CIVIL ENGINEERING PRACTICE PROBLEMS
REINFORCED CONCRETE DESIGN
CLOSED NOTES, HANDOUTS, BOOKS AND HOMEWORKS
*Read problems completely and carefully before beginning to solve.
Name:_______________________________________ School ID No.:_______________ Section: _________________
I. Multiple Choice ( 1.5 points each)
Instruction: Solved the following problems and write the corresponding letter of your answer on the space provided in the separate
answer sheet provided. If your answer is not on the choices choose the nearest among the choices. USE CAPITAL
LETTERS. Use NSCP 2010 otherwise stated.
75
SITUATION 1
A prestressed concrete beam 500 mm x 800 mm is simply supported over a span of L = 20 m. The tendons are placed 100
mm from the bottom of the beam. Initially the 2500 mm2 tendons are tensioned up to a maximum pressure of 188.60 ksi
after which the concrete is placed. After concrete hardens sufficiently, the tendons are cut there is a transfer of stress from
tendons to concrete. The beam is then loaded by total dead load of 10 kN/m and live load of 15 kN/m. There is loss of stress
at transfer of 10%. Use Working stress design.
Problem 1
Determine the initial stress in the beam at the bottom fiber, in MPa.
a. -23.77
b. -26.41
c. -8.13
d. -18.28
Problem 2
Calculate the total stress in the top fiber at L/3 from the ends after the application of the loads, in MPa.
a. -10.68
b. -10.16
c. –11.69
d. -9.14
Problem 3
Obtain the total stress in the bottom fiber at L/3 from the ends after the application of the loads, in MPa.
a. -5.57
b. -20.83
c. -7.31
d. -2.93
SITUATION 2
The 6 m long prestressed cantilever beam shown in the figure RC-FE001 carries a concentrated live load of 18 kN at the
free end and a uniform dead load due to its own weight. Unit weight of concrete is 24 kN/m3. The prestressing steel is
consists of 10 - 16 mm in diameter with total prestressing force applied at an eccentricity, “e” above the neutral axis of the
gross-section. Use Working stress design.
Use:
b = 400 mm;
h = 600 mm;
L=6m
Problem 4
Determine the required prestressing pressure (in MPa) if the stress on top is -11 MPa and at the bottom is
+3.5 MPa due to initial prestress.
a. 548.92
b. 447.62
c. 583.10
d. 763.39
Problem 5
Determine the required prestressing pressure (in MPa) if the stress on top is -0.5 MPa and at the bottom is
-12 MPa at the fixed end due to initial prestress and service loads.
a. 746.04
b. 484.29
c. 366.45
d. 556.25
Problem 6
Determine the required prestressing force (in kN) if the stress on top is -0.5 MPa and in the bottom is -12
MPa at the fixed end due to initial prestress and service loads.
a. 975
b. 740
c. 1,500
d. 1,120
SITUATION 3
A spiral column 500 mm in diameter, it is reinforced with 6 – 32 mm Ø bars and has an unsupported height of 3 m. The
column is bent in single curvature and is braced against sidesway. Bending is about the x-axis (see figure RC-FE005).
Compressive strength of concrete = 27.5 MPa (normal weight)
Steel yield strength = 413 MPa
Clear cover = 40 mm
Spirals = 10 mm spaced at 50 mm O.C.
Determine the ultimate concrete shear strength of the spiral column using NSCP 2010.
Problem 7
Problem 8
Problem 9
Determine the depth in the axis of bending, in mm.
a. 491
b. 400
c. 600
d. 468
Determine the nominal concrete shear strength along the x-axis, in kN.
a. 113.63
b. 116.84
c. 151.51
d. 155.79
Calculate the ultimate shear capacity of the column, in kN.
a. 551.26
b. 461.90
c. 527.08
d. 463.27
REINFORCED CONCRETE
Q1-1
CIVIL ENGINEERING FINAL EXAMINATION
Q8-2
REINFORCED CONCRETE
SITUATION 4
The flooring of a warehouse is made up of double-tee joists (DT) as shown RC-FE003. The joists are simply supported on
a span of 7.5 m and are pre-tensioned to a total initial force of 1,500 kN with one tendon in each stem, located at 75 mm
above the bottom fiber, loss of stress at service load is 20%. Unit weight of concrete is 24 kN/m 3.
