Preboard

CE GREAT MINDS PREBOARD 3 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.

The score in an NBA game produces at a mean of 0.90 points per possession and standard deviation of 0.10. If there are 500 possessions were recorded, how many of them will score 1 or more? a. 75 b. 80 c. 55 d. 90

2.

Find the volume generated by revolving about the line x – 2 = 0, the area in the first and fourth quadrants, bounded by the curve x^2 + y^2 – 4 = 0 and the line x = 0 a. 45.4 b. 55.7 c. 61.8 d. 23.8

3.

A small business company is preparing a schedule of funds to form a sinking fund for future expansion. The schedule of funds are as follows: Present year n n + 1 n + 2 n + 3 n + 4

P P P P P

8,000 7,000 6,000 5,000 4,000

By the end of the 5th year, the company will purchase an equipment needed for the improvement and expansion of the company costing P 60,000. If money is worth 16% by the company, how much money will be needed to supplement the sinking fund? a. P 8,436.36

b. P 9,789.42

c. P 5,432.40

d. P 4,842.60

4.

The maximum allowable rate of crashes at intersections is 9 per million entering vehicles. At an intersection of 2 roadways, average daily traffic is 18265. Find the maximum number of crashes per year before corrective action is needed. a. 55 b. 80 c. 74 d. 60

5.

In construction surveying, it parallels the actual construction line and is marked at full station intervals depending on the dimension of the project. a. Stadia line b. Marking line c. Offset line d. gradient

6.

A simple horizontal curve of radius of 125 m connects two tangents that intersect at an angle of 66°30’. Compute the external distance E. a. 88.15 m b. 76.59 c. 58.18 d. 81.91

7.

An automobile repair shop charged a client P 4480, listing P 630 for parts and the remainder for labor. If the cost of labor is P 350 per hour, how many hours of labor did it take to repair the car? a. 15 hours b. 11 c. 10 d. 8

8.

Evaluate the integral of cos^7 3x dx from 0 to π/6. a. 0.152 b. 0.217 c. 0.266

9.

d. 0.365

With wind velocity of 40 kph, it takes an airplane as long to travel 1200 km with the wind as 900 km against it. How fast can the airplane travel in still air? a. 250 kph b. 180 c. 200 d. 280

10. It is a transit provided with vertical circle and a long level tube on the telescope. a. Engineer’s Transit b. City transit c. Theodolite d. Geodimeter 11. You are directed to formulate the equation of a line that its slope must be three and intercept must be -2. Compute the zero of that function. a. 2/3 b. -2/3 c. -3/2 d. 3/2 12. The mooring fitting for mooring ships during a storm installed at the outside/inside of the berth far from the water line is called: a. Bitt b. Bollard c. Cleat d. Closed chock 13. How long will it take money to quadruple if it earns 7% compounded semi-annually? a. 21.77 years b. 28.18 c. 20.15 d. 27.56 14. A downgrade of 3.2% meets a rising grade of 4.6% at station 73 + 180 where the elevation is 998 m. A sag curve, 440 m long connects the gradelines from A at the downgrade to B at the upgrade. Find the elevation of B in meters.

a. 1120.18

b. 1059.5

c. 1008.12

d. 1261.29

15. The bases of a right prism are a hexagon with one of each side equal to 6 cm. If the volume of the right prism is 500 m^3 , find the distance between the bases. a. 5.35 cm b. 6.77 c. 4.19 d. 7.54 16. If the polar distance of a star 2° 30’, what is its declination? a. 177° 30’ b. 87° 30’ c. 92° 30’

d. 62° 30’

17. A vehicle traveling at 40 kph was stopped within 1.8 sec. after the application of brakes. Determine the average skid resistance. a. 0.77 b. 1.09 c. 0.83 d. 0.63 18. A painter needs to find the area of the gable end of a house. What is the area of the gable if it is a triangle with two sides of 4.2 meters that meet at 105° angle? a. 85.2 m b. 77.1 c. 107.5 d. 89.5 19. Determine the sum of the infinite geometric series of 1 , -1/5, 1/25… a. 5/7 b. 4/5 c. 4/6 d. 5/6 20. By how much should the edge of the cube be increased so as to increase its surface area by 25%? a. 18.5% b. 11.8% c. 20.7% d. 16.9% 21. An ellipse has a general equation of Ax^2 + By^2 + F = 0 passing through (8,0) and (0,6). Find the value of B. a. 32 b. 8 c. 64 d. 36 22. A man and a boy can do in 15 weeks a piece of work which would be done by 7 men and 9 boys in 2 weeks. How long would it take one man to do it? a. 18 weeks b. 14 c. 20 d. 35 23. The process of widening, enlarging , cleaning, or deepening of channels in harbors, rivers, and canals to maintain the idea depth of berthing areas due to fast siltation rate is known as: a. Distillation b. Dredging c. Meandering d. Excavation 24. What is the least amount of material in sq ft that can produce a box with a square base and open top having a volume of 32 cu ft? a. 48 ft^2 b. 54 c. 100 d. 120 25. A municipal hall needs P 2 billion to pay for the bridge construction in 6 years. To generate this sum, a sinking fund consisting of four annual payments is established now. For tax purposes, no further payments will be made after four years. What are the necessary payments if money is worth 18% per annum? a. P 183.4 M b. P 275.4 M c. P 316.2 M d. P 418.6 M 26. From the distribution shown, x f(x)

