
d. 15.44
24. Compute the interstitial velocity of water moving through the soil if it has the void
ratio of 0.60 and the hydraulic gradient of 0.0018 in cm/hr.
a. 0.0277
b. 0.0104
c. 0.0079
d. 0.0357
SITUATION 4: From the Figure FE – 001 shown, the soil has a unit weight of 17 kN/m^3 and
undrained shear strength cu = 20 kPa. The slope makes an angle of 60° with the horizontal. Assume
stability number ,m = 0.185.
25. Compute the stability factor.
a. 5.41
b. 6.36
c. 6.24
26. Compute the maximum depth up to which the cut could be made.
a. 7.66 m
b. 12.19
c. 5.79
d. 5.19
d. 6.36
27. Compute the angle that the failure plane makes with the horizontal if BC = 8 m.
a. 22.19°
b. 26.54°
c. 34.19°
d. 28.59°
SITUATION 5: Identify the following terms in water resources engineering.
28. A sewer intended to carry sanitary sewage.
a. Storm sewer
b. Sanitary sewer
c. Combined sewer
d. Outfall sewer
29. Which method of irrigation has the best control of water supplied?
a. furrow
b. sub irrigation
c. flooding
d. trickle irrigation
30. In wastewater treatment , the process of removing fine residual suspended solids is known
as:
a. Aeration
b. Filtration
c. Soda ash
d. Zeolite
SITUATION 6: Water is being pumped from reservoir A to reservoir B as shown in Figure HYD - 001.
The total length of pipe is 1090 m and the diameter of 600 mm. The rate of flow in the system is
0.65 m^3/s.
31. Compute the head loss of the pipe system if C = 120.
a. 7.67
b. 10.38
c. 8.96
d. 9.35
32. Compute the head added by the pump.
a. 19.47 m
b. 12.38
d. 18.64
c. 15.15
SITUATION 7: From the given Figure SM – 002 , the total height of soil sample is 25 cm. The water
table is located 5 cm below E.
33. Compute the difference between the pressure heads C and D.
a. 4.5 cm
b. 10.5
c. 12.5
d. 7.5
34. Compute the total head loss at C.
a. 50 cm
b. 30
c. 40
d. 20
35. Compute the head loss at D.
a. 15 cm
b. 20
c. 30
d. 10
SITUATION 8: The wet mass of a sample of saturated soil is 520 grams. The dry mass, after ovendrying, is 400 grams.
36. Determine the water content.
a. 25%
b. 30%
c. 15%
d. 45%
37. Determine the void ratio.
a. 0.81
b. 0.64
c. 0.90
d. 0.45
38. Determine the saturated unit weight.
a. 18.44 kN/m^3
b. 18.74
c. 19.00
d. 19.44
SITUATION 9: Refer to Figure FE – 002. Given that H = 3.5 m, q = 20 kPa, γ = 18.2 kN/m^3 , c’ = 0
ϕ’ = 35° and OCR = 1.5.
39. Determine the at-rest lateral earth force per meter length of the wall.
a. 88.48 kN/m
b. 97.63
c. 105.79
d. 112.64
40. Find the location of the resultant.
a. 1.39 m
b. 1.64
c. 1.95
d. 2.12
41. If the collapse potential of the foundation is 15% ,the severity of the problem in
foundation is:
a. Trouble
b. No problem
c. Moderate trouble
d. Severe trouble
42. Two and a half cm of rain per over an area of 200 km^2 is equivalent to average rate of
input of how many cubic metres per second of water to that area?
a. 38.77 m^3/s
b. 48.20
c. 57.87
d. 64.19
SITUATION 10: Following area the details for the backfill material used in a vibrofloation
project:
D10 = ______
D20 = 0.52 mm
D50 = 1.42 mm
If the suitability number is 6.1,
43. Determine the rating of the suitability number.
a. Poor
b. Good
c. Moderate
d. Excellent
44. Find the value of D10.
a. 0.36 mm
b. 0.75
d. 0.70
c. 0.64
SITUATION
11: The breadth of a rectangular channel is twice its length. Assuming the Chezy
coefficient c to be 55 m^(1/2) /s , assuming that the discharge when flowing full should be 0.8
m^3/s and the velocity when flowing half full should be 0.6 m/s.
