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7.

MATHEMATICS and SURVEYING MAY 2019 1.

2.

CE BOARD May 2019 >

3.

A germ population has a growth curve Ae0.4t. At what value of t does its original value doubled?

The Wollomombi Falls in Australia have a height of 1100 ft. A pebble is thrown upward from the top of the falls with an initial velocity of 20ft/sec. The height of the pebble “h” after the “I” sec is given by the equation h = - 16 t2 + 20t + 1100. How long after the pebble is thrown will hit the ground?

CE BOARD May 2019 > A person driving her car 45 kph approaches an intersection just as the traffic lights turns yellow. She knows that the yellow light lasts only 2.0 sec before turning red and she is 28 m from the near side of the intersection. Should she try to stop or she speeds up to cross the intersection before the light turns red? The intersection is 15 m wide. Her car’s maximum deceleration is -5.8 m/s2, whereas it can accelerate from 45 kph to 65 kph in 6.0 sec. Ignore the length of her car and her reaction time. a)

She should speed up to cross the intersection before the light turns red. b) She should adjust the rate of deceleration and wait for the next red light. c) She should maintain the rate of deceleration and continue as she would pass through the intersection against the green light. d) She should adjust the rate of deceleration, stop and wait for the next green light.

4.

CE BOARD May 2019 >

CE BOARD May 2019 >

Given the following cross-section notes for a road grading work: −3.2 1.2 1.2 2.8 + + + 𝑋1 0 3.5 𝑋2 The road bed is 9 m wide and the side slope for cut is 1:1 and for fill is 1.5:1. Determine the area of cut if the section. 5.

CE BOARD May 2019 >

A 2 kg body is tied to the end of a chord abd whirled in a horizontal circle of radius 1.5 m at 3 revolutions per sec. Neglecting the attraction due to gravity, find the acceleration of the body toward the center of the circle in m/s2? 6.

CE BOARD May 2019 >

Find the equation of the curve passing through the point (3, 2) and having the slope 5x2 – x at every point (x, y).

CE BOARD May 2019 >

Device mounted on a fixed support (permanent signs) or portable support (temporary signs) whereby a specific message is conveyed by means of words or symbols placed or erected for the purpose of regulating, warning or guiding traffic. a) b) c) d)

Roadwork signs Overhead signs Traffic signs Special instruction signs

12. CE BOARD May 2019 > A machine was purchased at an original cost of P400, 000 with a salvage value of P20, 000. Life of this machine expected to last for 6 years. It was used for 4000 hrs. in the first year, 6000 hrs. in the second year, and 6000 hrs. on the 3rd year. The machine is expected to last for 38000 hrs. in the period of 6 yrs. Which of the following gives the depreciation at the end of the second year? 13. CE BOARD May 2019 >

8.

CE BOARD May 2019 >

A maximum wave height and wave period of the maximum wave height in wave train. a) Deep water wave b)

9.

Equivalent depth water wave height

c) Highest wave d) Significant wave CE BOARD May 2019 >

Find a polar equation that has the same graph as the circle x2 + y2 = 4y. 10. CE BOARD May 2019 > Two trains going in opposite directions leave the time. One train travels 15 mph faster than the other, in 6 hours, the trains are 630 miles apart. Find the speed of each. 11. CE BOARD May 2019 > What is the process of proportioning the cement, water, aggregates and additives prior to mixing concrete called? a) b) c) d)

AB is diameter of a circle, BC is a chord 10 cm, long, CD is another chord. Angle ABC = 18֯ . What is the area of the circle in sq.cm.

Paving Mixing Batching Curing

14. CE BOARD May 2019 > Suppose you receive x dollars in January. Each month thereafter you receive $100 more than you received the month before. Write a factored polynomial that describes the total dollar amount you received from January through April. 15. CE BOARD May 2019 > A polyhedron having 12 faces and has for its face 12 regular pentagon is called dodecahedron. Determine the number of edges. 16. CE BOARD May 2019 > If the perimeter of a rectangle is 68 meters and the length is 14 m more than the width, what are the dimensions of the rectangle?

17. CE BOARD May 2019 >

22. CE BOARD May 2019 >

27. CE BOARD May 2019 >

32. CE BOARD May 2019 >

How many different ways are there to arrange six people in a round table?

The angle of elevation of the top of a building from point A on a ground is 24.2֯. From point B, which is 44.5 ft. closer, the angle of elevation is 38.1֯. What is the height of the building?

During the Winter Olympics Game in Torino, Italy, the total number of gold medals won by Germany, Canada, and United States were three consecutive odd integers. Of these three countries, Germany won the fewest. If the sum of the first integer, twice the second integer, and four times the third integer is 69, find the number of gold medals won by each country.

A circular pool of water is expanding at the rate of 16𝜋 in2/sec. at what rate is the radius expanding when the radius is 4 inches (in inches per minute)?

18. CE BOARD May 2019 > When directly generated and affected by local winds, a wind wave system is called: a) b) c) d)

A circle has an equation of x2 + y2 + 2ky = 0. Find the value of k when the length of the tangent from (5, 4) to the circle is equal to one.

Wind seiching Wind swell Wind wakes Wind sea

28. CE BOARD May 2019 >

19. CE BOARD May 2019 > From the given data shown: Score Frequency

1 14

2 15

3 14

23. CE BOARD May 2019 >

4 17

5 10

24. CE BOARD May 2019 > A new corporate bond is being offered in the market for $930. The bond has a face Value of P1, 000 and matures in 10 years. The issuing corporation promises to pay $70 in interest every year. What is the company’s cost of the capital raised though this bond issue if the stock broker’s fee is $15 per bond sold?

Determine the standard deviation. 20. CE BOARD May 2019 > An 80-m spiral connects a tangent with a 180m radius circular curve. The maximum velocity in kph that a car could pass through the curve without skidding is nearest to: 21. CE BOARD May 2019 > An engineer designs simple curve at a certain point of a highway. The data for the simple curve area: I = 44֯ R = 400 ft. P.C. = 11 + 10.57 P.T. = 14 + 17.75 Compute the deflection of station 13 + 00.

25. CE BOARD May 2019 > The passengers on an excursion bus consisted of 14 married couples, 8 of whom brought no children and, 6 of whom brought 3 children a piece. Counting the driver, the bus has 31 occupants How is this possible? 26. CE BOARD May 2019 > Players A and B matches pennies N times. They keep a tally of their gains and losses. After the first loss, what is the chance that at no time during the game will they be even? 𝑁 a) ( ) /2𝑁 𝑛 𝑁 b) ( ) /2𝑛 𝑛 𝑵 c) ( ) /𝟐N 𝒏 𝑁 d) ( ) /2 𝑛

Given that sin 34 = 0.5592, find an acute angle ɵ such that cos ɵ = 0.5592.

33. CE BOARD May 2019 > Many printing presses are designed with large plates that print a fixed number of pages as a unit. Each unit is called a signature. A particular press prints a signature is 16 pages each. Suppose C(p) is the cost of printing a book of p pages, assuming each signature printed cost $0.14. What is the cost of printing a book of 128 pages?

