Module 1 Part 1

1. A bucket of mass 1.5 kg is whirled in a vertical circle of

radius 1.2 m. At the lowest point of its motion the tension in
the rope supporting the bucket is 30 N. Find the speed of
the bucket in m/s.
2. A highway curve having a radius of 410 ft is banked so that
there will be no lateral pressure on the car's wheel at a
speed of 37 kph. What is the angle of elevation of the
embankment? Answer in degrees. Use 1 m = 3.28 ft.
3. A 0.020-kg tennis ball, moving with a speed of 5.6 m/s, has
a head-on collision with a 0.080-kg ball initially moving in
the same direction at a speed of 2.6 m/s. Assuming a
perfectly elastic collision, determine the speed of the
heavier ball in m/s.
4. Find the magnitude of the slope of the normal line at the
point of the curve y = x​2 ​where x is 4.2.
5. A manufacturing company has determined that the total cost
of producing an item can be determined from the equation C
= 4x2 − 165x + 1800, where x is the number of units that
the company makes. How many units should the company
manufacture in order to minimize the cost?
6. What average force in N is required to stop a 937-kg car in
10.0 s if the car is traveling at 89 kph?
7. At room temperature, an oxygen molecule, with mass of 4.6
x10-26 kg typically has a kinetic energy of about 8.9 x10-21
J. How fast is it moving in m/s?
8. A curve road 126 m in radius has a super elevation of 0.11
and a design speed of 61 kph. Determine the friction
between the tires and the pavement.
9. Karen Estes just received an inheritance of $17900 and
plans to place all the money in a savings account that pays
9% compounded quarterly to help her son go to college in 5
years. How much money will be in the account in 5 years?
10. On the first day of the year, a man deposits $2000 in a bank
at 6% per year, compounded annually. He withdraws $70.00
at the end of the first year, $90.00 at the end of the second
year, and the remaining balance at the end of the third year.
How much does he withdraw at the end of the third year?
11. How many years will be required for a sum of money to be 6
times its principal amount, if it is deposited in a bank
account that pays 7% per year, compounded 2 time/s a
year?
12. A 4.8-foot-tall woman is walking at the rate of 3.9 ft/sec
away from a street lamp that is 28 ft tall. How fast is the tip
of her shadow moving in ft/sec?
13. An industrial plant bought a generator set for 86,000. Other
expenses including installation amounted to 13,000. The
generator set is to have a life of 16 years with a salvage
 value at the end of life of 6,000. Determine the depreciation
charge during the 8th year by the declining balance method.
14. A rigid pavement is to be used to carry a wheel load of 46.9
kN, design the thickness in mm of the pavement. The
allowable tensile stress of concrete is 1.6 MPa. Sufficient
dowels are used across the joints at the edge of the
pavement.
15. Car A hits car B (initially at rest and of equal mass) from
behind while going 34 m/s. Immediately after the collision,
car B moves forward at 18 m/s and car A is at rest. What is
the coefficient of restitution?
16. Cynthia purchased a small lot in a subdivision, paying
P200,000 down and promising to pay P19,000 every 3
months for the next 11 years. The seller figured interest at
11% compounded quarterly. If Cynthia missed the first 10
payments, what must he pay when the 11th payment is due
to discharge his entire indebtedness?
17. Water is being withdrawn from a conical reservoir 4 ft in
radius and 14 ft deep at 3.5 ft3/min. How fast is the radius
of this surface diminishing in in/min when the depth of the
water is 5 ft?