Load imposed on the joists are:
Dead Load = 2.3 kPa
Properties of DT:
A = 200, 000 mm2;
Live load = 6 kPa
I = 1880 x 106 mm4;
yt = 88 mm;
yb = 267 mm;
a = 2.4 m
Problem 10
Compute the stress at the top fibers at midspan due to the initial pre stressing force alone, in MPa.
a. +5.98
b. +4.78
c. -48.40
d. -38.72
Problem 11
Compute the resulting stress at the top fibers of the DT at mid-span due to service loads and prestressing
force, in MPa.
a. -63.41
b. -23.72
c. -40.27
d. -14.04
Problem 12
What additional super imposed load can the DT carry such that the resulting stress at the top fibers at midspan
is zero, in kPa?
a. 10.18
b. 17.77
c. 4.24
d. 5.86
SITUATION 5
As shown in Figure RC-FE008, beam DEF is reinforced as follows:
Main reinforcements at supports:
Main reinforcements at midspan:
Top bars……………………………5 – 25 mm ɸ
Top bars……………………………3 – 25 mm ɸ
Bottom bars……………………..…3 – 25 mm ɸ
Bottom bars….………….…………3 – 25 mm ɸ
Stirrups………………………….…10 mm ɸ
Material strength:
Concrete:
fc’ = 27.5 MPa
Steel :
fy = 415 MPa (main bars)
fyv = 275 MPa (stirrups)
Problem 13
Dimensions:
Beam (below slab):
bw x h = 350 mm x 350 mm
Slab thickness:
tf = 100 mm
Column section:
350 mm x 350 mm
Clear cover:
50 mm
S1 = S2 = S3 = 2.6 m; S4 = S5 = 6.5 m
Find the ultimate load Wu (kN/m) which the beam DEF can support based on its flexural reinforcements at
supports. Use steel cover of 70 mm.
a. 83.01
b. 60.37
c. 75.47
d. 67.92
Problem 14
Find the factored moment capacity Mu in kN.m of the beam DEF at midspan. Use steel cover of 70 mm.
a. 285.44
b. 188.47
c. 194.93
d. 107.30
Problem 15
Find the shear (kN) at end E of span EF if Wu = 60 kN/m.
a. 212.18
b. 162.44
c. 194.93
d. 244.00
SITUATION 6
An isolated T beam is composed of a flange 550 mm wide and 150 mm deep cast monolithically with a web of 250 mm
width that extends 600 mm below the bottom surface of the flange to produce a beam of 750 mm total depth. Tensile
reinforcement consists of 4-32 mm ϕ bars placed in two horizontal rows separated by 25 mm clear spacing. The centroid of
the bar group is 650 mm from the top of the beam. The concrete has a strength of 20.68 MPa, and the yield strength of the
steel is 413.57 MPa. What is the design moment capacity of the beam?
Problem 16
Which of the following gives the location of the neutral axis from the extreme tension fiber, in mm?
a. 161.90
b. 144.42
c. 605.58
d. 588.10
Problem 17
Which of the following gives the actual strain of the tension bars, in MPa?
a. 0.00207
b. 0.00785
c. 0.00795
d. 0.00904
Which of the following gives the nominal moment capacity of the beam, in kN.m?
a. 695.24
b. 773.25
c. 864.80
d. 778.32
Problem 18
Q1-3
After frame analysis resulting bending moments at working loads of a beam are as follows:
MDL = 110 kN.m
MLL = 60 kN.m
MEQ = 45 kN.m
Given:
Concrete compressive strength:
fc’ = 28 MPa
Reinforcing steel yield strength:
fy = 415 MPa
Required strength:
U = 1.2D + 1.0L + 1.0E
Concrete cover to centroid of reinforcement = 70 mm
Problem 19
Using a beam 250 mm wide, find the required total beam depth (mm), if this beam is to be designed as
singly reinforced. Use design steel ratio, ρ = ¼ (ρmax+ ρb).
a. 650
b. 550
c. 600
d. 500
Problem 20
Using a beam with dimension b x h = 300 mm x 600 mm, calculate the minimum number of 20 mm Ø bars
required.
a. 4
b. 5
c. 6
d. 8
Problem 21
Using a beam with dimension b x h = 250 mm x 500 mm reinforced with 3 - 25 mm Ø bars, find the
resulting nominal bending strength Mn (kN.m).
a. 231
b. 208
c. 275
d. 237
SITUATION 8
The figure shown in RC-FE011 shows the shear force at the column section of a building with transverse confining
reinforcement.