2 1/3

3 1/2

11 1/6

find the expectiation. a. 10

b. 6

c. 4

d. 9

27. The formula W = 0.35 ln P + 2.74 is a model for the average walking speed (W in feet per sec) for a resident of a city whose population is P thousand. Find the average walking speed for the people living in the following cities: CITY Tacloban Manila a. Tacloban = 4.6, Manila = 5.9 b. Tacloban = 5.9, Manila = 4.6

2016 Population per 1,000 197 7273 c. Tacloban = 8.4, Manila = 11.6 d. Tacloban = 11.6, Manila = 8.4

28. In highway construction requirements, these shall not be placed on any wet surface, or when weather conditions would prevent the proper handling or finishing of the bituminous mixtures. a. Asphalt mix c. Bituminous plant b. Feeder for drier d. Bituminous road mix surface 29. Find the probability of a 4 turning up at least once in two tosses of a fair die. a. 15/36 b. 11/36 c. 7/36 d. 2/9

30. The DMD of the line BC is equal to 426.20. The departure of the previous line AB is 117.56. What is then the departure of the line BC? a. 115.79 b. 156.81 c. 168.20 d. 191.08 31. Water is pouring in a dam. After t days, there are t + √t cu m in the dam. At what rate is the water pouring into the dam when t = 9 days? a. 7/6 cpd b. 8/7 c. 6/5 d. 5/4 32. Solve the differential equation 2y dy = (x^2 + 1) dx. a. 3x^3 + x + C c. –x^3 + x + C b. 1/3 x^3 + x + C d. 1/3 x^2 – 3x + C 33. This involves using a per unit factor that can be estimated effectively. a. Economic technique b. Unit technique c. Value technique d. Cost technique 34. Determine the spacing between construction joints for 3.5 m slab width having a thickness of 200 mm, coefficient of friction is 1.5. Allowable tensile stress in concrete and steel are 0.8 and 1400 kg/cm^2 respectively. Use plain cement concrete. a. 3.76 m b. 4.15 c. 5.59 d. 4.44 35. You just inherited P 10 million. While you plan to squander some of it away, how much should you deposit in an account earning 5% interest per year if you’d like to have P 10 million in the account in 10 years? a. P 4.26 M b. P 1.59 M c. P 8.79 M d. P 6.14 M 36. A PBA rookie, playing for Ginebra is earning an average annual salary of P 5,000,000 for 10 years. Star would like to acquire his services as a replacement of the retired Marc Pingris, offered him an initial annual salary of P 3,000,000 but is increasing at the rate of $400,000 annually. If he can still play in the PBA for 10 years and money is worth 10%, which one is true? a. Star’s offer is smaller than that of Ginebra’s b. Star’s offer is exactly the same as Ginebra’s c. Star’s offer is just few Pesos more per year than that of Ginebra’s d. Star’s offer is over P 150,000 per year than that of Ginebra’s 37. Find the product of (4 – 2i) and (4 + 3i) a. 22 + 4i b. 16 + 6i

c. 18 + i

38. Find the value of θ in the following equation: 4 sin x = 3 a. 0.55 b. 0.85 c. 0.94

d. 20 + 3i d. 1.18

39. A 50 m. steel tape was standardized and supported throughout its whole length and found to be 0.00205 m. longer at an observed temperature of 31.8° C and a pull of 10 kilos. This tape was used to measure a line which was found to be 662.702 m. at an average temperature of 24.6°C using the same pull. Use coefficient of expansion of 0.000016 m. per degree centigrade. Compute the correct length. a. 662.67 m b. 662.45 c. 662.80 d. 662.01 40. The chainage of the intersection point of two straights is 1060 m, and the angle of intersection is 120°. If radius of a circular curve to be set out is 570 m, and peg interval is 30 m, determine the tangent length. a. 355.89 m b. 301.50 c. 329.09 d. 316.78 41. Imaginary lines passing through places where magnetic declinations are the same at a given time. a. Orthogonic lines b. Isogonic lines c. Agonic lines d. Isoclinic lines 42. If the effective rate is 24%, what nominal rate of interest is charged for a continuously compounded loan? a. 21.51% b. 23.25% c. 22.35% d. 21.90% 43. Find the surface area of the right cylinder of greatest surface which can be inscribed in a sphere of radius r. a. πr(1 - √5) b. πr(1 + √5) c. πr^2(1 + √5) d. πr^2(1 - √5) 44. The logarithm of 1 to any base is: a. indeterminate b. 0

c. infinity

d. 1

45. What is the power required to transfer 97,000 coloumbs of charge thorough a potential rise of 50 volts in one hour? a. 0.5 kW b. 1.3 c. 0.9 d. 2.8 46. Determine the no of ways to choose five numbers from the first 18 positive integers such that any two chosen numbers differ by at least 2.