18. The peak hour factor for a traffic during rush hour is equal
to 0.7 with a highest 5 min. volume of 219 vehicles. The
space mean speed of the traffic is 76 kph. Compute the
maximum spacing of vehicles.
19. A contract has been signed to lease a building at P21,000
per year with an annual increase of P1200 for 7 years.
Payments are to be made at the end of each year, starting
one year from now. The prevailing interest rate is 9%. What
lump sum paid today would be equivalent to the 7-year
lease payment plan?
20. If the spot speeds are 49 kph, 34 kph, 62 kph, 58 kph, and
43 kph, then find the space mean speed in m/s.
21. A flexible pavement having a thickness of 72 mm carries a
static wheel load of W. The circular contact area of tire has
an equivalent radius of 123 mm. If the load W is assumed to
be transmitted across a wide area of subgrade at an angle of
45 degrees, compute the value of the wheel load W in kN if
the bearing stress of the base is 0.49 MPa.
22. A hypothetical planet has a mass 8.4 times that of Earth, but
has the same radius. What is the gravity near its surface?
23. A vehicle moving at 69 kph downward an incline surface was
stopped by applying brakes and the braking distance was 45
m. If the slope of the inclined surface is 4%, compute the
coefficient of friction between the tire and the road.
24. A spring has a spring constant k of 78. How much must this
spring be compressed in meters to store 45.9 J of potential
energy?
25. What is the annual interest rate on a $1000 loan in which all
interest is paid at the end of 2 year/s, and a total of $1350
must be repaid at the end?
26. Find the abscissa on the curve y = √x that is a minimum
distance from the point (4, 0).
27. Find the volume generated by revolving the first-quadrant
area bounded by the parabola y2 = 8x and its latus rectum
about the x axis.
28. A car going on a speed of 60 mph on a curve highway. After
passing midpoint, the driver saw an accident in front of him.
With a reaction time if 2.55 seconds, the distance in feet
that will be passed from the moment the driver saw the
accident until he hit the brakes will be
29. A father wants to set aside money for his 5-year-old son's
future college education. Money can be deposited in a bank
account that pays 8% per year, compounded annually. What
equal deposits should be made by the father, on his son's
6th through 17th birthdays, in order to provide $5000 on the
son's 18th, 19th, 20th, and 21st birthdays?
30. Find the perimeter of the region between the parabola y = 1
− x2 and the line y = 1 – x.
31. For a top player, a tennis ball may leave the racket on the
serve with a speed of 55 m/s. If the ball has a mass of
0.060 kg and is in contact with the racket for about 4 ms,
estimate the average force on the ball in N.
32. A company has purchased an equipment whose first cost is P
100,000 with an estimated life of eight years. The estimated
salvage value of the equipment at the end of its lifetime is P
20,000. Determine the book value at the end 6 years using
the sum of the year’s digit.
33. Find the moment of inertia of the region between the curve
x = y2 and the curve x – y = 6 with respect to y-axis.
34. A company has purchased a bus for its officers for P
10,00,000. The expected life of the bus is eight years. The
salvage value of the bus at the end of its life is P 1,500,000.
Using the sinking fund method of depreciation, find the book
value at the end of the sixth year. Use i = 10%
35. What amount of money is equivalent to receiving $5000 two
years from today, if interest is compounded quarterly at the
rate of 2 ½ % per quarter?
Module​ ​1​ ​Part​ ​2