Use:
b = 400 mm;
h = 800 mm;
db = 28 mm
Clear cover of 12 mm ϕ ties (PC) = 40 mm
fc’ = 28 MPa
fy = 415 MPa (for main bars)
fyh = 278 MPa (for tie bars)
The NSCP specifies the transverse confining reinforcement in accordance with the code for seismic design.
Problem 22
Determine the required spacing (in mm) of lateral reinforcement for a factored shear load V uy = 500 kN if
the allowable concrete shearing stress is 0.88 MPa.
a. 100
b. 170
c. 150
d. 90
Problem 23
What is the maximum spacing (in mm) of the 12 mm ϕ transverse reinforcement?
a. 100
Problem 24
b. 150
c. 120
d. 90
Determine the required spacing (in mm) of the confining hoop reinforcement in accordance with the code
for seismic design.
a. 50
b. 160
c. 120
d. 70
SITUATION 9
A column shown in figure RC-FE010 is a T-section and has PVC pipes with outside diameters of 76 mm were embedded
on it.
Given Data:
Longitudinal bars:
Lateral Ties:
As1 = 6-20 mm Ø bars in compression
10 mm Ø bars with fyv = 275 MPa
As2 = 4-32 mm Ø bars in tension
Clear cover concrete cover ties = 40 mm
fy= 415 MPa
fc’ = 27.5 MPa
Use:
b1 = 600 mm;
b2 = 300 mm;
h1 = 250 mm;
h2 = 350 mm
Consider the concrete area displaced by the compression steel.
Problem 25
Problem 26
Problem 27
Determine the location of the geometric centroid of the section from y-axis, in mm.
a. 304.60
b. 278.23
c. 257.44
d. 290.85
Determine the location of the plastic centroid of the section from y-axis, in mm.
a. 289.48
b. 290.85
c. 304.60
d. 278.23
Calculate the percentage loss in strength of the column based on its axial capacity without embedment.
a. 7.99
b. 46.69
c. 2.30
d. 8.69
REINFORCED CONCRETE
CIVIL ENGINEERING PRACTICE PROBLEMS
SITUATION 7
CIVIL ENGINEERING FINAL EXAMINATION
Q8-4
REINFORCED CONCRETE
SITUATION 10
Refer to figure RC-FE007.
Given : fc’ = 27.6 MPa and fy = 413.6 MPa.
b1 = 125 mm;
b2 = 650 mm;
Bottom bars: 4 – 36 mm ɸ bars
Problem 28
Problem 29
Problem 30
t = 125 mm;
Calculate the depth of compression block, in mm.
a. 178.06
b. 93.83
h1 = 300 mm;
c. 22.06
Compute the ultimate moment capacity of the beam, in kN.m.
a. 544
b. 641
c. 712
S = 75 mm
d. 79.76
d. 408
Determine the safe service uniform live load in addition to its own weight, in kN/m. Assume that the beam
is having a simple span of 8 m.
a. 46.07
b. 80.06
c. 74.77
d. 42.73
SITUATION 11
Reinforced concrete tied columns are to support the fences of San Carlos Seminary located in Mabolo, Cebu City. The
columns are typical having dimensions of 250 mm x 250 mm, height of 3 m and reinforced with 4 – 16 mm φ vertical bars.
Given:
fc’ = 21 MPa;
fy = 415 MPa
Weight of concrete = 23.54 kN/m3
Clear cover = 40 mm;
main bar = 16 mm φ;
lateral ties = 10 mm φ
Problem 31
Calculate the ultimate axial capacity of the column at e = 0, in kN.
a. 1,435.03
b. 932.77
c. 1,148.03
d. 746.22
Problem 32
After 40 years some columns lean at an angle of 15º from the vertical because of the unstable soil
foundations. Calculate the actual nominal bending moment produced at the base, in kN.m.
a. 3.16
b. 5.30
c. 1.71
d. 2.06
Problem 33
Determine the nominal moment capacity of the column, in kN.m.
a. 50.45
b. 31.87
c. 36.05
d. 53.80
SITUATION 12
The figure shown in Fig. RC-FEQ008 is a floor framing plan of a reinforced concrete building.
