CHAPTER 1: INTRODUCTION TO REINFORCED CONCRETE (pg.
16)
SUPPLEMENTARY PROBLEMS:
PROBLEM 1.1:
Draw the details of the most efficient beam in terms of flexure if the beam is cast-in-place, non-
prestressed and not exposed to weather or in contact with the ground. Beam section:
250mmx360mm rectangular beam reinforced with 10mm Φ stirrups and 6 pcs- 16mm Φ
longitudinal bottom bars.
PROBLEM 1.2:
Draw the details of the most efficient beam in terms of flexure if the beam is cast-in-place, non-
prestressed and not exposed to weather or in contact with the ground. Beam section: 300mm x
450mm rectangular beam reinforced with 12mm Φ stirrups and 6pcs-32mm Φ longitudinal top
bars.
PROBLEM 1.3:
Draw the details of the most efficient beam in terms of flexure if the beam is cast-in-place, non-
prestressed and not exposed to weather or in contact with the ground. Beam section 280mm x
480mm rectangular beam reinforced with 10mm Φ stirrups and As=3122mm^2. Bending
moment is positive. Use 20mm Φ longitudinal bars.
PROBLEM 1.4:
Draw the details of the most efficient beam in terms of flexure if the beam is cast-in-place, non-
prestressed and exposed to weather or in contact with the ground. Beam section: 400mm x
600mm rectangular beam reinforced with 12mm Φ and stirrups and 12pcs-28mm Φ longitudinal
bottom bars.
PROBLEM 1.5:
Draw the details of the most efficient beam in terms of flexure if the beam is cast-in-place, non-
prestressed and exposed to weather or in contact with the ground. Beam section: 400mm x
600mm rectangular beam reinforced with 12mm Φ stirrups and 6pcs Φ-25mm longitudinal
bottom bars. Use dagg=20mm.
PROBLEM 1.6:
Draw the details of the most efficient beam in terms of flexure if the beam is cast-in-place, non-
prestressed and exposed to weather or in contact with the ground. Beam section: 300mm x
500mm rectangular beam reinforced with 12mm Φ and 11pcs-20mm Φ longitudinal bars.
CHAPTER 2: ANALYSIS AND DESIGN OF BEAMS FOR FLEXURE (STRENGTH
DESIGN METHOD pg.49)
SUPPLEMENTARY PROBLEMS:
PROBLEM 2.1
A rectangular beam has b=300mm and effective depth of 490mm. Concrete compressive strength
f’c=27.6MPa and steel yield strength fy=276MPa. Calculate the required tension steel area if the
factored moment Mu=100kNm
Ans: As=851.13 mm^2
PROBLEM 2.2:
A reinforced concrete rectangular beam has a width of 300mm and an effective depth of 500mm.
The beam is reinforced with 6-25mm diameter tension bars. Steel yield strength fy=415MPa and
concrete strength f’c=28MPa.
a. What is the balanced steel ratio
b. What is the maximum steel area for singly reinforced
c. What is the ultimate moment capacity of the beam
Answers:
a. Pb=0.02882
b. Asmax= 3133.735mm^2
c. Mu=432.061 kNm
PROBLEM 2.3:
Calculate the ultimate moment capacity of the rectangular beam with b=300mm, d-500mm,
As=9-28mm. Assume f’c=34MPa. Use the provisions of NSCP 2015.
Ans: Mu=522.463 kNm
PROBLEM 2.4:
Determine the required tension area of a rectangular beam with width b=320mm and effective
depth d=520mm. The beam is subjected to dead load moment Md=180 kNm and live load
moment Ml= 167 kNm. Assume f’c=27 MPa. Use the provisions of NSCP 2015.
Ans: As=3777.35mm^2
PROBLEM 2.5:
A reinforced concrete beam has a width of 300mm and an effective depth to tension bars of
600mm. Compression if needed will be placed as a depth of 60mm below the top. If f’c=30 MPa
and fy= 414 MPa, determine the tension steel area if the beam is to resist Mu=650 kNm.