29. CE BOARD May 2019 > Solve for x from the following equations: xy = 12 yz = 20 zx = 15 30. CE BOARD May 2019 > From the top of a lighthouse 120 m above lh sea, the angle of depression of a boat is 15֯. How far is the boat from the lighthouse? 31. CE BOARD May 2019 >

𝑘

[

2𝜋 365

A manufacturer of custom windows produces y windows per week using x hours of labor per week, where y = 1.75√𝑥. How many hours of labor are required to keep production at 28 windows per week? 35. CE BOARD May 2019 > Simplify if possible : 7x3 + 2x5.

The number of hours daylight D(t) at a particular time of the year can be approximated by

D(t) = 2 𝑠𝑖𝑛

34. CE BOARD May 2019 >

]

(𝑡 − 79) + 12

for t days and t = 0 corresponding to January 1. The constant k determines the total variation in day length and depends on the latitude of the locale. When is the day length the shortest? Assume k = 6.

36. CE BOARD May 2019 > Samsung, a computer chip manufacturer, has found that only 1 out of 2000 chips is defective. A certain company ordered a shipment of chips. How many chips will the company order before the probability that at least one chip is defective is 45%.

37. CE BOARD May 2019 >

42. CE BOARD May 2019 >

46. CE BOARD May 2019 >

50. CE BOARD May 2019 >

Determine the elevation of residual water level (RWL) for the sheet pile type if the following data are as follows: Elev. Of MLL, W (datum) = 0.00 m Elev. Of HWL = + 1.26 m Elev. Of LWL = - 0.23m

A wave generated in deep water, when reaching shoaling waters, charges not only in its height but also in its length but the period will ________.

The local weather forecaster says “no rain” and his recorded is 2/3 accuracy of prediction. But the Federal Meteorological Service predicts rain and their record is ¾ with no other data available, what is the chance of rain?

A line has been measure 10 times with the results shown in column (1) of the following table. It is assumed that these measurements have already been corrected for all the systematic errors. What is the standard error?

38. CE BOARD May 2019 > A rectangular soccer field is twice as long as it is wide. If the perimeter of soccer field is 300 yards, what are the field’s dimensions? 39. CE BOARD May 2019 > A long rectangular sheet of metal, 12 cm wide, is to be made a rain gutter by turning up two sides so that they are perpendicular to the sheet. How many centimetres should be turned up to turned up to give the gutter its greatest capacity? 40. CE BOARD May 2019 > A subdivision property was measured using a 100-m tape which was actually 0.01 m short. If the recorded area was 3000 sq.m, what is the true area and how much is the error? 41. CE BOARD May 2019 > A printing machine costs P400, 000 to purchase with a life of 10 years with no salvage value. If the rate of interest is 10% per annum, compounded annually, compute the equivalent uniform annual cost of the machine if it will cost P100, 000 per year to operate?

a) b) c) d)

Remain constant Increase Decrease None of the above

43. CE BOARD May 2019 > The cost of electricity in a certain city is given by formula C = 0.07n + 6.5, where C is the cost and n is the number of kilowatt hours used. Solve for n and find the number of kwh used. Solve for n and find the number of kwh used for costs of Php 49.97, Php 76.50 and Php 125.

47. CE BOARD May 2019 >

Length

A surveyor up a transit at point P, which is at the inner portion of a four-sided tract of land ABCD, and read the bearings and measures the distances as follows:

1000.57 1000.39 1000.37 1000.39 1000.48 1000.49 1000.33 1000.46 1000.47 1000.55

LINE PA PB PC PD

BEARING N 40֯ 30’ W N 38֯ 00’ E S 70֯ 00’ E S 60֯ 15’ W

DISTANCE 420.35 530.15 480.75 695.10

Residual (V) + 0.12 - 0.06 - 0.08 - 0.06 + 0.03 + 0.04 - 0.12 + 0.01 + 0.02 + 0.01

V2 0.0144 0.0036 0.0054 0.0036 0.0009 0.0016 0.0144 0.0001 0.0004 0.0100

44. CE BOARD May 2019 >

What is the area of the tract in hectares?

51. CE BOARD May 2019 >

The first cost of an electric rebar bender is P324, 000 and a salvage value of P50, 000 at the end of its life for 4 years. Money is worth 6% annually. If there is no salvage value and the annual maintenance cost is P18, 000, find the capitalized cost of perpetual service.

48. CE BOARD May 2019 >

A metal sphere with sp. gravity of 3 originally weighs 34 kg. It underwent a process of recasting and was formed into a solid cone with a base having a radius of 6 cm. Assuming 12% of the metal was lost in the process. What is the perpendicular height of the new cone?

If 300 pounds of face is required to push 1000pound safe up a ramp, then what is the angle of inclination of the ramp? 49. CE BOARD May 2019 >

45. CE BOARD May 2019 > In triangle ABC, AB = 30 m, BC = 36 m, and AC = 48 m. The perpendicular bisectors of the sides intersect at point P. How far is P from side BC?

The interior satellite TV antenna is a dish having the shape of a finite paraboloid that has a diameter 12 meters and is 2 meters deep. Find the distance from the center of the dish to the focus.

52. CE BOARD May 2019 > Determine the connection values for the latitude of line AB and departure of line BC using compass rule. STATION A-B B-C C-D D-E E-A

BEARING N 28֯ 10’ E S 75֯ 25’ E S 15֯ 30’ W N 1֯ 42’ W N 52֯ 06’ W

DISTANCE 285.10 610.45 720.45 203.00 647.02

53. CE BOARD May 2019 >

57. CE BOARD May 2019 >

To stimulate his son is the persuit of partial differential equations, a math professor offered to pay him $8 for every equation correctly solved and to fine him $5 for every incorrect solution. At the end of 26 problems, neither owed any money to the other. How many did the boy solved correctly?

In the measures of congestion of highway capacity, what will happen as the density continues to increase? a) Minimum rate flow is eventually reached b) Increase speeds and reduced flow rate c) The point is reached at which speed declines noticeably d) Running speed and traffic flow is minimum

54. CE BOARD May 2019 > A proposed manufacturing plant will require a fixed capital investment of P8 M and an estimated working capital of P1.5 M. The annual profit is P2 M and the annual depreciation is to be 8% of the fixed capital investment. Compute the rate of return of the total investment. 55. CE BOARD May 2019 > In 2 minutes, a conveyor belt can move 300 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt can move the same quantity of cans the same distance in 6 minutes. If both belts are used, find how long it takes to move the cans to the storage area. 56. CE BOARD May 2019 > Newton’s Law of cooling states that the rate at which an object cool is directly proportional to the difference in the temperature between the object and its surrounding medium. Newton’s law can be used to show that under certain conditions the temperature T (in ֯C) of an object at t (in hours) is given T = 75e-20. Express t as a function of T.

HYDRAULICS and GEOTECHNICAL ENGINEERING MAY 2019 1.

CE BOARD May 2019 >

If a container containing water 0.3 m deep is carried inside an elevator that accelerates at 3m/s2, evaluate the pressure, in kPa, exerted by the water at the base of the container if the elevator is travelling downward. 2.