45. Determine the length of the channel.
a. 1.48 m
b. 1.62
c. 2.12
d. 1.94
46. Determine the height of the rectangular channel.
a. 0.81 m
b. 1.06
c. 0.74
d. 0.97
47. Determine the slope of the rectangular channel.
a. 0.00044
b. 0.00048
c. 0.00064
d. 0.00090
48. It is a study of liquids that are in motion with respect to both to the earth and their
containers.
a. Hydrostatics
b. Hydrology
c. Hydrokinetics
d. Hydroponics
49. If the liquid limit of the soil is 60% and the plastic limit of the soil is 26%, assuming
that there is 23% of the soil is made of clay, determine the activity of the soil.
a. 1.5
b. 0.98
c. 0.75
d. 0.88
50. A circular area of diameter d is vertical and submerged in a liquid. Its upper edge is
coincident with the liquid surface. Compute the depth to its center of pressure in terms
of the diameter d.
a. 3d/4
b. 7d/8
c. 4d/9
d. 5d/8
--- END OF EXAMINATION IN HYDRAULICS AND GEOTECHNICAL ENGINEERING--GOOD LUCK‼
Figure FS – 001
Figure SM – 001
Figure FE – 001
Figure HYD – 001
Figure FE – 002
STRUCTURAL ENGINEERING AND CONSTRUCTION
INSTRUCTION: Select the best answer for each of the following questions. Mark only one answer for
each item by shading the box corresponding to the letter of your choice on the answer sheet
provided. STRICTLY NO ERASURES ALLOWED. Use pencil no. 2 only.
For tables, formulas, and specifications, kindly refer to NSCP 2001/2010 and modules provided by
respective review centers.
SITUATION 1: For the riveted bracket shown in the Figure SSD – 001. P = 250 kN. The rivets have
diameter of 25 mm. The connection can be analyzed by force alone acting through the centroid of
the rivets and a moment.
1.
Calculate the shearing stress in each rivet due to the vertical force alone acting at the
centroid.
a. 145.6 MPa
b. 127.3
c. 112.8
d. 186.4
2.
Determine the shearing stress at rivet D.
a. 113.9 MPa
b. 156.7
3.
c. 95.6
d. 134.7
Find the stress in rivet B when the instantaneous center is 200 mm to the left of center
of gravity.
a. 274.5 MPa
b. 187.5
c. 389.6
d. 341.8
SITUATION 2: Given: Total ultimate load = 12 kN/m
Beam, b x h = 300 x 400 mm
Slab thickness t = 100 mm
Slab reinforcement = 10 mm ϕ
Concrete = 20.7 MPa
Reinforcement steel = 275 MPa
Clear concrete cover to slab reinforcement = 20 mm
Dimensions: Column = 300 x 300 mm
S = 2.8 m
L1 = L2 = L3 = 6 m
Refer to Figure RCD - 001
4.
What is the design positive moment at the interior span bounded by FGJK ?
a. 5.8 kN m
b. 7.7
c. 4.7
d. 9.2
5.
What is required spacing of 10mmϕ bars for the negative moment at the interior beam
support FG?
a. 317.9 mm
b. 205.3
c. 300
d. 250
6.
What is the maximum spacing of 10 mm ϕ bars at panel FGKJ as prescribed by design codes?
a. 317.9 mm
b. 205.3
c. 300
d. 250
SITUATION 3: A 6 m long beam on fixed at both ends carries a uniform load of 20 kN/m.
7.
8.
9.
What is the moment at the let end?
a. -45 kN m
b. 45
c. 60
d. -60
Determine the max. shear in the beam.
a. -45 kN m
b. 45
c. 60
d. -60
Using E = 200 GPa , and I = 71,000,000 mm^4 , find the deflection at the beam.
a. 4.75 mm
b. 6.25
c. 8.15
d. 6.00
SITUATION 4: Identify the following in reinforced concrete design.
10. The strength reduction factor for reinforced concrete member under flexure without axial
load is:
a. 0.90
b. 0.75
c. 0.70
d. 0.85
11. The column is to be reinforced with 8 – 28 mmϕ bars. If 25 mm ϕ bars were used instead,
how many are needed if the column reinforcement has to be equal on all four sides?
a. 16
b. 12
c. 8
d. 20
12. In prestressed concrete , it refers to the stressing of high strength steel after the
concrete has been cast and has attained.
a. Post tensioning
b. Creep
c. Pre tensioning
SITUATION 5: The pin jointed assembly supports a billboard 3 m high x 4 m
total weight of the billboard is 30 kN as shown in the Figure ST1 – 001.