Ans: As=3441.600mm^2
PROBLEM 2.6:
A reinforced concrete rectangular beam with b= 400mm and d=730mm is reinforced for tension
only with 6-25mm diameter bars. If f’c=21MPa and fy=400MPa, determine the following:
a. The nominal moment capacity
b. The ultimate moment capacity
Answers:
A. Mn=751.038 kNm
B. Mu=675.935 kNm
PROBLEM 2.7:
A reinforced concrete rectangular beam with b=400mm and d=720mm is reinforced for tension
only with 6-25mm diameter bars. If f’c=21 MPa and fy=400MPa, determine the following:
a. The nominal moment capacity of the beam
b. The ultimate moment capacity of the beam
Answers:
Ans: Mn=751.039 kNm
Ans: Mu=675.935 kNm
PROBLEM 2.8:
A reinforced concrete rectangular beam has a width of 300mm and effective depth of 500mm.
The beam is reinforced with 6-25mm diameter bars. Steel yield strength fy=415MPa and
concrete strength f’c=28MPa.
a. What is the maximum steel area for singly reinforced.
b. What is the nominal moment capacity of the beam.
c. What is the ultimate capacity of the beam,
Answers:
a. Asmax=313.500 mm^2
b. 506.519 kNm
c. Mu=432.061 kNm
PROBLEM 2.9:
Calculate the ultimate moment capacity of the rectangular beam with b=350mm, d=540mm,
As=5-25mm. Assume f’c=24MPa, fy=345MPa. Use NSCP
Ans: Mu=366.335 kNm
PROBLEM 2.10:
A rectangular beam has the following properties: width b=250mm, effective depth d=460mm.
The beam is simply supported over a span of 6m and carries a uniform dead load of 680N/m
including its own weight. The beam is reinforced for tension only with As=3-25mm. Calculate
the uniform live load that the beam can carry. Use fy=276.6MPa and f’c=20.7MPa.
Ans: LL=20.547 kNm
CHAPTER 3: ANALYSIS AND DESIGN OF T-BEAMS AND DOUBLY REINFORCED
BEAMS (pg.100)
SUPPLEMENTARY PROBLEMS:
PROBLEM 3.1:
A 300mm wide rectangular beam has an effective depth d=460mm. The beam will be designed
to carry a service load of 230kNm and a service live load of 190 kNm. Compressive
reinforcement, if necessary, will have its centroid 70mm from extreme concrete fiber. Determine
the required steel area. Use fy=415MPa and f’c=30MPa. Use NSCP 2015
Ans: As=4493.656mm^2, A’s=1561.040mm^2
PROBLEM 3.2:
A rectangular beam has the following properties: width b=350mm, effective depth d=600mm.
Tension bars As=4-36mm, compression bars A’s=2-28mm, d’=60mm. Determine the design
strength of the beam. Use fy=345MPa and f’c=20.7MPa. Use NSCP 2015.
Ans: Mu=665.429kNm
PROBLEM 3.3:
A rectangular beam has the following properties: width b=320mm, effective depth d=578mm.
Tension bars As=10-28mm, compression bars A’s=2-25mm, d’=42.5mm. Determine the design
strength of the beam. Use fy=415MPa and f’c=21MPa. Use NSCP 2015.
Ans: Mu=627.169kNm
PROBLEM 3.4:
A rectangular beam has the following properties: width b=300mm, effective depth d=450mm.
Tension bars As=6-32mm, compression bars A’s=2-28mm, d’=65mm. Determine the design
strength of thebeam. Use fy=345MPa and f’c=34.5MPa. Use NSCP 2015.
Ans: Mu=556.159kNm
PROBLEM 3.5:
A 350mm x 650mm rectangular beam has an effective depth d=58mm. The beam will be
subjected to carry a maximum service dead load of 380 kNm. Tension bars As=12-28mm,
compression bars A’s=3-25mm, d’=42.5mm. Determine the safe service live load moment for
this beam. Use fy=415MPa and f’c=23MPa. Use NSCP 2015
Ans: Ml=208.951kNm
PROBLEM 3,6:
Calculate the design flexural strength of the T-beam as shown. Concrete strength f’c=21MPa.