1. The maximum velocity attained on the interval 0 ≤ t ≤ 5, by

the particle whose displacement is given by s(t) = 2t3 –
12t2 + 16t + 2 is
a. 286
b. 16
c. 46
d. 0
e. None of the above
2. Calculate the compounded future value of 20 annual
payments of $5,000 each into a savings account that earns
6% per year. The first 10 payments are made at the
beginning of each year and the last 10 payments are at the
end of each year.
a. $183,927.96
b. $187,882.19
c. $194,963.63
d. $191,009.39
e. None of the above
3. An underground conical tank, standing on its vertex, is being
filled with water at the rate of 18π ft3/min. If the tank has a
height of 30 feet and a radius of 15 feet, how fast is the
 water level rising when the water is 12 feet deep?

4. A 0.450-kg hockey puck, moving east with a speed of 5.80

m/s, has a head-on collision with a 0.900-kg puck initially at
rest. Assuming a perfectly inelastic collision, what will be the
direction of the 0.450-kg hockey puck after the collision?

5. What is the nominal rate of interest compounded

continuously for 8 years if the present worth factor is equal
to 1.7506725
6. Determine the capitalized cost of a research laboratory
which requires P5,000,000 for original construction;
P100,000 at the end of every year for the first 5 years and
then P120,000 each year thereafter for operating expenses,
and P500,000 every 6 years for replacement of equipment
with interest at 12% per annum?

7. A bicycle with tires 68 cm in radius travels 9.2 km. How

many revolutions do the wheels make?

8. A 5.0 kg object is to be given an upward acceleration of 0.30

m/s2 by a rope pulling straight upward on it. What must be
the tension in the rope?
9. Determine the perimeter of the curve r = cos θ.

10. Determine the rate of depreciation for an asset that costs

P15,000 now and has an estimated scrap value of P2,000 at
the end of 10 years by the declining balance method

11. Evaluate
12. Which of the following is not true?

13. A 0.145-kg baseball pitched horizontally at 27.0 m/s strikes

a bat. If the contact time between bat and ball is 2.5 ms,
calculate the impulse of the ball.
14. Physically, integrating means finding the

Ans: finding the area under the curve of the function from a
to b.

15. Two sides of a triangle are 6 meters and 8 meters in length,

and the angle between them is increasing at a rate of 0.12
radians per second. Find the rate at which the area of the
triangle is increasing when the angle between the sides is
pi/6.
Model 2 Part 1

1. The moist unit weight of a soil is = 16.63 kN/m3. The

moisture content of this soil is 0.1 when the degree of
saturation is 0.41. Compute the specific gravity of the soil.
2. The moist unit weight of a soil is = 16.49 kN/m3. The
moisture content of this soil is 0.17 when the degree of
saturation is 0.48. Compute the porosity of the soil.
3. Determine the value of the diameter at 60% passing, D60.
Round off to three decimal places.

4. Determine the value of the effective diameter/size. Round

off to three decimal places.
5. Determine the value of the diameter at 30% passing, D30.
Round off to three decimal places.

6. Compute the end-bearing capacity of the pile in N.

7. A prestressed concrete pile, 499 mm in diameter, is to be
driven in a clayey soil. The pile has a design capacity of 425
kN. Use FS = 2, unconfined shear strength = 53 kPa.
Compute the end bearing capacity (kN) of the pile. Use
frictional constant = 0.8 (if needed).
8. Compute the allowable load that the pile can carry using a
factor of safety of 3. Round off to two decimal places. Use
STORED VALUES at all times.

9. Find the hydraulic conductivity in cm/sec. Round off to three

decimal places.
10. Express your answer as _____ x 10^-3 cm/sec with three
decimal places. Only input the numeric part. Ex: if your
answer is 1.234 x 10^-3 cm/s, only input 1.234

11. Find the hydraulic conductivity in cm/min. Round off to three

decimal places.
12. Determine the settlement of the overconsolidated clay layer
in mm. Use the following data:

13. Determine the settlement of the overconsolidated clay layer

in mm. Use the following data:
14. A direct shear test was performed on two identical cohesive
soil samples. In test one, the sample shears at a stress of 80
kPa when the compressive normal stress is 99 kPa. In test
two, the sample shears at a stress of 104 kPa when the
normal stress is 145 kPa. Determine the value of the shear
stress (kPa) at a depth of 9 m. it the unit weight of the soil
is 15.05 kN/m3.
15. A dry sand sample is tested in direct shear. The test
procedure includes having a normal stress of 242 kPa
imposed while the sample undergoes shearing. The sample
fails when the shear stress reaches 105 kPa. Determine the
angle of internal friction of the sand sample.
16. A particular soil failed under a major principal stress of 484
kPa with a corresponding minor principal stress of 253 kPa.
If for the same soil, the minor principal stress had been 350
kPa, determine the corresponding major principal stress.
Round off to two decimal places. Hint: When a soil is tested
using the tri-axial apparatus, it will yield one value for the
angle of friction (most of the time).
17. A direct shear test was performed on two identical cohesive
soil samples. In test one, the sample shears at a stress of 83
kPa when the compressive normal stress is 91 kPa. In test
two, the sample shears at a stress of 106 kPa when the
normal stress is 141 kPa. Determine the value of the normal
stress (kPa) if the shear stress at a point on the soil is 87
18. A direct shear test was performed on two identical cohesive
soil samples. In test one, the sample shears at a stress of 88
kPa when the compressive normal stress is 90 kPa. In test
two, the sample shears at a stress of 109 kPa when the
normal stress is 149 kPa. Determine the value of the angle
of friction.
19. For a given sandy soil, emax = 0.72, emin = 0.42, Gs =
2.57. If the relative density of the soil is 58%, and its water
content is 7, determine the in-situ porosity.
20. For a given sandy soil, emax = 0.78, emin = 0.41, Gs =
2.55. If the relative density of the soil is 61%, and its water
content is 9, determine the dry unit weight in kN/m3.
21. Estimate the equivalent coefficient of permeability (cm/s)
considering perpendicular flow. ANSWER SHOULD BE _____
X 10^-4 THEN ROUND OFF TO FOUR DECIMAL PLACES.
22. Charyeong wants to determine the permeability of an
aquifer. The aquifer has a 300 mm diameter test well that
penetrates 27 m. below the static water table. After 24
hours of pumping at 62 liters/sec, the water level in an
observation well 90.54 m. from the test well was lowered to
25.6 m. and the other observation well at 30.52 m. from the
test well, was lowered to 24.25 m. Determine the coefficient
of permeability of the aquifer in m/day. Round off to two
decimal places.
23. Charyeong wants to determine the drawdown of an aquifer.
The aquifer has a 300 mm diameter test well that penetrates
Hw = 28 m. below the static water table. After 24 hours of
pumping at 77 liters/sec, the water level in an observation
well 93.61 m. from the test well was lowered by
(draw-down) 0.32 m. and the other observation well at
31.35 m. from the test well, was lowered by 'x' m. If the
coefficient of permeability of the unconfined aquifer is 72
m/day, find the draw-down 'x' in meters.
24. A 3-foot square footing has its bottom 2.28 ft. below the
ground surface. The ground water table is located at a depth
of 4 ft. below the ground surface. Unit weight of soil is 117
lb/ft3, Saturated unit weight is 124 lb/ft3, cohesion = 95
lb/ft2. Use angle of internal friction = 30° (Nc = 35, Nq =
22, begin mathsize 12px style text N end text subscript
straight gamma end style = 19). Compute the allowable load
 that the footing could carry. Use FS = 2.6. Round off to the
nearest whole number.
25. A rectangular footing (base = 1.32 m., length = 5.85 m.)
has its bottom 3.94 m. below the ground surface. Unit
weight of soil is 18.84 kn/m3, unconfined compressive
strength = 160 kPa. Use angle of internal friction = 10° (Nc
= 9, Nq = 2.5, begin mathsize 12px style text N end text
subscript straight gamma end style = 1.2). Compute the
allowable load that the footing could carry. Use FS = 2.4.
Round off to the nearest whole number.
26. For a given soil, the following are known. Gs = 2.62, Moist
unit weight = 18.59 kN/m3, and moisture content is
17.24%. Determine the void ratio.
27. For a given soil, the following are known. Gs = 2.62, Moist
unit weight = 15.8 kN/m3, and moisture content is 17.35%.
Determine the moist unit weight (kN/m3) is the degree of
saturation is 59%.
28. Determine the shrinkage ratio of the soil. Round off to two
decimal places.
29. Determine the shrinkage limit (%) of the soil. Round off to
two decimal places.