H = 1.5 m, θ = 60°
Wind pressure q = 1.7 kPa
Wind pressure coefficient C = 1.0
13. Determine the horizontal reaction at A.
a. 6.6 kN
b. 7.9
c. 8.4
d. Relaxation
wide on each end. The
d. 9.0
14. How much is the normal stress in strut BC with cross sectional dimensions of 6 mm x 76
mm?
a. 45.8 MPa
b. 47.2
c. 48.3
d. 44.7
15. If the strut AB were placed by a 16 mm ϕ steel cable, determine the normal stress in the
cable.
a. 45.8 MPa
b. 47.2
c. 48.3
d. 50.4
SITUATION 6: A 76 x 76 x 6 mm angular section is welded to a gusset plate having a thickness of 8
mm as shown in the Figure SSD – 002. The length L1 = 125 mm and L2 = 65 mm. The angular section
has a cross sectional area of 929 mm^2. Fy = 248 MPa and Fu = 400 MPa.
16. Determine the value of the tensile force P based on the gross area.
a. 115.79 kN
b. 137.18
c. 154.26
d. 138.24
17. Determine the value of the tensile force P based on the net area using strength reduction
coefficient of 0.85.
a. 157.93 kN
b. 304
c. 137.18
d. 138.24
18. Determine the value of the tensile force P based on the based shear in gusset plate along
the weld.
a. 157.93 kN
b. 304
c. 137.18
d. 138.24
SITUATION 7: A 120 kg man walk on 4 m plank resting on rough surfaces A and B as shown in Figure
ES – 001. Given that coefficient of Friction at A = 0.40 and at B = 0.20.
19. At what distance x will the plank start to slide?
a. 1.84 m
b. 1.27
c. 1.69
d. 1.45
20. What is the frictional force at A?
a. 502.75 N
b. 691.28
c. 256.72
d. 493
21. Find the vertical force (N) at B.
a. 502.75 N
b. 691.28
c. 256.72
d. 493
SITUATION 8: Light grade steel channel was used as a purlin of a truss. The top chord of the
truss is inclined 1 V : 3 H and distance between the trusses is equal to 3 m. The purlin has a
weight of 71 N/m and spaced at 1.2 m on centers. The dead load including roof materials is 1200
Pa , live load of 1000 Pa and wind load of 1440 Pa. Coefficient of pressure at leeward and
windward are 0.6 and 0.2 respectively. Sag roads are placed at the middle thirds and Fbx = Fby =
138 MPa.
Sx = 4.48 x 10^4 mm^3 and Sy = 1.18 x 10^4 mm^3
22. Determine the maximum ratio of actual to allowable bending stress for combination of D +
L load.
a. 0.616
b. 0.521
c. 0.438
d. 0.327
23. Determine the maximum ratio of actual to allowable bending stress for combination 0.75(D
+ L + W) load.
a. 0.616
b. 0.521
c. 0.438
d. 0.327
24. Determine the maximum ratio of actual to allowable bending stress for combination D + L
load if one line of sag rod was placed at the midspan.
a. 0.616
b. 0.521
c. 0.438
d. 0.327
SITUATION 9: The rigid bar AB is hanged at A and supported by a steel plate hanger , designated
as d. The hanger is fixed at C and bolted at D with two plates as shown in the Figure SOM – 001.
Given that L1 = 2.0 m , L2 = 1.2 m, and H = 3.0 m.
Width of plate hanger = 40 mm
Thickness of plate hanger = 10 mm
Bolt diameter = 20 mm
Allowable bolt shear stress = 68 MPa
Allowable bolt bearing stress = 240 MPa
25. What is the allowable stress in the hanger based on the bolt capacity in double shear at
D.
a. 116.55 MPa
b. 106.81
c. 97.20
d. 125.94
26. If the maximum tensile stress in the hanger is 138 MPa, find the allowable load W.
a. 27.9 kN
b. 30.16
c. 38.24
d. 34.5
27. If the load W = 60 kN, find the vertical displacement at B.
a. 3.6 mm
b. 4.8
c. 5.12
d. 5.76
SITUATION 10: Due to architectural requirements, a column is of T section as shown in Figure RCD
– 002.
Given:
As1 = 6 – 25 mm ϕ bars
As2 = 4 – 25 mm ϕ bars
h1 = 250 mm
h2 = 450 mm
b1 = 200 mm
b2 = 300 mm
f’c = 28 MPa
10 mm diameter ties
Concrete clear cover = 40 mm
Assume that fs = fy.