Steel strength fy=415MPa. If the beam is reinforced with As=6-28mm and A’s=2-28mm. Use
NSCP 2015
PROBLEM 3.7:
The T-beam shown has an effective depth of d = 412.5mm the beam will be designed to carry an
ultimate moment capacity of 600 kNm. Compression reinforcement, if necessary, will have its
centroid 40mm from the extreme concrete fiber. Determine the required steel area using f_{y} =
415MPa and tilde J_{c}' = 21MPa Use NSCP 2015.
Ans: A_{s} = 5002.946m * m ^ 2 A^ prime s = 913.343m * m ^ 2
CHAPTER 4: SERVICEABILTY REQUIREMENTS(pg.118)
SUPPLEMENTARY PROBLEMS:
PROBLEM 4.1:
Determine moment of inertia to be used for the rectangular beam shown. Use f = 28 MPa. f_{y}
= 415MPa and n = 8 Unfactored maximum moment M_{a} = 240kNm
ANS: 4394811772 mm³
PROBLEM 4.2:
Given the properties of a T-beam as shown, determine the cracked section moment of inertia.
Assume f_{c}' = 28 MPa, f_{y} = 414 MPa and n = 8
ANS: 4119611937 mm²
PROBLEM 4.3:
A reinforced concrete beam having a span of 6m carries a total dead load of 12kN/m including
its own weight and a live load of 16kN/m. The beam is reinforced for tension only. Material
strengths are fe 28 MPa and fy = 400 MPa. Assume effective moment of inertia I = 1922x106
mm^2
a Calculate the instantaneous deflection for DL + LL..
Ans: 9.885 mm
b. Calculate the initial deflection assuming 30% of the live load is sustained
Ans: 5.931mm
C. Calculate the deflection of the beam assuming 30% of the live load is continuously applied for
5 years.
Ans: 17.481 mm
d. Check the adequacy of the member stiffness.
Ans. Not Adequate
CHAPTER 5: SHEAR IN BEAMS (pg.139)
SUPPLEMENTARY PROBLEMS:
PROBLEM 5.1: A rectangular beam is to be designed to carry a factored shear force V₁ =
130kN. Assume f = 28MPa, fyt = 275MPa, and width of beam bw = 400mm. Using NSCP 2015,
-
a. Compute the minimum effective depth of a beam with no shear reinforcement is required.
b. Compute the effective depth of the beam if a minimum amount of shear reinforcement is
needed.
C. Compute the required spacing of minimum shear reinforcement using 10mmØ bar.
Ans:
a. 982.708mm
b. 491.354mm
c. 245.677mm
PROBLEM 5.2:
A rectangular beam has the following properties: b_{w} = 350mm d = 550mm f_{c}' = 21MPa
diameter of stirrup = 10mm, f yt =275MPa. Determine the required spacing vertical U-stirrup
when the required shear strength V_{u} is 150kN,. Use NSCP 2015.
Ans: 275 mm
PROBLEM 5.3:
A simply supported beam 7m long supports a uniformly distributed factored load equal to 130
kN/m and a concentrated factored load equal to 100 kN acting at the midspan. If b_{w} =
300mm , d = 450mm, f_{c}' = 24MPa and f_{y} = 276MPa design the shear reinforcements. Use
NSCP 2015 provisions.
Chapter 6: TORSION
PROBLEM 6.1: (Pg. 153)
A 300𝑚𝑚 𝑥 500𝑚𝑚 cantilever beam has a span of 4.0𝑚, carries a uniformly distributed factored
load of 20𝑘𝑁/𝑚 applied 200𝑚𝑚 away from the centroidal axis of the member. The beam has an
effective depth of 425𝑚𝑚. Concrete strength 𝑓𝑐′ = 20.7𝑀𝑃𝑎 and steel yield strength for
longitudinal bars is 𝑓𝑦 = 415𝑀𝑃𝑎. Use 12𝑚𝑚 stirrups with 𝑓𝑦𝑡 = 275𝑀𝑃𝑎.
a. Determine the spacing of stirrups required for shear.
b. Determine the spacing of stirrups required for torsion.
c. Determine the area of longitudinal bars required for torsion.
