尊敬的 微信汇率:1円 ≈ 0.046089 元 支付宝汇率:1円 ≈ 0.04618元 [退出登录]
SlideShare a Scribd company logo
Reinforced Concrete Design
Compressive Strength of Concrete
• fcr is the average cylinder strength
• f’c compressive strength for design
• f’c ~2500 psi - 18,000 psi, typically 3000 - 6000 psi
• Ec estimated as:
where w = weight of concrete, lb/ft3
f’c in psi
E in psi
for normal weight concrete ~145 lb/ft3
E w fc c= 3 3 1 5.
'
E fc c= 5 7 0 0 0, '
Concrete Stress-Strain Curve
For short term loading. Over time concrete will creep and shrink.
Concrete Strain
Strain in concrete will be caused by loading, creep,
shrinkage, and temperature change.
For scale, consider a 20’ section of concrete,
f’c = 4000 psi, under a stress, fc = 1800 psi.
Determine the change in length.
Tensile Strength of Concrete
• Tensile strength of concrete is about
• ~300 – 600 psi
• Tensile strength of concrete is ignored in design
• Steel reinforcement is placed where tensile
stresses occur
Where do tensile stresses occur?
f c'
1 0
Tensile Stresses
Restrained shrinkage
slab on grade
shrinkage strain, ε = 0.0006
σ = εE = 0.0006 x 3600 ksi = 2.16 ksi
Flexural member
compression
tension
Reinforcing Steel
• Deformed steel reinforcing bars
• Welded wire fabric
• 7-strand wire (for pre-stressing)
Deformed Steel Reinforcing Bars
Rebar
• Grade 60 (most common in US)
• Sizes #3 → #18 (number indicates
diameter in ⅛ inch)
Welded Wire Fabric
Readily available fabrics
Designation:
longitudinal wire spacing x transverse wire spacing –
cross-sectional areas of longitudinal wire x transverse wires in
hundredths of in2
Stress-Strain Curve, Steel and Concrete
Reinforce Concrete Design
Two codes for reinforced concrete design:
• ACI 318 Building Code Requirements for
Structural Concrete
• AASHTO Specifications for Highway Bridges
We will design according to ACI 318 which is an
‘LRFD’ design. Load and resistance factors for
ACI 318 are given on page 7, notes.
Short Reinforced Concrete
Compression Members
• Short - slenderness does not need to be
considered – column will not buckle
• Only axial load
L
Cross-sectional Areas:
As = Area of steel
Ac = Area of concrete
Ag = Total area
Fs = stress in steel
Fc = stress in concrete
From Equilibrium:
P = Acfc + Asfs
P
L
P
If bond is maintained εs = εc
Short Concrete Columns
For ductile failure – must assure that steel
reinforcement will yield before concrete crushes.
– Strain in steel at yield ~0.002
– ε = 0.002 corresponds to max. stress in concrete.
– Concrete crushes at a strain ~ 0.003
Equilibrium at failure: P = AsFy +Acf’c
Reinforcement Ratio
• ρ = As/Ag
• ACI 318 limits on ρ for columns:
0.01≤ρ≤0.08 (practical ρmax = 0.06)
• Substitute ρ=As/Ag and Ag=As+Ac into
equilibrium equation:
P = Ag[ρfy +f’c(1- ρ)]
Short Concrete Columns
P = Ag[ρfy +f’c(1- ρ)]
Safety Factors
• Resistance factor, Ф = 0.65 (tied), Ф = 0.70 (spiral)
• When fc>0.85f’c, over time, concrete will collapse
• Stray moment factor for columns, K1
– K1=0.80 for tied reinforcement
– K1=0.85 for spiral reinforcement
ФPn = Ф K1 Ag[ρfy +0.85f’c(1- ρ)]
Short Column Design Equation
ФPn = Ф K1 Ag[ρfy +0.85f’c(1- ρ)]
for design, Pu ≤ ФPn








−
−
≥ c
g
u
cy
f
AK
P
ff
'85.0
)'85.0(
1
1φ
ρ
[ ])1('85.01 ρρφ −+
≥
cy
u
g
ffK
P
A
Transverse Reinforcement
Used to resist bulge of concrete and buckling of steel
Concrete Cover
Used to protect steel reinforcement and
provide bond between steel and concrete
Short Concrete Column Example
Design a short, interior, column for a service dead
load of 220 kips and a service live load of 243
kips. Consider both a circular and a square cross
section. Assume that this column will be the
prototype for a number of columns of the same
size to take advantage of the economy to be
achieved through repetition of formwork. Also
assume that this column will be the most heavily
loaded (“worst first”). Available materials are
concrete with f’c = 4 ksi and grade 60 steel.
Available Steel Reinforcing Bars
Design of Spiral Reinforcement
• Asp = cross sectional area of spiral bar
• Dcc = center to center diameter of spiral coil
• Acore = area of column core to outside of spiral coils
• Pitch = vertical distance center to center of coils
with the limit: 1” ≤ clear distance between coils ≤ 3”
)('45.0 coregc
yccsp
AAf
fDA
−
≤
π
Pitch of spiral
Reinforced Concrete Design (2)