a. 1870

b. 2130

c. 1988

d. 2002

47. A force is given by a vector F = 3i + 4j + 5k and moves a particle from the point P (2,1,0) to the point Q(4,6,2). Find the work done. a. 55 J b. 81 c. 36 d. 60 48. Compute the impact factor for a horizontal curve radius of 400 m if the design speed is 120 kph. a. 0.283 b. 0.315 c. 0.447 d. 0.519 49. Evaluate the following: (4 cos^4 36° - 5cos^2 36° + 1)^2. a. 1 b. 5/16 c. 7/23

d. 10/29

50. The volume of the truncated prism is 8200 cu in. The base is right reaction which is rectangular with its length twice its width. The edges perpendicular to the base are 16 in, 12 in, 12 in, and 16 in. Determine the width of the base in inches. a. 17.1 in. b. 22.7 c. 19.5 d. 14.4 51. In a topographic survey, three triangulation stations A, B and C are sighted from point P. The distance between the stations are AB = 500 m., BC = 350 m., and CA = 450 m. At P, the angle subtending AC is 45° while for BC is 30°. AC is due north. Find the azimuth of PA. a. 88° b. 75° c. 94° d. 118° 52. The following data are the cross section notes at station 0 + 020 and 0 + 040. The natural ground slope is almost even. Base width

Side slope

Cut = 9 m Fill = 8 m

Cut 1:1 Fill = 1.5:1

Station 0 + 020

Station 0 + 040

Compute the volume of the borrow or waste in a 20 m distance assuming shrinkage factor of 1.20. a. 71.55 m^3 b. 60.06 c. 55.74 d. 83.76 53. Find the area bounded by the curves y = x, y = 2, and y = x^2. a. 8/5 b. 6/11 c. 5/4

d. 7/6

54. Find the remainder when x^2016 is divided by x^2 – x. a. 0 b. 2016 c. -1

d. x

55. A cylindrical round of cheese is cut into several pieces using seven cuts. Five cuts are vertical, perpendicular to the top of the round, and two at a diagonal, as shown in the diagram. Each cut is made with a straight blade and the diagonal cuts are made through the lines formed by the vertical cuts. The total number of pieces of cheese that result is: a. 21 b. 24 c. 36 d. 60 56. The chart datum for harbour works is generally the: a. Lowest observed water level c. Mean tidal high water level b. Lowest astronomical tide d. Mean tidal low water level 57. Obtain the general solution: y’ = xy^2. a. y(x^2 + C) + 2 = 0 b. y(x^2 + C) – 2 = 0

c. (x^2 + C) + 2 = 0 d. (x^2 + C) – 2 = 0

58. A man paid P 110,000 for a P 100,000 bond that pays P 4000 per year. In 20 years, the bond will be redeemed for P 105,000. What net rate of interest will the man obtain on his investment? a. 3.37% b. 3.47% c. 3.56% d. 3.40% 59. Find the polar coordinates for the point having a rectangular coordinate of (3, -4). a. 6,1178° 20’ b. 4,220° 12’ c. 5, 287° 20’ d. 5, 306° 52’ 60. A line was measured to have 5 tallies, 6 marking pins, and 63.5 links. How long is the line in ft? a. 5487.6 b. 5588.1 c. 5663.5 d. 5730.9 61. In triangle ABC, BC = 40 and AB = 50. Use angle A = 55°. Find the perimeter of the triangle. a. 188.9 m b. 177.2 c. 131.9 d. 122.4

62. The inside dimensions of a trunk are 4 m, 3 m, and 2 m. Find the dimensions of a trunk similar in shape that will hold 4 times as much in meters. a. 6.35 x 4.76 x 3.17 b. 6.88 x 5.15 x 2.44 c. 6.56 x 4.85 x 2.77 d. 6.21 x 4.59 x 3.85 63. Full breaks were applied when the car’s speed was 60 kph. If the length of skid mark is 59 m, find the average skid resistance. a. 0.19 b. 0.24 c. 0.38 d. 0.50 64. Equity sources of funding include not only stockholder’s capital but also earnings retained by the company for reinvestment in the business and the cash flow resulting from depreciation charges against income. This is also known as: a. After tax equity b. Equity capital c. Cost cutting d. Capital Asset 65. Given the equation of the ellipse x^2/16 + y^2/4 = 1, determine the largest rectangular area that can be inscribed in the ellipse. a. 24 b. 16 c. 18 d. 32 66. A line AB between the stations A and B was measured as 348.28 using a 20 m tape, too short by 0.05 m. Determine the correct length of AB. a. 347.12 b. 347.23 c. 347.41 d. 355.49 67. The sum of the sides of two polygons is 12 and the sum of their diagonals is 19. The polygons are: a. pentagon and heptagon c. quadrilateral and octagon b. both hexagon d. triangle and nonagon 68. How many ways are there for 7 people to sit in a row, if two people, Ian and Lemuel, have to sit at least two seats apart? a. 2400 b. 720 c. 120 d. 840 69. A GMA tower and a monument in Tomas Morato stand on a level plane. The angles of depression at the top and bottom of the monument viewed from the top of the GMA tower at 13° and 35° respectively. The height of the tower is 50 m. Find the height of the monument. a. 29.13 b. 30.11 c. 32.12 d. 33.51 70. An easement curve has a length of spiral equal to 60 m. having a central curve of a raduis of 400 m. The design velocity of the car allowed to pass thru this portion is 100 kph. Compute the rate of increase of the centripetal acceleration. a. 0.668 m/s^2 b. 0.755 m/s^2 c. 0.896 m/s^2 d. 0.954 m/s^2 71. If a letter is chosen at random from the English alphabet, find the probability that the letter is a vowel exclusive of y. a. 9/26 b. 5/26 c. 19/26 d. 4/5 72. Evaluate this complex expression: tan (3i). a. coth (-3) b. tanh (3)

c. tanh (-3)

d. coth (3)