PROBLEM 6.2: (Pg. 153)
A 300𝑚𝑚 𝑥 600𝑚𝑚 reinforced concrete beam has an effective depth of 525𝑚𝑚. Longitudinal
reinforcement to resist torsion is 28𝑚𝑚Ø arranged as shown. Concrete strength 𝑓𝑐′ = 24𝑀𝑃𝑎 and
steel yield strength for longitudinal bars is 𝑓𝑦 = 415𝑀𝑃𝑎. 12𝑚𝑚 stirrups with 𝑓𝑦𝑡 = 415𝑀𝑃𝑎.
Spacing of vertical stirrups is 100𝑚𝑚.
a. Compute the factored torsional moment of the section where torsion can be neglected.
b. Check the adequacy of the section if a factored torsional moment of 40𝑘𝑁𝑚 is applied to
the beam.
c. Determine the design torsional strength of the beam section.
Chapter 7: SHORT COLUMNS
PROBLEM 7.1: (Pg. 180)
A reinforced concrete tied column carries an axial dead load of 600𝑘𝑁 and a live load of 800𝑘𝑁.
Assume 𝑓𝑐′ = 27.6𝑀𝑃𝑎 and 𝑓𝑦 = 414𝑀𝑃𝑎.
a. Determine the smallest dimension of the column section.
𝐴𝑛𝑠: 𝑏 = 265.159 𝑚𝑚
b. Which of the following gives the number of 25𝑚𝑚Ø bars?
𝐴𝑛𝑠: 12 𝑝𝑐𝑠
PROBLEM 7.2: (Pg. 180)
To comply with architectural requirements, a column in a non-sway frame is of T-section as
shown. The longitudinal reinforcement consists of 6 – 20𝑚𝑚Ø bars in the flange and 3 – 28𝑚𝑚Ø
bars in the web with 10𝑚𝑚Ø lateral ties. Neglect the concrete area displaced by the steel. 𝑓𝑐′ =
27.5𝑀𝑃𝑎 and 𝑓𝑦 = 415𝑀𝑃𝑎. Clear concrete cover is 40𝑚𝑚.
a. Determine the location of the geometric centroid of the section measured from the x and
y-axes.
𝐴𝑛𝑠: 𝑥̅ = 248.529 𝑚𝑚, 𝑦̅ = 0
b. Determine the location of the plastic centroid of the section measured from the x and y-
axes. For all bars use 𝑓𝑠 = 𝑓𝑦 .
𝐴𝑛𝑠: 𝑥̅ = 262.751 𝑚𝑚, 𝑦̅ = 0.
c. Determine the bending moment 𝑀𝑢 induced by a factored load 𝑃𝑢 = 2800 𝑘𝑁 acting along
the x-axis at 400𝑚𝑚 from y-axis.
𝐴𝑛𝑠: 𝑀𝑢 = 384.297 𝑘𝑁𝑚
6 − 20𝑚𝑚Ø bars in compression
3 − 28𝑚𝑚Ø bars in tension
10𝑚𝑚Ø lateral ties
PROBLEM 7.3: (Pg. 181)
The corner column shown is reinforced with 12 – 20𝑚𝑚Ø bars, 𝑓𝑦 = 415 𝑀𝑃𝑎 and 𝑓𝑐′ =
21 𝑀𝑃𝑎.
a. Determine the location of the geometric centroid of the section measured from the x and
y-axes.
𝐴𝑛𝑠: 𝑥̅ = 258.333 𝑚𝑚, 𝑦̅ = 141.667 𝑚𝑚
b. Determine the location of the plastic centroid of the section measured from the x and y-
axes. For all bars use 𝑓𝑠 = 𝑓𝑦 .