CE BOARD May 2019 >

Evaluate the plastic settlement, in meter(s), on a layer of plastic clay due to an increase of pressure caused by loads above it under the following conditions: Initial intergranular pressure = 200 kPa Increase in intergranular pressure = 120 kPa Thickness of the clay layer = 8 m Coefficient of consolidation = 0.315 Void ratio of the clay = 1.132 3.

CE BOARD May 2019 >

Water flows through a rectangular irrigation canal 500 mm deep by 1 meter wide with a mean velocity of 2 m/sec. Determine the rate of flow in m3/min. 4.

5.

CE BOARD May 2019 >

The permeameter in a permeability test setup involves a soil sample 200 mm dia. and a length of 30 mm. the height of water is kept constant at 400 mm. in a duration of 4 min., water was collected in the graduated flask having a volume of 420 cu.cm. Determine the coefficient of permeability in percent. 6.

CE BOARD May 2019 >

A layer of soft clay having an initial void ratio of 2 is 10 m thick. Under a compressive load applied above it, the void ratio decreased by one-half. Evaluate the reduction in the thickness of the clay layer, in meters. 7.

CE BOARD May 2019 >

A 300 mm diameter test well penetrates 27 m. below the static water table. After 24 hours of pumping at 69 liters/sec. The water level in an observation well at a distance of 95 m from the test well is lowered 0.5 m and the other observation well at a distance of 35 m from the test well, the water level dropped by 1.1 m.

CE BOARD May 2019 >

The diameter of a pipe carrying water changes gradually from 150 mm at A to 450 mm at B, A lis 5 m lower than B. What will be the difference in pressure in kPa between A and B, when 180 liter/sec is flowing loss of energy being neglected?

① What is the rate of flow in m/day? ②Compute the coefficient of permeability of the aquifer in m/day. ③Compute the transmissibility of the aquifer in m3/day.

8.

CE BOARD May 2019 >

Water is pumped at a rate of 1 m3/sec through. The permeameter in a permeability test setup involves a cylindrical soil sample 40 mm in diameter and height 200 mm. The hydraulic head of the test was held constant at 300 mm. In a duration of one min., the water collected in the graduate was recorded at 1.5 liters. Evaluate the coefficient of permeability of the soil sample, in cm2/sec. 9.

11. CE BOARD May 2019 >

14. CE BOARD May 2019 >

16. CE BOARD May 2019 >

A square footing 1.2 m on a side in embedded 1.00 m into a cohesive soil deposit. The unit weight of the soil is 18 kN/m3 and the angle of internal friction is 30֯. The soil cohesion strength is 10 kPa. Using Terzagih’s Formula for general shear failure,

A layer of clay 8.6 m thick is overlain by a deposit of sand 15.2 m thick to ground surface. When the water table is at ground surface level, the saturated unit weight of the sand was determined to be 21.2 kN/m3 for which its dry unit weight is 18.2 kN/m3. The saturated unit weight of the clay is 18.8 kN/m3. When the ground water table lowered by 7.6 m, the degree of saturation of the sand above the water table was lowered at 30%. At the midheight of the clay layer,

A rectangular gate 1.60 m wide and 2.0 m. high has water on one side and is inclined 45֯ with the horizontal. Water is 1.50 m. above the top of the gate

From the given table: Nc = 37.6 Ns = 22.45 Nf = 19.13

CE BOARD May 2019 >

A cylinder having a diameter of 1.20 m and weighing 800 N is held in position is sea water by a wire tied to an anchor block resting at the bottom of the sea such that 0.30 m of the cylinder is below the surface of the water with its axis vertical. The anchor block has a volume of 0.50 cubic meter and weighs 24 kN per cubic meter in air. Assume sea water to have a specific gravity = 1.03. Neglecting the weight and volume of the cable. ① Evaluate the buoyant force on the cylinder for the position described, in kN. ② Evalaute the tensile force in the wire when the top of the cylinder is 0.60 m above the water surface, in kN. ③ Evaluate the rise in the tide that will lift the anchor from the bottom of the sea, in meters. 10. CE BOARD May 2019 > A sample of saturated clay has a water content of 56 percent. Assume Gs = 2.72. Compute the following: ① Void ratio (e) ② Saturated unit weight (ꙋsat) ③ Porosity (n)

12. CE BOARD May 2019 > A circular gate 1.5 m., in diameter is inclined at an angle of 45 deg. Fresh water stands on one side of the gate to a height of 10 m above the center of the gate. ① Evaluate the total force on the gate ② Locate the point of action of the total force From the bottom on the plane of the gate. ③ If the gate is hinged at the top, evaluate the force normal to the gate at the bottom that will require to open it in kN. 13. CE BOARD May 2019 > In a tri-axial test for a normally consolidated soil, the normal stress at failure is equal to 450 kPa and the shear stress at failure is equal to 300 kPa. ① Compute the angle of friction. ② Compute the angle of failure plane with the major principal axis. ③ Compute the max. principal stress of failure.

① Evaluate the effective pressure, in kPa, before lowering of the water table. ② Evaluate the effective pressure, in kPa, After lowering of the water table. ③ Evaluate the effective pressure, in kPa, when there is no water in the sand layer but remain in moist condition at the same degree of saturation. 15. CE BOARD May 2019 > A footing 2 m. x 2 m. in plan and 0.050 m. thick, is designed to support a 0.60 m. square column. Due to architectural requirement, the column is so located that its external face is flush with shorter edge of the footing. The column load, including the weight of the column itself, is 50 kN. Assume the concrete to weigh 24 kN/m3. ① Evaluate the total downward load on the supporting ground, in kN. ② Evaluate the overturning moment on the footing, in kN. ③ Evaluate the maximum pressure induced on the supporting soil, in kPa.

① Compute the hydrostatic force acting on the gate. ② Compute its location of the center of the Pressure from B. ③ If the gate is hinged at the top (B), what force is needed at the bottom (A) to open the gate. 17. CE BOARD May 2019 > Three pipes A, B and C are connected in parallel. If the combined discharged of the 3 pipes is equal to 0.61 m3/s. and assuming they have equal values of friction factor “f”, compute the following using the tabulated data shown: PIPELINE A B C

LENGTH 600 m. 480 m. 750 m.

DIAM. 150 m. 200 m. 100 m.

① Compute the rate of flow of pipeline A in lit/sec. ② Compute the rate of flow of pipeline B in lit/sec. ③ Compute the rate of flow of pipeline C in lit/sec.

STRUCTURAL DESIGN and CONSTRUCTION MAY 2019 1.

CE BOARD May 2019 >

A wooden log is to be used as a foot bridge to span a 2m. gap. The log is to support a concentrated load of 27 kN. Allowable shear stress = 1.2 MPa Allowable bending strees = 6.6 MPa ① What is the diameter of the log needed for a maximum shear? ② Find the diameter of the log needed so that the allowable bending stress is not exceeded. ③ A 150 wide rectangular log is to be used instead of the circular log. What is the required minimum depth of the log so as not to exceed the allowable bending stress? 2.

CE BOARD May 2019 >

4.