73. What is the eccentricity of the curve 9x^2 + 25y^2 – 144x + 200y + 751 = 0? a. 0.75 b. 1.00 c. 0.80 d. 1.15 74. In transportation planning, it entails transportation facilities and programs. a. Planning process b. Right of way process 75. Find the 6th term in the expansion of (4x/5 a. 5040x b. -5040x

the

generation

of

plans

for

various

c. Programming process d. Construction process – 5/2x)^9. c. 5040/x

d. -5040/x

types

of

CE GREAT MINDS PREBOARD 3 HYRAULICS 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. 1.

A canal has hydraulic radius of 0.41 m, slope = 0.008, roughness coefficient = 0.025. Find the value of C using Kutter Formula. a. 33.7 b. 34.2 c. 35.8 d. 32.9

2.

Carbon tetrachloride with a mass of 500 kg is placed in a container with 0.315 m^3 in volume. Find the specific gravity. a. 1.587 b. 1.618 c. 1.954 d. 0.876

3.

A saturated clay layer has a thickness of 10 m with a water content of 51% and a sp gr. of 2.72. Find the effective stress at the bottom. a. 61.9 kPa b. 70.6 c. 84.7 d. 91.2

SITUATION 1: The moist unit weight of a soil is 16.5 kN/m^3. Given that the ω = 0.15, Gs = 2.70, 4. 5. 6.

Determine the porosity of the soil. a. 0.46 b. 0.64

c. 0.31

d. 0.55

Determine the degree of saturation. a. 0.84 b. 0.36

c. 0.48

d. 0.75

Determine the mass of water in kg/m^3 that must be added to reach full saturation. a. 2986 b. 2079 c. 2340 d. 2716

SITUATION 2: A jet discharges 5.19 L/s from a 35 mm ϕ orifice in a vertical plane under a head of 4 m. The jet centreline passes through the point 4.28 m horizontally from the vena contracta and 1.2 m below the center of the orifice. 7. 8. 9.

Find the coefficient of discharge. a. 0.719 b. 0.609

c. 0.551

d. 0.389

Find the coefficient of velocity. a. 0.977 b. 0.516

c. 0.781

d. 0.638

Find the coefficient of contraction. a. 0.623 b. 0.571

c. 0.489

d. 0.712

SITUATION 3: A given layer of soil has a dry unit weight of 14.72 kN/m3 and a saturated unit weight of 20.12 kN/m3. The ground water table is located 2m. below the ground surface. 10. Determine the total stress point at A 4.5 m below the ground surface. a. 88.15 kPa b. 107.59 c. 91.23 d. 79.74 11. Find the pore pressure at A at the same surface a. 24.53 kPa b. 37.20 c. 51.19

d. 64.77

12. Find the effective stress at A at the same surface. a. 59.13 kPa b. 68.12 c. 44.87

d. 55.21

SITUATION 4: A confined aquifer shown in the figure has a source of recharge. The hydraulic conductivity of the aquifer is 35 m/day with a porosity of 25%. The head surface in the two observation wells 1000 m apart are shown. The aquifer has an average thickness of 4 m and and average width of 4 km.

13. Determine the nearest value to the rate of flow of water through the aquifer. a. 5500 m^3/day b. 5600 c. 5200 d. 5800 14. Determine the seepage velocity in m/day. a. 1.4 m/day b. 1.5

c. 1.3

d. 1.2

15. Find the time of travel from the head of aquifer to a point 4 km downstream in days. a. 2667 b. 2857 c. 3077 d. 3333 SITUATION 5: The elasticity and dimensions of the pipe are such that celerity of the pressure wave is 970 m/s. Suppose the pipe has the length of 1600 m and 1.2 m ϕ flowing at 0.85 m^3/s. 16. Find the water hammer pressure for instantaneous valve closure. a. 447.9 kPa b. 319 c. 727.5

d. 918.6

17. Find the time allowed for closing a valve to avoid water hammer. a. 5.16 s b. 1.88 c. 3.30

d. 4.68

18. Find the water hammer pressure of the valve if it is closed in 4 secs. a. 600.19 kPa b. 557.13 c. 648.21 d. 733.96 SITUATION 6: A consolidated drained tri axial test was conducted on a normally consolidated clay. The results as follows: Chamber confining pressure = 138 kPa Deviator stress = 258 kPa 19. Find the friction angle of soil. a. 28.89° b. 33.18°

c. 34.73°

d. 39.12°

20. Find the normal stress at failure. a. 179.20 kPa b. 204.68

c. 222.19

d. 181.45

21. Find the shear stress at failure. a. 107.47 kPa b. 256.79

c. 112.95

d. 184.45

22. The potential energy at the optimum cost , the design criteria focus on the choice of location, design discharge and head by suitable numerical techniques. This system is known as: a. Water supply optimization c. Water power utilization b. Wastewater treatment d. Sanitary management SITUATION 7: A liquid having a Reynolds number of 1900 flows through a 200 mm ϕ pipe, 150 m long. The head loss of the pipe due to friction is 22 m. 23. Compute the friction factor. a. 0.034 b. 0.047