𝐴𝑛𝑠: 𝑥̅ = 252.374 𝑚𝑚, 𝑦̅ = 146.136 𝑚𝑚
c. If the factored axial load on the column is 3000 𝑘𝑁 and is applied 350𝑚𝑚 from the y-axis
and 180𝑚𝑚 from x-axis, what is the factored moment on the column about the plastic
centroid?
𝐴𝑛𝑠: 𝑀𝑢𝑥 = 292.878 𝑘𝑁𝑚, 𝑀𝑢𝑦 = 101.592 𝑘𝑁𝑚
PROBLEM 7.4: (Pg. 181)
The reinforced concrete column shown is reinforced with 8 − 25𝑚𝑚Ø bars with 𝑓𝑦 = 415 𝑀𝑃𝑎
and 𝑓𝑐′ = 27 𝑀𝑃𝑎.
a. Determine the nominal load 𝑃𝑛 when 𝑒 = 150𝑚𝑚
𝐴𝑛𝑠: 𝑃𝑛 = 2129.483 𝑘𝑁
b. Determine the nominal load 𝑃𝑛 when 𝑒 = 350𝑚𝑚
𝐴𝑛𝑠: 𝑃𝑛 = 781.332 𝑘𝑁
CHAPTER 8: LONG/SLENDER COLUMNS
PROBLEM 8.1: (Pg. 194)
The tied column is to be used in a braced frame against sidesway. It is subjected to a factored axial
load 𝑃𝑢 = 530 𝑘𝑁 The column is bent in single curvature about the y-axis with an unsupported
length of 𝐿𝑢 = 4.9𝑚. The factored moment at the top is 110 𝑘𝑁 and the bottom is 120 𝑘𝑁.
Assume 𝑘 = 1.0. Use 𝑓𝑐′ = 27.6 𝑀𝑃𝑎 and 𝑓𝑦 = 415 𝑀𝑃𝑎. Assume factored dead axial load 𝑃𝑑 =
180 𝑘𝑁.
Given:
0.4𝐸𝑐 𝐼𝑔
(𝐸𝐼 )𝑒𝑓𝑓 =
1 + 𝛽𝑑𝑛𝑠
𝐸𝑐 = 4700√𝑓𝑐′
a. Determine the critical load using Euler’s Formula
𝐴𝑛𝑠: 𝑃𝑐 = 2045.121 𝑘𝑁
b. Determine the moment magnification factor
𝐴𝑛𝑠: 𝛿 = 1.478
c. Determine the equivalent eccentricity of the column section
𝐴𝑛𝑠: 𝑒 = 335 𝑚𝑚
PROBLEM 8.2: (Pg. 195)
The tied column with an unsupported length 𝐿𝑢 = 7.5 𝑚. is to be used in a braced frame against
sidesway is subjected to a service axial load and service moment loads as shown. The column is
bent in single curvature about the y-axis. Assume 𝑘 = 1.0. Use 𝑓𝑐′ = 28 𝑀𝑃𝑎 and 𝑓𝑦 = 415 𝑀𝑃𝑎.
Given:
0.4𝐸𝑐 𝐼𝑔
(𝐸𝐼 )𝑒𝑓𝑓 =
1 + 𝛽𝑑𝑛𝑠
𝐸𝑐 = 4700√𝑓𝑐′
Determine the value of the magnified factored moment 𝑀𝑐 . Use NSCP 2015.
𝐴𝑛𝑠: 𝑀𝑐 = 667.368 𝑘𝑁𝑚
PROBLEM 8.3: (Pg. 195)
Repeat problem 8.2 if the column is bent in single curvature about x-axis. Assume 𝑘 = 1.0. Use
𝑓𝑐′ = 28 𝑀𝑃𝑎 and 𝑓𝑦 = 415 𝑀𝑃𝑎. Determine the value of the magnified factor moment 𝑀𝑐 . Use
NSCP 2015.