A bridge truss is subjected to a standard highway load at the bottom chord. The highway load consists of a uniformly distributed load of 9.35 kN/m and concentrated load of 1.16 kN Angle, Ɵ = 45 ֯ S=4m Lt = 16 m Lc = 8 m

① What is the tension T2 (kN) in cable AC? ② Find the tension T2 (kN) in cable AD. ③ Determine the tension T1 (kN) in the cable AB. For the computation of design force, apply the moving concentrated load at the truss joint only, ① Find the maximum vertical reaction at A due to the highway load. ② What is the maximum ordinate of the influence line for the force developed in member JK? ③ Determine the maximum force (kN) that can be developed in member JK due to the highway load.

3.

5.

A 250 mm Ø pole, 3 m high is fixed at the base. It is subjected to the compressive force of 3 kN acting at its centroid and a 0.45 kN internal force applied at the top. What is the max. shear stress in the pole?

x1 = 1 m. x2 = 4 m.

CE BOARD May 2019 >

A solid pole, 3 m. high and 250 mm in diameter is fixed at the base. It is subjected to a compressive force of 3 kN acting at an eccentricity of 100 mm from its centroidal axis and a lateral load of 0.45 kN applied at the top. What is the max. compressive stress at the base of the pole? Unit weight of pole is 22 kN/m3? CE BOARD May 2019 >

Dimensions: y1 = 3 m. y2 = 4 m. z = 12 m

CE BOARD May 2019 >

An antenna tower on the top of a building is subjected to an uplift force of 370 kN acting along the z-axis. The tower is braced by 3 cables AB, AC, and AD.

6.

CE BOARD May 2019 >

Given: As = 8 – 28 mmØ As’ = 4 – 28 mmØ ds = 12 mm diam. Bar h1 = 125 mm h2 = 475 mm a = 65 mm fc’ = 28 MPa fyb = 415 MPa (longitudinal bars) fyv = 275 MPa (ties) Shear strength reduction factor = 0.75 Clear concrete cover = 40 mm Specified maximum aggregates size is the concrete mixture = 20 mm

① Find the minimum width of beam “b” required to satisfy on cover requirements. ② Find the minimum width of the beam “b” adequate for a factor shear force Vs = 600 kN if the spacing of 12 mm diameter ties is 60 mm. ③ If Vc = 450 kN and spacing of 12 mm diameter ties is 70 mm, what is the required minimum width of the beam “b”, mm? 7.

CE BOARD May 2019 >

The figure shows a one-way slab having a total depth of 200 mm with a 25 mm clear covering at the bottom. The steel reinforcement is 20 mm diameter. Spacing of steel reinforcement is 125 mm on centers. Fc’ = 30 MPa, fy = 400 MPa. Considerinf 1 m. width of slab. Determine the moment capacity of a strip slab.

8.

CE BOARD May 2019 >

A W 450 x 90 beam is to be supported by a 250 mm wide concrete wall with fc’ = 27.5 MPa. Beam loads induce and end reaction of 240 kN. Beam properties are as follows:

d = 450 mm tw = 10 mm tf = 18 mm K = 35 mm bf = 190 mm Fy = 248 MPa Allowable bearing stress on support, Fc = 0.35 fc’ Allowable bending stress in plate, Fc = 0.75 Fy

Ultimate load: U = 1.2 DL + 1.0 LL Given: S = 2.4 m Lt = L2 = L1= 7.5 m Total DL = 4.5 kPa LL = 3.6 kPa ① Calculate the max. reaction at K. ② What is the max. shear at span KL? ③ Find the max. negative moment at K.

Super imposed loads: DL = 2.6 kPa LL = 3.6 kPa Concrete unit weight = 24.4 kN/m3 Clear concrete cover to stirrups = 50 mm Stirrups = 10 mm Ø Concrete column = 300 mm x 300 mm

11. CE BOARD May 2019 > The figure shows an element in pure shear and the corresponding Mohr’s circle. Points A and B represents the stresses in the x face and on the y face respectively. ① What is the width of bearing plate required if the bearing length is 100 mm. ② If the critical section for bending in bearing plates is at distance “K” from the centroidal y-axis of the web, find the required bearing plate thickness. ③ Determine the web yielding stress which occurs at distance (N + 2.5K), where N is the length of bearing plate = 100 mm.

① What is the moment (kN-m) at the end of the F of beam EF? ② What is the moment (kN-m) at the misdpan of beam FG? ③ What is the shear (kN) at the end F of beam EF?

9.

10. CE BOARD May 2019 >

CE BOARD May 2019 >

From the figure shown: Given: L1= 6 m Ls = 7 m L2 = 8 m S = 2.5 m Beam section b x h = 350 mm x 450 mm Slab thickness, t = 100 mm Material strength” Fc’ = 27.5 MPa

fy = 415 MPa

Loads: U = 1.2D + 1.6L Dead load: WD = 5.0 kPa including slab and beam Live load: WL = 3.8 kPa All beams are 350 mm wide,

① What is the value of the normal axial stress? ② How much is the max. in plane shear stress? ③ At what angle in degrees from the x-axis does the max. in plane shear stress occur?

① Compute the total ultimate load Wu (kN/m) to design beam I-J-K-L. Ultimate load: U = 1.4 DL + 1.7 LL ② If the design ultimate load Wu = 32kN/m, find the negative moment (kN-m) at the end of K of span JK. ③ How many 25 mm Ø bars are required at the end K of span KL if the design ultimate load, Wu = 32 kN/m.

Longitudinal beams, EFGH and IJKL are simply supported at E, F, G and H, and at I, J, K, L.

13. CE BOARD May 2019 > Identify the material property described by the following material:

12. CE BOARD May 2019 > Given beam: B x h = 300 mm x 450 mm Slab thickness, t = 100 mm S = 2.8 m. L1 = L2 = L3= 8 m

The material has the same composition at every point but the elastic may not be the same in all directions. a) b) c) d)

Isotropic Orthotropic Homogeneous Prismatic

14. CE BOARD May 2019 >

18. CE BOARD May 2019 >

Identify the material property described by the following material:

It is measured by the Richter scale. a) Ground acceleration b) Intensit of observed effects c) Magnitude of Earthquake d) Period of Earthquake

The composite material exhibits elastic properties in one direction different from that in the perpendicular direction. a) b) c) d)

Isotropic Homogeneous Prismatic Orthotropic

15. CE BOARD May 2019 > Identify the material property described by the following material: The material has the same elastic properties in all directions. a) b) c) d)

Prismatic Isotropic Orthotropic Homogeneous

16. CE BOARD May 2019 > Besides the epicentre, it describes the location of the earthquake. a) b) c) d)

Geologic formation Focal depth Fault line Dip angle

17. CE BOARD May 2019 > It is measured by seismometer. a) b) c) d)

Reference points Attenuation Components of ground motion Actual displacement

19. CE BOARD May 2019 > Given: W x L = 450 mm x 600 mm Ast = 16 – 25 mm Ø bars Ties = 12 mm Ø spaced at 100 mm on center Concret: fc’ = 27.5 MPa Steel:fyy for lateral ties = 275 MPa Effective cover to centroid of vertical steel reinforcement on each side = 65 mm Shear strength reduction factor = 0.65 ① Find the shear capacity of the column along the y-axis Vuy (kN)? ② What is the shear capacity of the column along the x-axis Vux (kN0? ③ Which of the following gives the maximum allowable factored shear force, Vux (kN)?