c. 0.055

24. Determine the kinematic viscosity. a. 1.774 x 10^-5 m^2/s b. 1.623 x 10^-5

c. 1.815 x 10^-5 d. 1.368 x 10^-5

25. Compute the rate of flow in L/s. a. 1470 b. 1555

c. 1389

d. 0.060

d. 1929

26. An object weighs 4 N in water and 5 N in an alcohol (S = 0.80). Use γw = 9.79 kN/m^3. Find the density of the object. a. 1900 kg/m^3 b. 1868 c. 1519 d. 1796 27. The specific gravity and density of water is highest when the temperature is : a. 0℃ b. 4℃ c. Below zero d. 100℃ SITUATION 8: A 600 mm ϕ pipe , 10 mm thick carries water under a head of 325 m. 28. Determine the actual stress in kN per meter length of pipe. a. 95.65 MPa b. 100.77 c. 109.21

d. 74.58

29. If the head is increased to 500 meters, what is the actual stress on the wall in MPa? a. 124.58 MPa b. 100.21 c. 147.15 d. 158.61 30. If the head is increased to 500 meters, what thickness is required assuming , an allowable tensile stress of 113 MPa and efficiency of the connection is 80%? a. 15.2 mm b. 16.3 c. 19.3 d. 21.6 31. It refers to the ice coating generally clear and smooth , formed on exposed surfaces by the freezing super cooled water deposited by rain or drizzle. a. Rime b. Snow c. Glaze d. Drizzle SITUATION 9: From a given data , shows a sieve analysis of soil samples A, B and C. Sieve No. 4 8 10 20 40 60 100 200

Diameter(mm) 4.760 2.380 2.000 0.840 0.420 0.250 0.149 0.074

Liquid Limit Plastic Limit

A 90 64 54 34 22 17 9 4

B 100 90 77 59 51 42 35 33

c 100 100 98 92 84 79 70 63

-----

46 29

47 24

Refer to the last page of the exam. 32. Classify soil A. a. SW

b. SC

c. SP

d. CL

33. Classify soil B. a. SC

b. GP

c. CL

d. GW

c. 93

d. 23

34. Find the Plasticity index in soil C. a. 1 b. 0

SITUATION 10: A vertical retaining wall 6 m high retains a horizontal backfill having the following properties: Void ratio = 0.60 Sp gr = 2.60 Water content = 24% Angle of internal friction = 25° 35. Compute the magnitude of the active force acting on the wall if the water surface is on the ground surface which is on level with the top of the wall. a. 222.16 kN/m b. 262.48 c. 219.06 d. 248.27 36. Compute the magnitude of the active force acting on the wall if the water table is lowered at a depth of 3 m. from the ground surface. a. 119.36 kN/m b. 124.58 c. 131.90 d. 149.42 37. Compute the magnitude of the active force acting on the wall if the water table is at the bottom of the wall. a. 108.30 kN/m b. 116.30 c. 144.48 d. 100.38 SITUATION 11: The flow rate of the pipe system is shown is 50 L/s under a total head loss from A to D equal to 9 m. Using C = 120 for all pipes.

38. Compute the head loos of pipeline B. a. 1.90 m b. 0.88

c. 1.32

d. 1.61

39. Compute the discharge of pipeline B. a. 0.078 m^3/s b. 0.019

c. 0.117

d. 0.036

40. Compute the diameter of pipeline C. a. 150 mm b. 180

c. 130

d. 220

SITUATION 12: A group of friction piles in deep clay is shown in the figure. The total load on the piles reduced by weight of soil displayed by the foundation is 1800 kN. Thickness of silt is 2 m. and that of clay is 16 m.

41. Compute the effective overburden pressure. a. 131.78 kPa b. 142.59

c. 161.58

42. Compute the compression index of the clay layer. a. 0.226 b. 0.268 c. 0.315

d. 127.20 d. 0.417

43. Compute the approximate total settlement of the pile foundation. a. 145 mm b. 180 c. 215

d. 160

44. He observed that, if the soil behind the sheet-pile wall has grain sizes that are predominantly smaller than those of coarse sand, the active earth pressure after construction sometimes increases to an at-rest earth-pressure condition. a. Das b. Boussinesq c. Casagrande ` d. Terzaghi SITUATION 13: A straight tube 1.2 m long closed at the bottom and filled with water is inclined 30° with vertical and rotated about a vertical axis through its midpoint at 8.02 rad/s as shown in the figure.

45. Compute the value of y. a. 0.318 b. 0.412

c. 0.295

d. 0.107

46. Compute the pressure at the bottom of the tube. a. 11.18 kPa b. 19.22 c. 10.20

d. 8.77

47. Compute the pressure at the midpoint of the curve. a. 2.20 kPa b. 1.77 c. 0.89

d. 3.37

48. An aeroplane weighing 65 kN, has a wing area of 27.5 m^2 and a drag coefficient of Cd = 0.02 + 0.061x(CL)^2 . Assume for air at ambient conditions, Density is 0.96 kg/m^3. Determine the lift coefficient if the craft is cruising at 700 km/h. a. 0.077 b. 0.021 c. 0.038 d. 0.088 SITUATION 14: A pump draws water from reservoir A and lifts it to reservoir B as shown. The loss of head from A to 1 is three times the velocity head in the 150 mm pipe and the loss from 2 to B is 15 times the velocity head in the 100 mm pipe when the discharge is 20 L/s.