𝐴𝑛𝑠: 𝑀𝑐 = 870.012 𝑘𝑁𝑚
CHAPTER 9: SEISMIC DESIGN & DETAILING OF SPECIAL MOMENT FRAME
MEMBERS (NSCP 2015 SECTION 418)
PROBLEM 9.1: (Pg. 216)
The section of a column shown is reinforced with 10 − 28𝑚𝑚Ø bars with 𝑓𝑦 = 414 𝑀𝑃𝑎. The
ties are 12𝑚𝑚Ø with 𝑓𝑦𝑡 = 275 𝑀𝑃𝑎. Concrete strength 𝑓𝑐′ = 21 𝑀𝑃𝑎. The factored shear load
𝑉𝑢𝑦 = 450𝑘𝑁.
a. Calculate the required spacing of lateral ties for the factored shear load. The allowable
concrete shear stress is 0.88𝑀𝑃𝑎.
b. Calculate the maximum spacing of the transverse reinforcement.
c. Calculate the required spacing of the confining hoop reinforcement according with the
provisions for seismic design.
PROBLEM 9.2: (Pg. 216)
The section of a column shown is reinforced with 12 − 20𝑚𝑚Ø bars with 𝑓𝑦 = 414 𝑀𝑃𝑎. The
ties are 10𝑚𝑚Ø with 𝑓𝑦𝑡 = 275 𝑀𝑃𝑎. Concrete strength 𝑓𝑐′ = 21 𝑀𝑃𝑎. Determine the required
spacing of transverse reinforcement for seismic design.
PROBLEM 9.3: (Pg. 217)
The section of a column shown is reinforced with 28 − 32𝑚𝑚Ø bars with 𝑓𝑦 = 414 𝑀𝑃𝑎. The
loops and crossties are 16𝑚𝑚Ø with 𝑓𝑦𝑡 = 275 𝑀𝑃𝑎 and are spaced 110𝑚𝑚. Concrete strength
𝑓𝑐′ = 21 𝑀𝑃𝑎. Determine the following:
a. The maximum spacing of confinement reinforcement
b. The minimum cross-sectional area of confinement reinforcement parallel to short direction.
c. The minimum cross-sectional area of confinement reinforcement parallel to long direction.
CHAPTER 10: BOND, DEVELOPMENT LENGTH, HOOKS, AND SPLICING OF
REINFORCEMENT
PROBLEM 10.1: (Pg. 242)
A concrete cantilever beam is reinforced with 6 − 28𝑚𝑚Ø top bar uncoated with 𝑓𝑦 = 276 𝑀𝑃𝑎
and concrete compressive strength 𝑓𝑐′ = 28 𝑀𝑃𝑎. Assume side, top and bottom cover to be greater
the 60𝑚𝑚. Using NSCP 2015, determine the following:
a. The required development length if the bars are straight using NSCP Table 425.4.2.4.
𝐴𝑛𝑠: 𝐿𝑑 = 645.779 𝑚𝑚
b. The required development length if a 180° hook is used.
𝐴𝑛𝑠: 𝐿𝑑ℎ = 250.164 𝑚𝑚
c. The required development length if a 90° hook is used.
𝐴𝑛𝑠: 𝐿𝑑ℎ = 250.164 𝑚𝑚
PROBLEM 10.2: (Pg. 242)
A 3𝑚 wide wall footing supports a 300𝑚𝑚 wall. It is reinforced with 20𝑚𝑚Ø bars with concrete
covering of 75𝑚𝑚. If 𝑓𝑐′ = 20.7 𝑀𝑃𝑎 and 𝑓𝑦 = 414 𝑀𝑃𝑎,
a. Which of the following gives the available space for development.
𝐴𝑛𝑠: 1275 𝑚𝑚
b. Which of the following gives the required development length.