MATHEMATICS and SURVEYING MAY 2019 1.

2.

CE BOARD May 2019 >

3.

A germ population has a growth curve Ae0.4t. At what value of t does its original value doubled?

The Wollomombi Falls in Australia have a height of 1100 ft. A pebble is thrown upward from the top of the falls with an initial velocity of 20ft/sec. The height of the pebble “h” after the “I” sec is given by the equation h = - 16 t2 + 20t + 1100. How long after the pebble is thrown will hit the ground?

CE BOARD May 2019 > A person driving her car 45 kph approaches an intersection just as the traffic lights turns yellow. She knows that the yellow light lasts only 2.0 sec before turning red and she is 28 m from the near side of the intersection. Should she try to stop or she speeds up to cross the intersection before the light turns red? The intersection is 15 m wide. Her car’s maximum deceleration is -5.8 m/s2, whereas it can accelerate from 45 kph to 65 kph in 6.0 sec. Ignore the length of her car and her reaction time. a)

She should speed up to cross the intersection before the light turns red. b) She should adjust the rate of deceleration and wait for the next red light. c) She should maintain the rate of deceleration and continue as she would pass through the intersection against the green light. d) She should adjust the rate of deceleration, stop and wait for the next green light.

4.

CE BOARD May 2019 >

CE BOARD May 2019 >

Given the following cross-section notes for a road grading work: −3.2 1.2 1.2 2.8 + + + 𝑋1 0 3.5 𝑋2 The road bed is 9 m wide and the side slope for cut is 1:1 and for fill is 1.5:1. Determine the area of cut if the section. 5.

CE BOARD May 2019 >

A 2 kg body is tied to the end of a chord abd whirled in a horizontal circle of radius 1.5 m at 3 revolutions per sec. Neglecting the attraction due to gravity, find the acceleration of the body toward the center of the circle in m/s2? 6.

CE BOARD May 2019 >

Find the equation of the curve passing through the point (3, 2) and having the slope 5x2 – x at every point (x, y).

CE BOARD May 2019 >

Device mounted on a fixed support (permanent signs) or portable support (temporary signs) whereby a specific message is conveyed by means of words or symbols placed or erected for the purpose of regulating, warning or guiding traffic. a) b) c) d)

Roadwork signs Overhead signs Traffic signs Special instruction signs

12. CE BOARD May 2019 > A machine was purchased at an original cost of P400, 000 with a salvage value of P20, 000. Life of this machine expected to last for 6 years. It was used for 4000 hrs. in the first year, 6000 hrs. in the second year, and 6000 hrs. on the 3rd year. The machine is expected to last for 38000 hrs. in the period of 6 yrs. Which of the following gives the depreciation at the end of the second year? 13. CE BOARD May 2019 >

8.

CE BOARD May 2019 >

A maximum wave height and wave period of the maximum wave height in wave train. a) Deep water wave b)

9.

Equivalent depth water wave height

c) Highest wave d) Significant wave CE BOARD May 2019 >

Find a polar equation that has the same graph as the circle x2 + y2 = 4y. 10. CE BOARD May 2019 > Two trains going in opposite directions leave the time. One train travels 15 mph faster than the other, in 6 hours, the trains are 630 miles apart. Find the speed of each. 11. CE BOARD May 2019 > What is the process of proportioning the cement, water, aggregates and additives prior to mixing concrete called? a) b) c) d)

AB is diameter of a circle, BC is a chord 10 cm, long, CD is another chord. Angle ABC = 18֯ . What is the area of the circle in sq.cm.

Paving Mixing Batching Curing

14. CE BOARD May 2019 > Suppose you receive x dollars in January. Each month thereafter you receive $100 more than you received the month before. Write a factored polynomial that describes the total dollar amount you received from January through April. 15. CE BOARD May 2019 > A polyhedron having 12 faces and has for its face 12 regular pentagon is called dodecahedron. Determine the number of edges. 16. CE BOARD May 2019 > If the perimeter of a rectangle is 68 meters and the length is 14 m more than the width, what are the dimensions of the rectangle?

17. CE BOARD May 2019 >

22. CE BOARD May 2019 >

27. CE BOARD May 2019 >

32. CE BOARD May 2019 >

How many different ways are there to arrange six people in a round table?

The angle of elevation of the top of a building from point A on a ground is 24.2֯. From point B, which is 44.5 ft. closer, the angle of elevation is 38.1֯. What is the height of the building?

During the Winter Olympics Game in Torino, Italy, the total number of gold medals won by Germany, Canada, and United States were three consecutive odd integers. Of these three countries, Germany won the fewest. If the sum of the first integer, twice the second integer, and four times the third integer is 69, find the number of gold medals won by each country.

A circular pool of water is expanding at the rate of 16𝜋 in2/sec. at what rate is the radius expanding when the radius is 4 inches (in inches per minute)?

18. CE BOARD May 2019 > When directly generated and affected by local winds, a wind wave system is called: a) b) c) d)

A circle has an equation of x2 + y2 + 2ky = 0. Find the value of k when the length of the tangent from (5, 4) to the circle is equal to one.

Wind seiching Wind swell Wind wakes Wind sea

28. CE BOARD May 2019 >

19. CE BOARD May 2019 > From the given data shown: Score Frequency

1 14

2 15

3 14

23. CE BOARD May 2019 >

4 17

5 10

24. CE BOARD May 2019 > A new corporate bond is being offered in the market for $930. The bond has a face Value of P1, 000 and matures in 10 years. The issuing corporation promises to pay $70 in interest every year. What is the company’s cost of the capital raised though this bond issue if the stock broker’s fee is $15 per bond sold?

Determine the standard deviation. 20. CE BOARD May 2019 > An 80-m spiral connects a tangent with a 180m radius circular curve. The maximum velocity in kph that a car could pass through the curve without skidding is nearest to: 21. CE BOARD May 2019 > An engineer designs simple curve at a certain point of a highway. The data for the simple curve area: I = 44֯ R = 400 ft. P.C. = 11 + 10.57 P.T. = 14 + 17.75 Compute the deflection of station 13 + 00.

25. CE BOARD May 2019 > The passengers on an excursion bus consisted of 14 married couples, 8 of whom brought no children and, 6 of whom brought 3 children a piece. Counting the driver, the bus has 31 occupants How is this possible? 26. CE BOARD May 2019 > Players A and B matches pennies N times. They keep a tally of their gains and losses. After the first loss, what is the chance that at no time during the game will they be even? 𝑁 a) ( ) /2𝑁 𝑛 𝑁 b) ( ) /2𝑛 𝑛 𝑵 c) ( ) /𝟐N 𝒏 𝑁 d) ( ) /2 𝑛

Given that sin 34 = 0.5592, find an acute angle ɵ such that cos ɵ = 0.5592.

33. CE BOARD May 2019 > Many printing presses are designed with large plates that print a fixed number of pages as a unit. Each unit is called a signature. A particular press prints a signature is 16 pages each. Suppose C(p) is the cost of printing a book of p pages, assuming each signature printed cost $0.14. What is the cost of printing a book of 128 pages?