49. Determine the horsepower output of the pump in kW. a. 40.20 kW b. 49.77 c. 48.10

d. 44.36

50. Compute the pressure head at point 1. a. 11.38 m b. 9.16

d. 19.74

c. 15.26

CE GREAT MINDS 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. Notes: For structural provisions, see NSCP 2010 and NSCP 2001. SITUATION 1: The width of the rectangular beam is 300 mm. The depth of the compression block for a balanced condition is 255 mm. If f’c = 28 MPa, fy = 414 MPa, Es = 200000 MPa. Use 70 mm as steel covering. Unit weight of concrete is 24 kN/m^3. 1. 2. 3.

Determine the total depth of the beam for a balanced condition. a. 510 mm b. 580 c. 600

d. 450

Compute its area of reinforcement. a. 4100 mm^2 b. 3500

d. 4000

c. 4400

Determine the factored super imposed uniform load that a 6 m simple span beam could support for a balanced condition. a. 114.98 kN/m b. 134.27 c. 155.47 d. 184.21

SITUATION 2: A hollow circular pole 6 m thick, with 300 mm outside diameter and height of 3 m. weighs 150 N/m. The pole is subjected to the following vertical load P = 3 kN at an eccentricity e = 100 mm from the centroid of the section, lateral force H = 0.45 kN at the top of the pole. 4.

Determine the maximum compressive stress at the base due to the loads. a. 1.29 MPa b. 1.55 c. 1.78 d. 2.12

5.

Determine the maximum tensile stress at the base due to vertical and lateral loads. a. 3.66 MPa b. 4.05 c. 2.48 d. 3.58

6.

If the hollow hole is replaced by a solid wood pole of 250 mm diameter, determine the maximum shear stress at the base. a. 0.007 MPa b. 0.012 c. 0.025 d. 0.004

7.

A simply supported girder of a bridge spans 25 m. The standard truck load (H load) consists of two moving loads, P1 = 142.4 kN and P2 = 35.6 kN spaced at 4.3 m apart. Calculate the maximum moment in the girder. a. 1037.3 kN m b. 1154.6 c. 1286.9 d. 1520.8

SITUATION 3: A concrete block of weight W, holds a ring anchor bolt to which are fastened two guy wires as shown in Figure JLS.

8. 9.

Calculate the resultant force acting on the bolt. a. 11.6 kN b. 8.8 c. 10.9

d. 7.5

Determine the angle which the resultant pull makes with the horizontal. a. 26.8° ` b. 44.7° c. 54.5° d. 61.2°

10. To prevent uplift, what is the minimum weight of the concrete block W if the required factor of safety is 1.3? a. 12.75 kN b. 15.50 c. 10.11 d. 11.53 11. A simply supported beam with a span of 6.0 meters carries a vertical load that decreases uniformly from zero at the left end to a maximum value of 9 kN/m at the right end. The larger reaction occurs at the right and has a value of: a. 27 kN b. 18 c. 45 d. 9

SITUATION 4: In the figure shown that DL = 5 kN/m , LL = 3.5 kN/m , P = 0, C1 to C4 = 0, H1 = 3 m, H2 = 6 m and L1 = L2 = 4 m.

12. Solve the axial force at AC. a. 55.7 kN b. 33.8

c. 42.5

13. Compute the maximum shear at CD. a. 42.5 kN b. 57.6

c. 83.5

14. What is the maximum moment at CDE? a. 79 kN m b. 110

c. 66

d. 56.3 `

d. 33.2 d. 85

SITUATION 5: A block having a weight of 400 N moves at a velocity of 1.5 m/s at point A, slides vertically along the surface of a smooth cylinder 2.4 m in radius. It leaves the surface at B. 15. Determine the angle at which the block leaves the surface of the cylinder. a. 33.18° b. 45.69° c. 55.12° d. 60.56° 16. Find the velocity of the block as it leaves the surface. a. 2.12 m/s b. 1.77 c. 5.19

d. 4.06

17. Find the distance that the block will move horizontally measured from the center of the cylinder before it strikes the ground. a. 5.36 m b. 6.64 c. 8.18 d. 12.79 18. A beam is fixed at both ends and determinancy of the beam. a. 1° indeterminate b. unstable

has

an

internal

hinge

c. 2° indeterminate

along

the

d. determinate

SITUATION 6: A rectangular footing is subjected to the following service loads: Axial loads – DL = 580 kN LL = 420 kN Moment along x-axis – DL = 105 kN m Moment along y-axis – DL = 140 kN m

LL = 45 kN m LL = 110 kN m

Height of earthfill along the footing = 1.5 m Soil unit weight = 17 kN/m^3 Concrete unit weight

= 24 kN/m^3

19. Calculate the maximum soil pressure. a. 325 kPa b. 350

c. 360

d. 400

20. Calculate the minimum soil pressure. a. 10.77 kPa b. 8.34

c. 6.79

d. 5.18

21. Calculate the required soil bearing capacity. a. 364.9 kPa b. 412.6 c. 318.5 SITUATION 7: Given the truss shown in the figure,

span.