All beams are 300 mm x 600 mm.
Slab thickness = 100 mm;
Super imposed dead load = 3.6 kPa;
Live load = 4.0 kPa
Concrete unit weight = 24 kN/m3
Columns at E and H are deleted thus girder BEHK alone supports beam DEF at E and beam GHI at H.
Dimensions are:
S1 = 2.5 m
S2 = 2.5 m
S3 = 2.5 m
S4 = 6.0 m
S5 = 6.0 m
Problem 34
Calculate the uniformly distributed service dead load at beam DEF, in kN/m.
a. 22.32
b. 26.04
c. 18.60
d. 17.00
Problem 35
Problem 36
Calculate the uniformly service live load at beam DEF, in kN/m.
a. 17.00
b. 10.00
c. 16.00
d. 14.40
Calculate the total ultimate load (in kN) concentrated at E induced by beam DEF using the tributary area
method.
a. 115
b. 145
c. 86
d. 230
SITUATION 13
A rectangular concrete beam having a width of 450 mm has a total depth of 575 mm. It is reinforced for tension having a
steel area of 3200 mm2 and steel area for compression equal to 900 mm2. The compression bars are placed at a distance of
62.5 mm from the top of the beam while tension bars are placed 75 mm from the bottom of the beam.
Given: fc’ = 21 MPa and fy = 345 MPa.
Problem 37
Which of the following gives the location of the neutral axis from the extreme compression fiber, in mm?
a. 122.84
b. 104.42
c. 137.44
d. 161.70
Problem 38
Which of the following gives the actual stress of the compression bars, in MPa?
a. 345.0
b. 294.74
c. 1,842.11
d. 1,255.33
Q1-5
CIVIL ENGINEERING PRACTICE PROBLEMS
Problem 39
Which of the following gives the ultimate moment capacity of the beam, in kN.m?
a. 491.63
b. 476.13
c. 442.57
d. 428.52
The figure shown in Fig. RC-FE009 is a floor framing plan of a reinforced concrete building.
bw x h (below the slab) = 300 mm x 350 mm;
Slab thickness, t f = 100 mm
Super imposed dead load = 2.4 kPa
Live load = 3.8 kPa
Concrete: fc’=20.7 MPa
Steel: fy= 414 MPa
Concrete unit weight = 24 kN/m3
Clear cover to stirrups = 50 mm
Stirrups = 10 mm ɸ
Column = 300 mm x 300 mm
S1 = S2 = S3 = 3.0 m
S4 = S5 = S6 = 8.0 m
Problem 40
Compute the total ultimate load to design beam I-J-K-L, in kN/m.
a. 37.10
b. 36.86
c. 41.81
REINFORCED CONCRETE
SITUATION 14
d. 28.32
Problem 41
If the design ultimate load, Wu = 45 kN/m, find the negative moment at the end of K of span JK, in kN.m.
a. 266.81
b. 166.75
c. 242.55
d. 190.58
Problem 42
How many 25 mm ɸ bars are required at the end K of span KL if the design ultimate load, Wu = 50 kN/m?
a. 6
b. 7
c. 8
d. 4
SITUATION 15
Refer to Fig. RC-FE014. Use ACI Moment Coefficient as shown on section 408.4.