29. CE BOARD May 2019 > Solve for x from the following equations: xy = 12 yz = 20 zx = 15 30. CE BOARD May 2019 > From the top of a lighthouse 120 m above lh sea, the angle of depression of a boat is 15֯. How far is the boat from the lighthouse? 31. CE BOARD May 2019 >

𝑘

[

2𝜋 365

A manufacturer of custom windows produces y windows per week using x hours of labor per week, where y = 1.75√𝑥. How many hours of labor are required to keep production at 28 windows per week? 35. CE BOARD May 2019 > Simplify if possible : 7x3 + 2x5.

The number of hours daylight D(t) at a particular time of the year can be approximated by

D(t) = 2 𝑠𝑖𝑛

34. CE BOARD May 2019 >

]

(𝑡 − 79) + 12

for t days and t = 0 corresponding to January 1. The constant k determines the total variation in day length and depends on the latitude of the locale. When is the day length the shortest? Assume k = 6.

36. CE BOARD May 2019 > Samsung, a computer chip manufacturer, has found that only 1 out of 2000 chips is defective. A certain company ordered a shipment of chips. How many chips will the company order before the probability that at least one chip is defective is 45%.

37. CE BOARD May 2019 >

42. CE BOARD May 2019 >

46. CE BOARD May 2019 >

50. CE BOARD May 2019 >

Determine the elevation of residual water level (RWL) for the sheet pile type if the following data are as follows: Elev. Of MLL, W (datum) = 0.00 m Elev. Of HWL = + 1.26 m Elev. Of LWL = - 0.23m

A wave generated in deep water, when reaching shoaling waters, charges not only in its height but also in its length but the period will ________.

The local weather forecaster says “no rain” and his recorded is 2/3 accuracy of prediction. But the Federal Meteorological Service predicts rain and their record is ¾ with no other data available, what is the chance of rain?

A line has been measure 10 times with the results shown in column (1) of the following table. It is assumed that these measurements have already been corrected for all the systematic errors. What is the standard error?

38. CE BOARD May 2019 > A rectangular soccer field is twice as long as it is wide. If the perimeter of soccer field is 300 yards, what are the field’s dimensions? 39. CE BOARD May 2019 > A long rectangular sheet of metal, 12 cm wide, is to be made a rain gutter by turning up two sides so that they are perpendicular to the sheet. How many centimetres should be turned up to turned up to give the gutter its greatest capacity? 40. CE BOARD May 2019 > A subdivision property was measured using a 100-m tape which was actually 0.01 m short. If the recorded area was 3000 sq.m, what is the true area and how much is the error? 41. CE BOARD May 2019 > A printing machine costs P400, 000 to purchase with a life of 10 years with no salvage value. If the rate of interest is 10% per annum, compounded annually, compute the equivalent uniform annual cost of the machine if it will cost P100, 000 per year to operate?

a) b) c) d)

Remain constant Increase Decrease None of the above

43. CE BOARD May 2019 > The cost of electricity in a certain city is given by formula C = 0.07n + 6.5, where C is the cost and n is the number of kilowatt hours used. Solve for n and find the number of kwh used. Solve for n and find the number of kwh used for costs of Php 49.97, Php 76.50 and Php 125.

47. CE BOARD May 2019 >

Length

A surveyor up a transit at point P, which is at the inner portion of a four-sided tract of land ABCD, and read the bearings and measures the distances as follows:

1000.57 1000.39 1000.37 1000.39 1000.48 1000.49 1000.33 1000.46 1000.47 1000.55

LINE PA PB PC PD

BEARING N 40֯ 30’ W N 38֯ 00’ E S 70֯ 00’ E S 60֯ 15’ W

DISTANCE 420.35 530.15 480.75 695.10

Residual (V) + 0.12 - 0.06 - 0.08 - 0.06 + 0.03 + 0.04 - 0.12 + 0.01 + 0.02 + 0.01

V2 0.0144 0.0036 0.0054 0.0036 0.0009 0.0016 0.0144 0.0001 0.0004 0.0100

44. CE BOARD May 2019 >

What is the area of the tract in hectares?

51. CE BOARD May 2019 >

The first cost of an electric rebar bender is P324, 000 and a salvage value of P50, 000 at the end of its life for 4 years. Money is worth 6% annually. If there is no salvage value and the annual maintenance cost is P18, 000, find the capitalized cost of perpetual service.

48. CE BOARD May 2019 >

A metal sphere with sp. gravity of 3 originally weighs 34 kg. It underwent a process of recasting and was formed into a solid cone with a base having a radius of 6 cm. Assuming 12% of the metal was lost in the process. What is the perpendicular height of the new cone?

If 300 pounds of face is required to push 1000pound safe up a ramp, then what is the angle of inclination of the ramp? 49. CE BOARD May 2019 >

45. CE BOARD May 2019 > In triangle ABC, AB = 30 m, BC = 36 m, and AC = 48 m. The perpendicular bisectors of the sides intersect at point P. How far is P from side BC?

The interior satellite TV antenna is a dish having the shape of a finite paraboloid that has a diameter 12 meters and is 2 meters deep. Find the distance from the center of the dish to the focus.

52. CE BOARD May 2019 > Determine the connection values for the latitude of line AB and departure of line BC using compass rule. STATION A-B B-C C-D D-E E-A

BEARING N 28֯ 10’ E S 75֯ 25’ E S 15֯ 30’ W N 1֯ 42’ W N 52֯ 06’ W

DISTANCE 285.10 610.45 720.45 203.00 647.02

53. CE BOARD May 2019 >

57. CE BOARD May 2019 >

To stimulate his son is the persuit of partial differential equations, a math professor offered to pay him $8 for every equation correctly solved and to fine him $5 for every incorrect solution. At the end of 26 problems, neither owed any money to the other. How many did the boy solved correctly?

In the measures of congestion of highway capacity, what will happen as the density continues to increase? a) Minimum rate flow is eventually reached b) Increase speeds and reduced flow rate c) The point is reached at which speed declines noticeably d) Running speed and traffic flow is minimum

54. CE BOARD May 2019 > A proposed manufacturing plant will require a fixed capital investment of P8 M and an estimated working capital of P1.5 M. The annual profit is P2 M and the annual depreciation is to be 8% of the fixed capital investment. Compute the rate of return of the total investment. 55. CE BOARD May 2019 > In 2 minutes, a conveyor belt can move 300 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt can move the same quantity of cans the same distance in 6 minutes. If both belts are used, find how long it takes to move the cans to the storage area. 56. CE BOARD May 2019 > Newton’s Law of cooling states that the rate at which an object cool is directly proportional to the difference in the temperature between the object and its surrounding medium. Newton’s law can be used to show that under certain conditions the temperature T (in ֯C) of an object at t (in hours) is given T = 75e-20. Express t as a function of T.

HYDRAULICS and GEOTECHNICAL ENGINEERING MAY 2019 1.

CE BOARD May 2019 >

If a container containing water 0.3 m deep is carried inside an elevator that accelerates at 3m/s2, evaluate the pressure, in kPa, exerted by the water at the base of the container if the elevator is travelling downward. 2.