d. 601.2

Classify

the

22. Compute the force AC. a. 4 kN (C) b. 4 kN (T)

c. 5.66 kN (C)

d. 0

23. Compute the force BE. a. 4 kN (C) b. 4 kN (T)

c. 5.66 kN (C)

d. 0

24. Compute the force BD. a. 2 kN (C) b. 0

c. 4 kN (C)

d. 5.66 kN (T)

SITUATION 8: Two A 36 L 150 x 90 x 10 angles are used with a 10 mm gusset plate to create a top chord of a truss. The long legs are back to back making the short legs unstiffened elements. 25. Determine the radius of gyration along the y axis. a. 44.78 mm b. 35.69 c. 53.53

d. 61.02

26. Determine the actual slenderness ratio,kL/r. a. 82.02 b. 77.06 c. 64.85

d. 56.04

27. Determine the axial force of the column. a. 319 kN b. 447

d. 568

c. 490

28. A project has been bid out by DPWH. The approved agency estimate is P 500 million. The results of responsible bidders are as follows: Bidder A = P 550.234 million Bidder B = P 610.346 million Bidder C = P 454.219 million Bidder D = P 389.123 million Bidder E = p 284.758 million Which of the following gives the bidder to which the award can be made? Please refer to PD 1594 for the provisions. a. D b. C c. A d. E SITUATION 9: A steel moment resisting frame is shown having the different loads for each storey, Ct = 0.0853. The building was designed to have a base shear of 2400 kN.

29. Compute the period of vibration of the structure. a. 0.665 sec b. 0.745 c. 1.156

d. 1.515

30. Compute the lateral force acting on the 3rd floor. a. 418.20 kN b. 520.76 c. 573.48

d. 600.21

31. Compute the moment of the structure. a. 55132.11 kN m b. 44581.12

d. 24556.18

c. 30812.60

SITUATION 10: The four gears are attached to a steel shaft that is rotating at 2 Hz. Gear B supplies 70 kW of power to the shaft. Of that power, 20 kW are used by gear A, 20 kW by gear C, and 30 kW by gear D. Use G = 83 GPa for steel. 32. Determine the torsion along segment BC. a. 3979 N m b. 2248

c. 4523

d. 1988

33. Determine the uniform shaft diameter if the shear stress in the shaft is not exceeded to 60 MPa. a. 55 mm b. 70 c. 115 d. 90 34. If a uniform shaft diameter of 100 mm is specified, determine the angle by which one end of the shaft lags behind the other end. a. 0.277° b. 0.332° c. 0.448° d. 0.519° 35. It was devised by Otto Mohr in 1915 that applies to the analyses that uses the relation of the slope and deflection of the indeterminate structures. a. Three Moment Equation c. Slope Deflection Method b. Conjugate Beam Method d. Influence Lines SITUATION 11: Define the following in materials engineering. 36. In the system of designating wrought aluminium alloys, the letter F that follows the number indicates what condition of the alloy? a. As fabricated b. Strain hardened c. Annealed d. Artificially aged 37. The commercial size designation of width and depth, in standard sawn lumber and glued laminated lumber grades somewhat larger than the standard size of dressed number. a. nominal size b. rough size c. normal size d. dressed size 38. It is generally a sand which consists of particles that will pass through No. 4 sieve. a. Coarse aggregate b. Fine aggregate c. Sand d. Gravel SITUATION 12: In the given beam shown,

39. Calculate the shear at B considering the left side. a. 11.5 kN b. 10.6 c. 17.4

d. 14.5

40. Compute the maximum moment. a. 22.8 kN m b. 16.6

d. 31.8

c. 20.7

SITUATION 13: A T section has a flange thickness of 125 mm with an effective depth of 437.5 mm. The width of the stem is 400 mm. The beam carries a negative moment of 610 kN m. f’c = 27.6 MPa, fy = 414.6 MPa. Balanced steel ratio is 0.0285. Use steel covering for top and bottom bars if any is 62.5 mm. 41. Determine the maximum moment capacity of the section as singly reinforced. a. 318.6 kN m b. 684.9 c. 555.6 d. 494.9 42. Determine the total steel area needed for tension. a. 4233 mm^2 b. 4461 c. 4567

d. 4819

43. Determine the steel area needed for compression if the maximum moment capacity of the beam is not sufficient. Assume steel in compression will yield. a. 695 mm^2 b. 788 c. 822 d. 1061

SITUATION 14: 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. The length L1 equals to 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.

44. Find the tensile force P based on gross area. a. 101.48 kN b. 138.24 c. 133.16

d. 156.49

45. Find the tensile force based on net area, if the strength reduction factor is 0.85. a. 177.46 kN b. 157.93 c. 138.19 d. 101.43 46. Find the tensile force based on block shear. a. 375 kN b. 393 c. 304

d. 313

SITUATION 15: A beam is formed by connecting two timber joists each 100 x 400 mm with a steel plate 12 x 300 mm placed symmetrically between them. The beam is subjected to a moment of 50 kN m. the ratio of Young’s modulus for steel to that of timber is 2:1. 47. Compute the moment of inertia for the system. a. 94 x 10^6 mm^4 b. 116 x 10^6 c. 175 x 10^6

d. 152 x 10^6

48. Determine the maximum stress in steel. a. 64.7 MPa b. 55.4

c. 79.0

d. 85.9

49. Determine the maximum stress in timber. a. 7.2 MPa b. 8.7

c. 3.9

d. 10.6

SITUATION 16: The cross section shown of a hollow beam with effective depth of 400 mm. The beam is reinforced with 4 – 16 mm ϕ bars placed 60 mm from the center of the bottom of the beam. If f’c = 7 MPa, fs = 124 MPa and n = 12, at 6 m span with a concentrated load of 8 kN.