From the given floor plan, the following data are obtained:
Dimensions:
Ultimate Load, Wu = 20 kN/m
Beam b x h = 300 mm x 400 mm
fy(main bar) = 275MPa
Clear cover to slab reinforcement = 20 mm
fy(temp. bar) = 275 MPa
Slab reinforcement = 12 mm ϕ
fc’ = 20.7 MPa
Slab thickness = 90 mm
S1 = S2 = 2.8 m;
S3 = 6.0 m
Problem 43
What is the spacing of reinforcement (mm) required for the moment at the interior beam support BE?
a. 210
b. 200
c. 150
d. 120
Problem 44
What is the spacing of reinforcement (mm) required for the positive moment at the span bounded by BEFC?
a. 150
b. 200
c. 170
d. 180
Problem 45
Determine the maximum spacing (mm) of the 12 mm ϕ bars. (Hint: Check for spacing for crack control.)
a. 250
b. 270
c. 300
d. 450
SITUATION 7
A deck of slab of the bridge in a section over intermediate supports as shown in RC-FE002 is prestressed to limit cracking
and deflection. Unit weight of concrete is 24 kN/m3. The total prestressing force is 45,500 kN. Assume that there is a loss
of prestress of 15% at service loads where the uniform live load is 240 kN/m. Assuming intermediate supports are fixed and
having uniform clear distances of 30 m.
Use:
bf = 11.0 m;
h = 2.75 m;
t1 = 250 mm;
t2 = 450 mm
Ixx = 8.3 m4;
A = 8.0 m2;
y = 1.025 m;
e = 575 mm
Problem 46
Determine the stress on top fiber due to prestress, in MPa.
a. -7.58
b. -8.92
c. -11.12
d. -9.46
Problem 47
Calculate the total stress in the bottom fiber at fixed end due to prestress and service loads, in MPa.
a. -6.98
b. -4.21
c. -4.25
d. -6.95
Problem 48
Obtain the eccentricity in order that the total stress on the top fiber at the fixed will be -6 MPa, in mm.
a. 593.70
b. 1,653.92
c. 505.39
d. 1,081.80
Problem 49
It is the point through which the resultant of the resistance to the applied lateral force acts.
a. shear wall
b. center of mass
c. eccentricity
d. center of rigidity
Problem 50
A standard hook has a ___ degree bend plus 12db (bar diameters) extension at the free end of bar.
a. 180
b. 90
c. 45
d. 30
CIVIL ENGINEERING FINAL EXAMINATION
PL
Q8-6
a
REINFORCED CONCRETE
Service loads
yt
b
N.A.
e
d
yb
y3
L
Fig. RC-FE003
Fig. RC-FE001
bf
t1 t
2
e
N.A.
x
h
x
y
PC
Fig. RC-FE002
𝒚
db
b
x
ds
D
h
Fig. RC-FE006
Fig. RC-FE005
Fig. RC-FE007
t
h1
S
S
b1
b2
b
b1
h
x
Q1-7
CIVIL ENGINEERING PRACTICE PROBLEMS
beams
B
C
A
S2
S3
bf
E
D
G
H
J
K
I
S1
S2
S3
h
S5
FRAMING PLAN
B
As’
As
bw
AT SUPPORTS
bw
AT MIDSPAN
Fig. RC-FE008
C
D
F
G
H
I
J
K
L
M
N
O
P
S5
TYPICAL BEAM SECTION
tf
As’
h
As
S6
FRAMING PLAN
As’
h
E
S4
tf
As
L
S4
A
tf
F
bf
bw
BEAM SECTION
Fig. RC-FE009
y
Embedded pipes
4-d2
b1
b2
6-d1
h1
h2
Fig. RC-FE010
x
REINFORCED CONCRETE
S1
CIVIL ENGINEERING FINAL EXAMINATION
Vuy
REINFORCED CONCRETE
Line 1
Q8-8
PC
db
b
x
ds
h
Fig. RC-FE011
D
A
tf
S1
B
As’
E
h’
S2
C
As
F
S3
FRAMING PLAN
Fig. RC-FE014
bw
BEAM SECTION
410.7.4 MAXIMUM SPACING FOR CRACK CONTROL
The spacing s of reinforcement closest to a surface in tension shall not exceed that given by:
 280 
s  380 
  2.5cc
 fs 
 280 
 , where cc is the least distance from the surface of reinforcement or reinforcing steel to the
 fs 
but not greater than 300 
tension face. If there is only one bar or wire nearest to the extreme tension face, s used is the width of the extreme tension
face.
Calculated stress in reinforcement fs in MPa closest to the tension face shall be computed based on the unfactored moment.
It shall be permitted to take fs as 2/3 of specified yield strength fy.