30. What is the liquid limit of the soil? Round off to two decimal
places.

31. What is the liquid limit of the soil? Round off to two decimal
places.

32. The moist weight of 0.0058 m3 of a soil is 103.5 N. The

moisture content and the specific gravity of soil solids are
 determined in the laboratory to be 10% and 2.63,
respectively. Calculate the dry unit weight in kN/m3.
33. The moist weight of 0.0051 m3 of a soil is 104.5 N. The
moisture content and the specific gravity of soil solids are
determined in the laboratory to be 14% and 2.62,
respectively. Calculate the void ratio.
34. Find the coefficient of active pressure for an angle of friction
= 109°.
35. Find the angle of friction for a coefficient of active pressure
of 0.513.
Module 2 Part 2

1. Determine its classification using USCS.

2. A liquid limit test was done on a soil sample using the
Casagrande Apparatus & the Fall-Cone method. Water was
added to the sample and its resulting moisture content was
recorded then the sample was subjected to the two tests.
Data recorded are as follows:

3. Yuri has a soil sample that has a specific gravity of 2.67. Its
maximum and minimum void ratio, determined by
laboratory tests are 0.75 and 0.52, respectively. If the
relative density of the soil is 65%, determine the following:
4. In solving the permeability of a soil sample, the temperature
correction factor for T = 22°C is:

5. A 5 m-thick clay (Gs = 2.65, water content = 0.28) is

overlain by a 4.50m-thick layer of sand (Gs = 2.60, e =
 0.70, S = 0.85). The ground water table is located 4.50 m
from the ground surface. Compute for the following:

6. A tri-axial test was conducted on a cohesive soil sample.

Failure occurred the normal stress was 400 kPa and the
shear stress is 300 kPa. Use angle of friction = 32°.
7. ___ generally, are defined as particles smaller than 0.002
mm. However, in some cases, particles between 0.002 and
0.005 mm in size are also referred to as ____.
 Module 3 Part 1

0.025 1. A singly reinforced rectangular beam 350 mm wide and 450

mm deep is reinforced with 4 -16-mm-diameter bottom bars
enclosed with 10-mm-dia stirrups covered with 40 mm of
concrete. Calculate the tensile steel strain compatible with
concrete strain of 0.003. Use f'c = 21 MPa and fy = 280
MPa. Express your answer in 3 decimal places
1133 2. A simply supported beam with a span of L = 6.1 m must be
designed to support a uniformly distributed total dead load
of 15 kN/m and live load of 11 kN/m. Using material
strengths f'c = 21 MPa and fy = 420 MPa, Calculate the
required area (mm2 ) of flexure bars 20 mm in diameter for
a size of 250 mm x 500 mm. Write your answer as a whole
number, rounded up.
64.49 3. A singly reinforced rectangular beam 350 mm wide and 450
mm deep is reinforced with 3 -16-mm-diameter bottom bars
enclosed with 10-mm-dia stirrups covered with 40 mm of
concrete. Calculate the nominal moment strength in kN-m.
Use f'c = 28 MPa and fy = 280 MPa. Express your answer in
two decimal places.
452.82 4. A simply supported beam with span of L = 5.2 m must be
designed to support a uniformly distributed total dead load
of 15 kN/m and live load of 11 kN/m. Using material
strengths f'c = 21 MPa and fy = 420 MPa, consider b=0.55d,
calculate the required effective depth in mm if the tensile
 steel strain compatible with concrete strain of 0.003 is set at
0.013. Express your answer in two decimal places.
5. The image shown is a reference for the next question. Write
"ok" in the blank provided and click next.