50. Compute the moment capacity of the concrete. a. 95.59 kN m b. 41.27 c. 88.21

d. 83.74

51. Compute the moment capacity of steel. a. 23.89 kN m b. 54.27

d. 35.15

c. 40.17

52. Compute the total uniform load (includes own weight) could the beam carry. a. 5.14 kN/m b. 3.77 c. 6.84 d. 11.71 53. A stone is dropped from the deck of a bridge. The sound of the splash reaches the deck 3 seconds later. The speed of the sound is 342 m/s in still air. Find the height of the deck above the water. a. 24.7 m b. 40.6 c. 33.1 d. 55.2 54. Concrete hollow blocks are tested for its: a. compression b. absorption SITUATION 17: In the figure shown,

c. dimension

d. All of these

55. Determine the centroid along the x – axis. a. 77.1 mm b. 48.2

c. 33.9

d. 81.8

56. Compute the moment of inertia along the y – axis. a. 39.42 x 10^6 mm^4 b. 53.23 x 10^6 c. 84.44 x 10^6

d. 49.12 x 10^6

57. Compute the product of inertia at v axis using Mohr’s circle. a. 275 x 10^6 mm^4 b. 308 x 10^6 c. 258 x 10^6

d. 347 x 10^6

SITUATION 18: Built up column 10 m long consists of W 350 x 90 with two plates 12 mm thick welded to form a box section with respect to x axis column is fixed, y axis column is braced at mid height. Properties of WF section: A = 11,540 mm^2 Ix = 2.66 x 10^8 mm^4 Iy = 0.44 x 10^8 mm^4

bf tr tw Fy

= = = =

250 mm 16 mm 10 mm 248 MPa

58. Compute the effective slenderness ratio with respect to x axis. a. 55.19 b. 37.64 c. 44.27

d. 49.15

59. Compute the effective slenderness ratio with respect to y axis. a. 36.02 b. 50.27 c. 58.13

d. 61.24

60. Compute the Compressive stress of the column. a. 188.21 MPa b. 119.21 c. 164.29

d. 133.14

SITUATION 19: From the figure shown,

61. Find the area of M/EI diagram for the entire span of a given beam shown. a. 0.0033 b. 0.0049 c. 0.0068 d. 0.0021 62. Determine the deviation of the left support. a. 7.55 mm b. 6.21 c. 2.22

d. 3.84

63. Determine the slope at maximum. a. 0.044° b. 0.079°

d. 0.029

c. 0.095°

64. In this technique, a plain or reinforced concrete slab is overlaid on top of the existing slabs or beams to increase the section dimension in order to increase flexural strength. a. Over Slabbing b. Shotcreting c. Steel Bonding d. Extrenal Prestressing 65. One span of a continuous reinforced concrete beam subjected to gravity loading of 44 kN/m is shown in the figure. Neglect the effect of compression reinforcement. F’c = 27.6 MPa and fy = 414.7 MPa. Find the length of L2.

a. 3.53 m

b. 4.27

c. 3.66

d. 3.08

SITUATION 20: A reinforced concrete beam has a width of 300 mm and an effective depth of 520 mm is reinforced for tension with 4 – 28 mm ϕ bars. The beam is subjected to an ultimate shear force of 220 kN and a factored moment of Mu = 56 kN m. 66. Determine the nominal shear strength using detailed calculations. a. 177.21 kN b. 156.29 c. 184.77

d. 141.80

67. Determine the spacing of the 10 mm ϕ web reinforcement. a. 200 mm b. 150 c. 275

d. 150

68. Find the minimum area of the shear reinforcement required. a. 56.25 mm^2 b. 70.70 c. 59.92

d. 84.73

SITUATION 21: The cross section of a beam is formed by gluing two pieces of wood together as shown.

69. Determine the moment of inertia of the section shown. a. 10.57 x 10^6 mm^4 b. 11.77 x 10^6 c. 15.55 x 10^6

d. 13.91 x 10^6

70. Find the shear stress at the neutral axis. a. 3.77 MPa b. 3.28

c. 4.55

d. 5.19

71. Find the shear stress on glue joint. a. 24.7 MPa b. 22.9

c. 31.8

d. 39.2

72. Quality control testing in DPWH projects is the responsibility of the: a. Structural engineer c. Owner b. Contractor d. Architect

SITUATION 22: If each cable can withstand a maximum tension of 1000 N in the figure shown,

73. Find the tension in the cable AD. a. 57.99 N b. 218.23

c. 500

74. Find the largest mass of the cylinder for equilibrium. a. 90.3 kg b. 88.2 c. 57.9

d. 1000 d. 98.1

75. Determine the vertical displacement of joint A in the figure shown. Each bar is made of steel and has a cross sectional area of 600 mm^2. Use E = 200 GPa and solve via virtual work method.

a. 0.536 mm

b. 0.456

c. 0.237

d. 0.188