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)?