-15.92 6. The two span beam shown in the figure has spans L1 = 4.8
m and L2 = 5.4 m. The service loads are total dead load of
5.4 kN/m and live load of 11.5 kN/m. If live load is placed
on both spans, calculate the maximum factored negative
bending moment in kN-m. Write your answer in 2 decimal
places only without the unit.
28.99 7. The two span beam shown in the figure has L1 = L2 = 3.5
m. The service loads are total dead load of 7.5 kN/m and
live load of 11.4 kN/m. If live load is placed on span AB
only, calculate the maximum factored positive bending
moment at span AB in kN-m. Write your answer in 2
decimal places only without the unit.
519 8. A 2-span-continuous beams has equal spans of L = 5.4 m
and equal loads. Calculate the prismatic gross depth in mm
of a rectangular section considering the smallest factored
bending moment with minimum steel ratio and b/d = 0.55.
Service loads are wD = 10 kN/m and wL = 12 kN/m. Use
 material strengths f'c = 21 MPa and fy = 420 MPa for 20
mm flexure bars enclosed in 10 mm stirrups. Round up the
final depth to the next larger whole number.
767 9. A 2-span-continuous beams has equal spans of L = 5.8 m
and equal uniformly distributed loads. Calculate the
required amount of top bars in mm2 at B given that the
prismatic size is 250 mm x 450 mm. Service loads are wD
= 9 kN/m and wL = 10 kN/m. Use material strengths f'c =
21 MPa and fy = 420 MPa for 20 mm flexure bars enclosed
in 10 mm stirrups. Round up the final answer to the next
larger whole number.
2050 10. A floor slab 125 mm thick is cast monolithically with beams
325 mm wide and 500 mm deep, spaced 2.1 m on centers
on simple supports over a span of 6.9 m. The floor supports
a superimposed service dead load of 4.7 kPa and live load of
2.8 kPa. Using f'c = 21 MPa and flexure bar fy = 420 MPa,
calculate the effective flange width of a typical interior beam
in mm.
1224 11. A floor slab 125 mm thick is cast monolithically with beams
300 mm wide and 500 mm deep, spaced 2.1 m on centers
on simple supports over a span of 6.9 m. The floor supports
a superimposed service dead load of 3.6 kPa and live load of
4.1 kPa. Using f'c = 21 MPa, 20-mm-diameter flexure bar
and 10-mm-diameter stirrups with fy = 420 MPa, calculate
the required amount of flexure bars in mm2 using a
 T-beam geometry. Write your answer to the nearest whole
number.
154 12. A simply supported beam 350 mm wide by 640 mm deep,
6.7 m between faces of supports is reinforced with
25-mm-diameter flexure bars at and effective depth of 535
mm. The beam supports a service, concentrated live load of
90 kN in addition to a total service uniformly distributed
dead load of 45 kN/m. With material strengths f'c = 21 MPa
and fy = 280 MPa for 10-mm-diameter stirrups, calculate
the required spacing of stirrups at the critical section. Write
your answer to the nearest whole number.
201.824
13. A simply supported beam 350 mm wide by 640 mm deep,
5.3 m between faces of supports is reinforced with
25-mm-diameter flexure bars at and effective depth of 535
mm. The beam supports a service, concentrated live load of
100 kN in addition to a total service uniformly distributed
dead load of 48 kN/m. With material strengths f'c = 21 MPa
and fy = 280 MPa for 10-mm-diameter stirrups, calculate
the factored critical shear force in kN. Write your answer in
2 decimal places.
2527.0414. A circular, tied column 490 mm in diameter is reinforced
with 12 20-mm-dia. vertical bars. Calculate the design axial
strength of the column in kN. Use material strengths f'c =
28 MPa and fy = 420 MPa.
1631.93615. A rectangular, tied column 460 mm wide along x-axis and
460 mm wide along y-axis is reinforced with 4
25-mm-diameter vertical bars with fy = 420 MPa enclosed in
10-mm-dia. ties. Using f'c = 21 MPa, calculate the nominal
axial strength at balanced condition in kN with bending
about the x axis. Write your answer with 2 decimal places
only.
53 16. A circular, spiral column 430 mm in diameter is reinforced
with 10 20-mm-dia. vertical bars. Calculate the required
spacing of spiral bar 10-mm-diameter. Use material
strengths f'c = 23 MPa and fyh = 420 MPa. The column is
exposed to weather with concrete cover of 50 mm. Write
your answer to the nearest whole number.
1.46 17. A wall footing slab 0.34 m thick sustains a uniform service
dead load of 117 kN/m and service live load of 84 kN/m