28. What is the distance of the plastic centroid of the section from the line 1 along the xaxis?
a. 255
b. 286
c. 312
d. 356
29. Which of the following gives the location of the geometric centroid from line 1 along the
x – axis?
a. 277.4
b. 256.9
c. 282.7
d. 291.1
30. A load Pu = 4155 kN acts along the x axis at 420 mm from the line 1 , what is the
resulting bending moment in kN m?
a. 518.9
b. 520.7
c. 548.2
d. 556.8
SITUAITON 11: A given frame shown in Figure ST2 - 001 is subjected to lateral loads of 30 kN and
50 kN at joints C and B respectively. Using Portal Method of analysis,
31. Compute the moment at D.
a. 120 kN m
b. 60
c. 90
d. 150
32. Compute the moment at FC at joint F.
a. 12 kN m
b. 15
c. 20
d. 18
33. Compute the axial force of column AB.
a. 15 kN
b. 30
c. 22.5
d. 35
SITUATION 12: A beam having a span of 5 m is fixed at both ends. It carries axial loads of 20 kN
and 30 kN as shown in Figure ST2 – 002. Neglect the weight of the beam.
34. Compute the moment at A.
a. -24.8 kN m
b. 24.8
c. -27.2
d. 27.2
35. Compute the moment at B.
a. -24.8 kN m
b. 24.8
c. -27.2
d. 27.2
36. Compute the maximum positive moment of the beam.
a. 14.77 kN m
b. 31.18
c. 25.53
d. 18.24
SITUATION 13: A wooden rectangular beam 200 mm x 350 mm has a simple span of 6 m. Neglecting the
weight of the beam.
37. Which of the following gives the value of the shear force at the support if there is a
notch at the end of the beam which is 100 mm deep if the allowable shearing stress is
1.10 MPa?
a. 22.79 kN
b. 28.20
c. 18.12
d. 26.19
38. Which of the following gives the value of the concentrated load it could carry at its
midspan if the allowable bearing stress is 10.35 MPa?
a. 22.84 kN
b. 28.17
c. 25.54
d. 30.07
SITUATION 14: An element in bi axial stress is subjected to stresses σx = +60 MPa and σy = 20
MPa.
39. Find the max. normal stress.
a. 60 MPa
b. -60
c. 20
d. -20
40. Find the max. shearing stress.
a. 60 MPa
b. -60
c. 20
d. -20
SITUATION 15: A boiler is constructed of 8-mm thick steel plates that are fastened together at
their ends using a butt joint consisting of two 8-mm cover plates and rivets having a diameter of
10 mm and spaced 50 mm apart as shown in Figure SOM – 002. If the steam pressure in the boiler is
1.35 MPa,
41. Determine the circumferential stress in the boiler’s plate apart from the seam.
a. 115 MPa
b. 127
c. 150
d. 176
42. Determine the the circumferential stress in the outer cover plate along the rivet line a–
a.
a. 77.4 MPa
b. 84.6
c. 97.6
d. 79.1
43. Determine the shear stress in the rivets.
a. 284
b. 310
c. 322
d. 405
44. Various defects in timber are the following EXCEPT:
a. due to kaingin system
b. due to natural forces
c. due to defective seasoning
d. due to attack by insects
SITUATION 16: For the beam cross section shown in Figure RCD – 003 , given that f’c = 20.7 MPa
and As = 645.16 mm^2
45. Compute the compression block.
a. 85 mm
b. 75
c. 90
d. 105
46. Calculate the steel ratio.
a. 0.0078
b. 0.0080
c. 0.0037
d. 0.0064
47. Compute the ratio of the neutral axis to the effective depth of the beam.
a. 0.318
b. 0.419
c. 0.508
d. 0.216
48. The elevator E and its freight have a total mass of 400 kg. Hoisting is provided by the
motor M and the 60-kg block C as shown in Figure ED - 001. If the motor has an efficiency
of ϵ = 0.6 , determine the power that must be supplied to the motor when the elevator is
hoisted upward at a constant speed of vE = 4 m/s.
a. 31.5 kW
b. 15.6
c. 22.2
d. 11.7
SITUATION 17: Identify the following in CE Laws, Specifications and Contracts.
49. Within _____ from receipt by the bidder of the notice from the BAC that the bidder has
the Lowest Calculated Bid or Highest Rated Bid, the bidder shall submit to the BAC its
latest income and business tax returns, and other appropriate licenses and permits
required by law and stated in the Bidding Documents.
a. 7 working days
b. 7 calendar days
c. 5 working days
d. 5 calendar days
50. Rooms or spaces housing industrial or heating equipment shall be provided with to prevent
excessive accumulation of hot and/or polluted.
a. Skylights
b. Window openings
c. Ventilation
d. Air shafts
--- END OF EXAMINATION IN STRUCTURAL ENGINEERING AND CONSTRUCTION---
Figure SD – 001
Figure RCD – 001
Figure ST1 – 001
Figure SSD – 002
Figure EM – 001
Figure SOM – 001
Figure RCD – 002
Figure ST2 – 001
Figure SOM – 002
Figure RCD – 003
Figure ED – 001
Figure ST2 - 002
GOOD LUCK!