𝐴𝑛𝑠: 𝐿𝑑 = 866.614 𝑚𝑚
PROBLEM 10.3: (Pg. 242)
A rectangular beam is reinforced with 4 − 28𝑚𝑚Ø top bars uncoated to resist tensile forces. If
𝑓𝑐′ = 21 𝑀𝑃𝑎 and 𝑓𝑦 = 415 𝑀𝑃𝑎. Concrete cover is 40𝑚𝑚. Using 10𝑚𝑚Ø stirrups spaced at
200𝑚𝑚, determine the required development length if the bars have clear spacing of 30𝑚𝑚 using
a. NSCP Table 425.4.2.2
𝐴𝑛𝑠: 𝐿𝑑 = 2585.411 𝑚𝑚
b. NSCP Equation 425.4.2.3a with computed value of 𝐾𝑡𝑟
𝐴𝑛𝑠: 𝐿𝑑 = 3036.197 𝑚𝑚
c. NSCP Equation 425.4.2.3a with 𝐾𝑡𝑟 = 0
𝐴𝑛𝑠: 𝐿𝑑 = 3856.791 𝑚𝑚
CHAPTER 11: ANALYSIS AND DESIGN OF ONE-WAY SLABS
PROBLEM 11.1: (Pg. 259)
Design a simply supported one-way solid slab with a span of 4𝑚 subjected to service live load of
3𝑘𝑃𝑎. Assume 𝑓𝑐′ = 25 𝑀𝑃𝑎 and 𝑓𝑦 = 400 𝑀𝑃𝑎. Use 10𝑚𝑚Ø for main and temperature bars.
Use NSCP 2015.
PROBLEM 11.2: (Pg. 259)
A reinforced concrete slab is built integrally with its supports and consists of two equal spans, each
with a clear span of 3𝑚. The service live load is 4.8𝑘𝑁/𝑚2 . Assume 𝑓𝑐′ = 28 𝑀𝑃𝑎 and 𝑓𝑦 =
420 𝑀𝑃𝑎 for all bars. Unit weight of concrete is 𝛾𝑐 = 23.5𝑘𝑁/𝑚3 . The slab is not exposed to
earth or weather. Design the slab following provisions of NSCP 2015. Use 12𝑚𝑚Ø for all bars.
PROBLEM 11.3: (Pg. 259)
A reinforced concrete slab consists of two equal spans, each with a clear span of 4.5𝑚. The service
live load is 4.8 𝑘𝑃𝑎. Assume 𝑓𝑐′ = 27.6 𝑀𝑃𝑎 and 𝑓𝑦 = 415 𝑀𝑃𝑎 for all bars. Unit weight of
concrete is 𝛾𝑐 = 23.5𝑘𝑁/𝑚3 . The slab is not exposed to earth or weather. Design the slab
following provisions of NSCP 2015. Use 12𝑚𝑚Ø for all bars.
PROBLEM 11.4: (Pg. 259)
Design a one-way slab for the inside of the building having a simple span of 3𝑚. The slabs is to
carry a uniform live load of 3 𝑘𝑃𝑎. Assume 𝑓𝑐′ = 27.6 𝑀𝑃𝑎 and 𝑓𝑦 = 276 𝑀𝑃𝑎 for all bars. Unit
weight of concrete is 𝛾𝑐 = 23.5𝑘𝑁/𝑚3 . The slab is not exposed to earth or weather. Use 12𝑚𝑚Ø
for main bars and 10𝑚𝑚Ø for temperature bars.
CHAPTER 12: ANALYSIS AND DESIGN OF TWO-WAY SLABS
PROBLEM 12.1: (Pg. 315)
A conventional floor framing plan of a commercial building is shown in the figure has been
assumed to have a slab thickness of 175𝑚𝑚. Use 𝑓𝑦 = 414 𝑀𝑃𝑎 and 𝑓𝑐′ = 21 𝑀𝑃𝑎. Assume 𝐸𝑐
be the same for slab, beam, and column. Check the NSCP equation to determine if the slab
thickness is satisfactory for an interior panel.
𝐴𝑛𝑠: 𝛼𝑓𝑚 = 2.417 & ℎ𝑚𝑖𝑛 = 161.221𝑚𝑚
PROBLEM 12.2: (Pg. 315)
Design the slab (Panel C) assuming that the floor carries a uniform dead load of 1.5𝑘𝑁/𝑚2
excluding its own weight and a uniform live load of 4.8𝑘𝑁/𝑚2 . Use 12𝑚𝑚 main bars and 𝛾𝑐 =
23.5𝑘𝑁/𝑚3 .