CE BOARD May 2019 >

Evaluate the plastic settlement, in meter(s), on a layer of plastic clay due to an increase of pressure caused by loads above it under the following conditions: Initial intergranular pressure = 200 kPa Increase in intergranular pressure = 120 kPa Thickness of the clay layer = 8 m Coefficient of consolidation = 0.315 Void ratio of the clay = 1.132 3.

CE BOARD May 2019 >

Water flows through a rectangular irrigation canal 500 mm deep by 1 meter wide with a mean velocity of 2 m/sec. Determine the rate of flow in m3/min. 4.

5.

CE BOARD May 2019 >

The permeameter in a permeability test setup involves a soil sample 200 mm dia. and a length of 30 mm. the height of water is kept constant at 400 mm. in a duration of 4 min., water was collected in the graduated flask having a volume of 420 cu.cm. Determine the coefficient of permeability in percent. 6.

CE BOARD May 2019 >

A layer of soft clay having an initial void ratio of 2 is 10 m thick. Under a compressive load applied above it, the void ratio decreased by one-half. Evaluate the reduction in the thickness of the clay layer, in meters. 7.

CE BOARD May 2019 >

A 300 mm diameter test well penetrates 27 m. below the static water table. After 24 hours of pumping at 69 liters/sec. The water level in an observation well at a distance of 95 m from the test well is lowered 0.5 m and the other observation well at a distance of 35 m from the test well, the water level dropped by 1.1 m.

CE BOARD May 2019 >

The diameter of a pipe carrying water changes gradually from 150 mm at A to 450 mm at B, A lis 5 m lower than B. What will be the difference in pressure in kPa between A and B, when 180 liter/sec is flowing loss of energy being neglected?

① What is the rate of flow in m/day? ②Compute the coefficient of permeability of the aquifer in m/day. ③Compute the transmissibility of the aquifer in m3/day.

8.

CE BOARD May 2019 >

Water is pumped at a rate of 1 m3/sec through. The permeameter in a permeability test setup involves a cylindrical soil sample 40 mm in diameter and height 200 mm. The hydraulic head of the test was held constant at 300 mm. In a duration of one min., the water collected in the graduate was recorded at 1.5 liters. Evaluate the coefficient of permeability of the soil sample, in cm2/sec. 9.

11. CE BOARD May 2019 >

14. CE BOARD May 2019 >

16. CE BOARD May 2019 >

A square footing 1.2 m on a side in embedded 1.00 m into a cohesive soil deposit. The unit weight of the soil is 18 kN/m3 and the angle of internal friction is 30֯. The soil cohesion strength is 10 kPa. Using Terzagih’s Formula for general shear failure,

A layer of clay 8.6 m thick is overlain by a deposit of sand 15.2 m thick to ground surface. When the water table is at ground surface level, the saturated unit weight of the sand was determined to be 21.2 kN/m3 for which its dry unit weight is 18.2 kN/m3. The saturated unit weight of the clay is 18.8 kN/m3. When the ground water table lowered by 7.6 m, the degree of saturation of the sand above the water table was lowered at 30%. At the midheight of the clay layer,

A rectangular gate 1.60 m wide and 2.0 m. high has water on one side and is inclined 45֯ with the horizontal. Water is 1.50 m. above the top of the gate

From the given table: Nc = 37.6 Ns = 22.45 Nf = 19.13

CE BOARD May 2019 >

A cylinder having a diameter of 1.20 m and weighing 800 N is held in position is sea water by a wire tied to an anchor block resting at the bottom of the sea such that 0.30 m of the cylinder is below the surface of the water with its axis vertical. The anchor block has a volume of 0.50 cubic meter and weighs 24 kN per cubic meter in air. Assume sea water to have a specific gravity = 1.03. Neglecting the weight and volume of the cable. ① Evaluate the buoyant force on the cylinder for the position described, in kN. ② Evalaute the tensile force in the wire when the top of the cylinder is 0.60 m above the water surface, in kN. ③ Evaluate the rise in the tide that will lift the anchor from the bottom of the sea, in meters. 10. CE BOARD May 2019 > A sample of saturated clay has a water content of 56 percent. Assume Gs = 2.72. Compute the following: ① Void ratio (e) ② Saturated unit weight (ꙋsat) ③ Porosity (n)

12. CE BOARD May 2019 > A circular gate 1.5 m., in diameter is inclined at an angle of 45 deg. Fresh water stands on one side of the gate to a height of 10 m above the center of the gate. ① Evaluate the total force on the gate ② Locate the point of action of the total force From the bottom on the plane of the gate. ③ If the gate is hinged at the top, evaluate the force normal to the gate at the bottom that will require to open it in kN. 13. CE BOARD May 2019 > In a tri-axial test for a normally consolidated soil, the normal stress at failure is equal to 450 kPa and the shear stress at failure is equal to 300 kPa. ① Compute the angle of friction. ② Compute the angle of failure plane with the major principal axis. ③ Compute the max. principal stress of failure.

① Evaluate the effective pressure, in kPa, before lowering of the water table. ② Evaluate the effective pressure, in kPa, After lowering of the water table. ③ Evaluate the effective pressure, in kPa, when there is no water in the sand layer but remain in moist condition at the same degree of saturation. 15. CE BOARD May 2019 > A footing 2 m. x 2 m. in plan and 0.050 m. thick, is designed to support a 0.60 m. square column. Due to architectural requirement, the column is so located that its external face is flush with shorter edge of the footing. The column load, including the weight of the column itself, is 50 kN. Assume the concrete to weigh 24 kN/m3. ① Evaluate the total downward load on the supporting ground, in kN. ② Evaluate the overturning moment on the footing, in kN. ③ Evaluate the maximum pressure induced on the supporting soil, in kPa.

① Compute the hydrostatic force acting on the gate. ② Compute its location of the center of the Pressure from B. ③ If the gate is hinged at the top (B), what force is needed at the bottom (A) to open the gate. 17. CE BOARD May 2019 > Three pipes A, B and C are connected in parallel. If the combined discharged of the 3 pipes is equal to 0.61 m3/s. and assuming they have equal values of friction factor “f”, compute the following using the tabulated data shown: PIPELINE A B C

LENGTH 600 m. 480 m. 750 m.

DIAM. 150 m. 200 m. 100 m.

① Compute the rate of flow of pipeline A in lit/sec. ② Compute the rate of flow of pipeline B in lit/sec. ③ Compute the rate of flow of pipeline C in lit/sec.

STRUCTURAL DESIGN and CONSTRUCTION MAY 2019 1.

CE BOARD May 2019 >

A wooden log is to be used as a foot bridge to span a 2m. gap. The log is to support a concentrated load of 27 kN. Allowable shear stress = 1.2 MPa Allowable bending strees = 6.6 MPa ① What is the diameter of the log needed for a maximum shear? ② Find the diameter of the log needed so that the allowable bending stress is not exceeded. ③ A 150 wide rectangular log is to be used instead of the circular log. What is the required minimum depth of the log so as not to exceed the allowable bending stress? 2.

CE BOARD May 2019 >

4.