from an monolithic wall 250 mm thick. If the base of the
footing is 1.5 m from the grade line and soil properties are
as follows: unit weight = 17.1 kN/cu.m. and allowable gross
bearing capacity = 166 kPa, calculate the required size of
the footing slab in "m". Write your answer in 2 decimal
places only.
54.17 18. A wall footing 1.7 m wide, 0.32 m thick sustains a uniform
service dead load of 108 kN/m and service live load of 138
kN/m from an monolithic wall 250 mm thick. If the flexure
bar diameter is 12 mm, calculate the maximum factored
 moment in kN-m. Write your answer in 2 decimal places
only.
0.57 19. A wall footing 1.9 m wide, 0.34 m thick sustains a uniform
service dead load of 145 kN/m and service live load of 124
kN/m from an monolithic wall 250 mm thick. If the flexure
bar diameter is 12 mm, calculate the nominal wide beam
shear stress at the critical section in MPa. Write your
answer in 2 decimal places only.
20. The attached file will be reference to questions 21 to 23.
Save the file and type OK in the space and proceed.
149 21. An angle bar 100x100x11 mm tension member is connected
with 23 mm diameter bolts with damaged hole diameter 4
mm larger. Both legs of are connected as shown in FIG.
UHFG 4857 designed to resist axial tensile live load of 178
kN. If the angle bar is A36 steel with Fy = 248 MPa and Fu
= 400 MPa, calculate the maximum service axial dead load
the member can sustain using LRFD under the limiting state
of net tensile rupture. Write your answer to the nearest
whole number in kN.
57.48 22. A tension member is connected by 27 mm bolts as shown in
FIG. HTGAWM 101. With the following given: a = 60 mm, x
= 100 mm and t = 18 mm, calculate the value of "b" so that
the net area along fracture line 1-2-3-5 is equal to the net
area across fracture line 1-2-5. Hole diameter for net area
calculation is 4 mm larger than bolt diameter. Write your
answer in two decimal places only.
473 23. An angle bar 100x100x12 mm tension member is connected
with 27 mm diameter bolts with damaged hole diameter 4
mm larger. Both legs of are connected as shown in FIG.
 UHFG 4857. If the angle bar is A36 steel with Fy = 248 MPa
and Fu = 400 MPa, calculate the design axial strength using
LRFD under the limiting state of net tensile rupture. Write
your answer to the nearest whole number in kN.
3414 24. A W12x79, A573 Grade 60 (Fy = 415 MPa) steel is used as a
compression member. It is 5 m long, fixed at top and
bottom, and has an additional support in the weak direction
2.7 m from the top. Properties of the section are A =
14,500 mm2, Ix = 258.6x106 mm4 and Iy = 84.375x106
mm4. Calculate the allowable axial strength of the column in
kN, rounded to the nearest whole number.
216 25. A W12x79, A573 Grade 60 (Fy = 415 MPa) steel is used as a
compression member. It is 7.1 m long, pinned at top and
bottom. Properties of the section are A = 14,500 mm2, Ix =
258.6x106 mm4 and Iy = 84.375x106 mm4. Calculate the
maximum service axial live load the member can sustain in
addition to an axial service dead load of 1,818.3 kN under
the provisions of LRFD. Write answer in kN, rounded to the
nearest whole number.
541.710 26. A symmetrical built up steel beam consists of a 9 mm x 210
mm top and bottom flange and a 9 mm x 220 mm web.
Determine the plastic section modulus about the strong axis.
Write the answer in the format ________x103 mm3 with 2
decimal places only.
60.12 27. A W14x68 (Fy = 345 MPa) is used as a simply supported
beam, span L = 6.3 m, with continuous lateral support by
the flooring. Given the properties below, calculate the
maximum service, uniformly distributed live load in kN/m
the beam can sustain under the provisions of LRFD if the
total service dead load is 16 kN/m: A = 12,903 mm2, d =
356 mm, tw = 10.5 mm, bf = 255 mm, tf = 18.3 mm
305.31 28. A T-shape, built up A36 steel beam consists of a 27 mm x
240 mm top flange and a 24 mm x 310 mm web.
Determine the nominal moment strength about the strong
axis (kN-m) if the concrete slab it supports provides full
lateral suppport. Write your answer in 2 decimal places
only.
79.57 29. A T-shape, built up steel beam consists of a 26 mm x 240
mm top flange and a 28 mm x 330 mm web. Determine the
location in mm of the plastic neutral axis from the top edge
of the flange. Write your answer in 2 decimal places only.
 Module 3 Part 2