401.01.01 Effective span for simply supported and continuous beams are as follows:
1) Simply supported beams
The effective span of a simply supported beam shall be taken as the smaller of the distance between the centers of bearing,
or the clear distance between supports plus the effective depth.
Q1-9
CIVIL ENGINEERING PRACTICE PROBLEMS
a) For end span with one fixed and the other continuous or for intermediate spans, the effective span shall be the clear span
between supports.
b) For end span with one end free and other continuous, the effective span shall be equal to the clear span plus half the
effective depth of the beam or the clear span plus half the width of the discontinuous support, whichever is less.
3) Monolithic frames
In case of monolithic frames, the effective span shall be equal to the distance between intersections of the center lines of the
connecting members.
4) Cantilever beams
The effective length of the cantilever shall be taken as its length to the face of the supports plus half its effective depth
except where it forms the end of a continuous beam where the length to the center of the support shall be used.
408.4 Method of Analysis
408.4.3 As an alternate to frame analysis, the following approximate moments and shears shall to be used in design of
continuous beams and one-way slabs (slabs reinforced to resist flexural stresses in only one direction), provided:
1. There are two or more spans.
2. Spans are approximately equal, with the larger of two adjacent spans not greater than the shorter by more than 20
percent.
3. Loads are uniformly distributed.
4. Unfactored live load, L does not exceed three times Unfactored dead load, D.
5. Members are prismatic.
For calculating negative moments, ln is taken as the average of the adjacent clear spans lengths.
POSITIVE MOMENT
End Spans
wu ln 2
11
wl2
Discontinuous end integral with support…………………………………………………………..  u n
14
wl2
Interior Spans……………………………………………………………..……………………………..  u n
16
Discontinuous end unrestrained………………………………………………………………….. 
Negative MOMENT
At exterior face of first interior supports
wu ln 2
a) Two spans…………………...………………………………………………………………….. 
9
wl2
b) More than two spans……………….…………………………………………………………..  u n
10
wl2
c) At other faces of interior supports….…………………………………………………………..  u n
11
d) At face of all supports for: slabs with spans not exceeding 3 m ; and beams where ratio of sum of column
stiffness to beam stiffness exceeds eight at each end of the span …………..……….. 
wu ln 2
12
REINFORCED CONCRETE
2) Continuous beams
If the width of support is less than 1/12 of the clear span, the effective span shall be taken as stated (1) above. If the supports
are wider than 1/12 of the clear span or 600 mm, whichever is less, the effective span shall be as follows:
REINFORCED CONCRETE
CIVIL ENGINEERING FINAL EXAMINATION
At interior face of exterior support for members built integrally with supports:
Q8-10
wu ln 2
24
wl2
b) Where support is a column………….…………………………………………………………..  u n
16
a) Where support is a spandrel beam……..……………………………………………………….. 
shear
1.15wu ln
2
wl
b) At face of all other supports………….………………………………………………………….. u n
2
a) At face of first interior support..………………………………………………………………..
Limits for compression reinforcement
A) Minimum ratio of spiral reinforcement
 Ag
 f'
 1 c
 Ac
 f yh
Equation 410.10-1
f 'c
f yh
Equation 410.10-2
a)  s  0.45 
b)  s  0.12
Note: whichever is bigger
where:
Ag = gross area of column
Ach = core area to outside of spirals
fyh = specified yield strength
B) Minimum area of rectangular hoop reinforcement in (tied) column.
 Ag
 f'
 1 c
 Ac
 f yh
a) Ash  0.3Shc 
b) Ash  0.09 Shc
f 'c
f yh
Equation 410.10-3
Equation 410.10-4
where:
Ach = the cross sectional area of the column core, measured out to out of the transverse reinforcement
S = spacing of transverse reinforcement
hc = cross-sectional dimension of the column core, measured center to center of the confining reinforcement
fyh = specified yield strength of transverse reinforcement
C) Maximum spacing of transverse reinforcement (tied column).
a) ¼ of minimum dimension
b) 6db or 150 mm
 350  hx 

3


c) The distance, So  100  
where:
hx = maximum horizontal spacing between hoops or cross tie legs on all faces of the column, maximum
value of 350 mm
Note: So shall not less than 100 mm nor more than 150 mm