A bridge truss is subjected to a standard highway load at the bottom chord. The highway load consists of a uniformly distributed load of 9.35 kN/m and concentrated load of 1.16 kN Angle, Ɵ = 45 ֯ S=4m Lt = 16 m Lc = 8 m

① What is the tension T2 (kN) in cable AC? ② Find the tension T2 (kN) in cable AD. ③ Determine the tension T1 (kN) in the cable AB. For the computation of design force, apply the moving concentrated load at the truss joint only, ① Find the maximum vertical reaction at A due to the highway load. ② What is the maximum ordinate of the influence line for the force developed in member JK? ③ Determine the maximum force (kN) that can be developed in member JK due to the highway load.

3.

5.

A 250 mm Ø pole, 3 m high is fixed at the base. It is subjected to the compressive force of 3 kN acting at its centroid and a 0.45 kN internal force applied at the top. What is the max. shear stress in the pole?

x1 = 1 m. x2 = 4 m.

CE BOARD May 2019 >

A solid pole, 3 m. high and 250 mm in diameter is fixed at the base. It is subjected to a compressive force of 3 kN acting at an eccentricity of 100 mm from its centroidal axis and a lateral load of 0.45 kN applied at the top. What is the max. compressive stress at the base of the pole? Unit weight of pole is 22 kN/m3? CE BOARD May 2019 >

Dimensions: y1 = 3 m. y2 = 4 m. z = 12 m

CE BOARD May 2019 >

An antenna tower on the top of a building is subjected to an uplift force of 370 kN acting along the z-axis. The tower is braced by 3 cables AB, AC, and AD.

6.

CE BOARD May 2019 >

Given: As = 8 – 28 mmØ As’ = 4 – 28 mmØ ds = 12 mm diam. Bar h1 = 125 mm h2 = 475 mm a = 65 mm fc’ = 28 MPa fyb = 415 MPa (longitudinal bars) fyv = 275 MPa (ties) Shear strength reduction factor = 0.75 Clear concrete cover = 40 mm Specified maximum aggregates size is the concrete mixture = 20 mm

① Find the minimum width of beam “b” required to satisfy on cover requirements. ② Find the minimum width of the beam “b” adequate for a factor shear force Vs = 600 kN if the spacing of 12 mm diameter ties is 60 mm. ③ If Vc = 450 kN and spacing of 12 mm diameter ties is 70 mm, what is the required minimum width of the beam “b”, mm? 7.

CE BOARD May 2019 >

The figure shows a one-way slab having a total depth of 200 mm with a 25 mm clear covering at the bottom. The steel reinforcement is 20 mm diameter. Spacing of steel reinforcement is 125 mm on centers. Fc’ = 30 MPa, fy = 400 MPa. Considerinf 1 m. width of slab. Determine the moment capacity of a strip slab.

8.

CE BOARD May 2019 >

A W 450 x 90 beam is to be supported by a 250 mm wide concrete wall with fc’ = 27.5 MPa. Beam loads induce and end reaction of 240 kN. Beam properties are as follows:

d = 450 mm tw = 10 mm tf = 18 mm K = 35 mm bf = 190 mm Fy = 248 MPa Allowable bearing stress on support, Fc = 0.35 fc’ Allowable bending stress in plate, Fc = 0.75 Fy

Ultimate load: U = 1.2 DL + 1.0 LL Given: S = 2.4 m Lt = L2 = L1= 7.5 m Total DL = 4.5 kPa LL = 3.6 kPa ① Calculate the max. reaction at K. ② What is the max. shear at span KL? ③ Find the max. negative moment at K.

Super imposed loads: DL = 2.6 kPa LL = 3.6 kPa Concrete unit weight = 24.4 kN/m3 Clear concrete cover to stirrups = 50 mm Stirrups = 10 mm Ø Concrete column = 300 mm x 300 mm

11. CE BOARD May 2019 > The figure shows an element in pure shear and the corresponding Mohr’s circle. Points A and B represents the stresses in the x face and on the y face respectively. ① What is the width of bearing plate required if the bearing length is 100 mm. ② If the critical section for bending in bearing plates is at distance “K” from the centroidal y-axis of the web, find the required bearing plate thickness. ③ Determine the web yielding stress which occurs at distance (N + 2.5K), where N is the length of bearing plate = 100 mm.

① What is the moment (kN-m) at the end of the F of beam EF? ② What is the moment (kN-m) at the misdpan of beam FG? ③ What is the shear (kN) at the end F of beam EF?

9.

10. CE BOARD May 2019 >

CE BOARD May 2019 >

From the figure shown: Given: L1= 6 m Ls = 7 m L2 = 8 m S = 2.5 m Beam section b x h = 350 mm x 450 mm Slab thickness, t = 100 mm Material strength” Fc’ = 27.5 MPa

fy = 415 MPa

Loads: U = 1.2D + 1.6L Dead load: WD = 5.0 kPa including slab and beam Live load: WL = 3.8 kPa All beams are 350 mm wide,

① What is the value of the normal axial stress? ② How much is the max. in plane shear stress? ③ At what angle in degrees from the x-axis does the max. in plane shear stress occur?

① Compute the total ultimate load Wu (kN/m) to design beam I-J-K-L. Ultimate load: U = 1.4 DL + 1.7 LL ② If the design ultimate load Wu = 32kN/m, find the negative moment (kN-m) at the end of K of span JK. ③ How many 25 mm Ø bars are required at the end K of span KL if the design ultimate load, Wu = 32 kN/m.

Longitudinal beams, EFGH and IJKL are simply supported at E, F, G and H, and at I, J, K, L.

13. CE BOARD May 2019 > Identify the material property described by the following material:

12. CE BOARD May 2019 > Given beam: B x h = 300 mm x 450 mm Slab thickness, t = 100 mm S = 2.8 m. L1 = L2 = L3= 8 m

The material has the same composition at every point but the elastic may not be the same in all directions. a) b) c) d)

Isotropic Orthotropic Homogeneous Prismatic

14. CE BOARD May 2019 >

18. CE BOARD May 2019 >

Identify the material property described by the following material:

It is measured by the Richter scale. a) Ground acceleration b) Intensit of observed effects c) Magnitude of Earthquake d) Period of Earthquake

The composite material exhibits elastic properties in one direction different from that in the perpendicular direction. a) b) c) d)

Isotropic Homogeneous Prismatic Orthotropic

15. CE BOARD May 2019 > Identify the material property described by the following material: The material has the same elastic properties in all directions. a) b) c) d)

Prismatic Isotropic Orthotropic Homogeneous

16. CE BOARD May 2019 > Besides the epicentre, it describes the location of the earthquake. a) b) c) d)

Geologic formation Focal depth Fault line Dip angle

17. CE BOARD May 2019 > It is measured by seismometer. a) b) c) d)

Reference points Attenuation Components of ground motion Actual displacement

19. CE BOARD May 2019 > Given: W x L = 450 mm x 600 mm Ast = 16 – 25 mm Ø bars Ties = 12 mm Ø spaced at 100 mm on center Concret: fc’ = 27.5 MPa Steel:fyy for lateral ties = 275 MPa Effective cover to centroid of vertical steel reinforcement on each side = 65 mm Shear strength reduction factor = 0.65 ① Find the shear capacity of the column along the y-axis Vuy (kN)? ② What is the shear capacity of the column along the x-axis Vux (kN0? ③ Which of the following gives the maximum allowable factored shear force, Vux (kN)?