1. A rectangular beam 250 mm wide, 500 mm deep is

reinforced at the bottom with 4-20-mm-diameter bars and
at the top with 2-16-mm bars. Concrete cover to bar
centroid at the top is 80 mm and at the bottom is 70 mm.
Use concrete strength f’c = 21 MPa and steel yield strength
fy = 415 MPa for 20-mm bars and fy = 275 MPa for 16-mm
bars. Determine the nominal moment capacity in kN∙m of
the beam in positive bending.

ANSWER

2. A short rectangular column 500 mm on one side and 800

mm on the other side. It is reinforced with
10-28-mm-diameter longitudinal bars equally distributed to
the shorter sides of the column. The centroid of the bars are
76 mm from the concrete surface. Use f’c = 28 MPa and fy
= 420 MPa. Determine the nominal moment in kN∙m the
column can sustain at balanced condition.
ANSWER

3. The dimensions of a rectangular beam are limited to b = 300

mm and effective depth, d = 700 mm. Using f’c = 28 MPa,
long bar fy = 415 MPa, calculate the maximum steel ratio
limiting the tensile strain to 0.004.

ANSWER

4. Determine the size of a square column (mm) using an 3%

vertical bar steel ratio.

450

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5. A rectangular beam 250 mm wide, 400 mm deep is

reinforced at the bottom with 4-20-mm-diameter bars and
at the top with 2-16-mm bars. Concrete cover to bar
 centroid at the top is 80 mm and at the bottom is 70 mm.
Use concrete strength f’c = 21 MPa and steel yield strength
fy = 420 MPa for 20-mm bars and 16-mm bars.

ANSWER

ANSWER

ANSWER

6. A square footing must sustain an axial column load of 300

kN due to dead load and 450 kN due to live load. The
footing is pre-designed to be 2.5 m wide, 350 mm thick
 supporting a 300 mm square column. Assume flexure bars
20 mm in diameter, Grade 420 and concrete strength 21
MPa.

ANSWER

ANSWER

ANSWER

7. A 500-mm-diameter, non-slender, tied column is

symmetrically reinforced with six 25 mm vertical bars.
Calculate the design strength (kN) of this column if
 subjected to axial load only. Given f’c = 27 MPa and fy =
414 MPa.

8. Determine the size of a square column (mm) using an 2%

vertical bar steel ratio.

9. A W21 x 62 beam (Fy = 248 MPa) is resting on a concrete

wall, f’c = 21 MPa. The end reaction 150 kN due to dead
load and 300 kN due to live load. Section properties are d =
525 mm, bf = 250 mm, tw = 10 mm, tf = 20 mm and k =
28 mm. Use LRFD method. Provisions are given at the back
pages.