More Related Content

What's hot

Design and Detailing of RC Deep beams as per IS 456-2000
Design and Detailing of RC Deep beams as per IS 456-2000Design and Detailing of RC Deep beams as per IS 456-2000
Design and Detailing of RC Deep beams as per IS 456-2000
VVIETCIVIL
 
CSI ETABS & SAFE MANUAL: Slab Analysis and Design to EC2
CSI ETABS & SAFE MANUAL: Slab Analysis and Design to EC2CSI ETABS & SAFE MANUAL: Slab Analysis and Design to EC2
CSI ETABS & SAFE MANUAL: Slab Analysis and Design to EC2
Eur Ing Valentinos Neophytou BEng (Hons), MSc, CEng MICE
 
Design of slender columns as per IS 456-2000
Design of slender columns as per IS 456-2000Design of slender columns as per IS 456-2000
Design of slender columns as per IS 456-2000
PraveenKumar Shanmugam
 
Repair and strengthening of reinforced concrete beam column joints
Repair and strengthening of reinforced concrete beam column jointsRepair and strengthening of reinforced concrete beam column joints
Repair and strengthening of reinforced concrete beam column joints
Pavan Kumar N
 
Design of floor slab
Design of floor slabDesign of floor slab
Design of floor slab
sathananthankartheep
 
Tower design-Chapter 2-pile caps design
Tower design-Chapter 2-pile caps designTower design-Chapter 2-pile caps design
Tower design-Chapter 2-pile caps design
Nada Zarrak
 
Steel building design worked example
Steel building design worked exampleSteel building design worked example
Steel building design worked example
Md. Shahadat Hossain
 
limit state method
limit state methodlimit state method
limit state method
illpa
 
Design of reinforced concrete beam
Design of reinforced concrete beamDesign of reinforced concrete beam
Design of reinforced concrete beam
civilengineeringfreedownload
 
Pile foundation design
Pile foundation designPile foundation design
Pile foundation design
UTHM
 
Shear wall and its design guidelines
Shear wall and its design guidelinesShear wall and its design guidelines
Shear wall and its design guidelines
Muhammad Zain Ul abdin
 
ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8
ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8 ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8
ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8
Eur Ing Valentinos Neophytou BEng (Hons), MSc, CEng MICE
 
Introduction to Capacity-based Seismic Design
Introduction to Capacity-based Seismic DesignIntroduction to Capacity-based Seismic Design
Introduction to Capacity-based Seismic Design
Fawad Najam
 
BIAXIAL COLUMN DESIGN
BIAXIAL COLUMN DESIGNBIAXIAL COLUMN DESIGN
BIAXIAL COLUMN DESIGN
shawon_sb
 
Final Report (Steel Bridge Design)
Final Report (Steel Bridge Design)Final Report (Steel Bridge Design)
Final Report (Steel Bridge Design)
Josia Tannos, EIT
 
Simplified design of reinforced concrete buildings
Simplified design of reinforced concrete buildings Simplified design of reinforced concrete buildings
Simplified design of reinforced concrete buildings
Sarmed Shukur
 
Construction process''column,beam,slab''
Construction process''column,beam,slab''Construction process''column,beam,slab''
Construction process''column,beam,slab''
Nabeel Rajpoot
 
Bs8110 design notes
Bs8110 design notesBs8110 design notes
Bs8110 design notes
Lawrence Omai
 
CE 72.52 - Lecture 8a - Retrofitting of RC Members
CE 72.52 - Lecture 8a - Retrofitting of RC MembersCE 72.52 - Lecture 8a - Retrofitting of RC Members
CE 72.52 - Lecture 8a - Retrofitting of RC Members
Fawad Najam
 
BALANCED CANTILEVER BRIDGE
BALANCED CANTILEVER BRIDGEBALANCED CANTILEVER BRIDGE
BALANCED CANTILEVER BRIDGE
srinivas cnu
 

What's hot (20)

Design and Detailing of RC Deep beams as per IS 456-2000
Design and Detailing of RC Deep beams as per IS 456-2000Design and Detailing of RC Deep beams as per IS 456-2000
Design and Detailing of RC Deep beams as per IS 456-2000
 
CSI ETABS & SAFE MANUAL: Slab Analysis and Design to EC2
CSI ETABS & SAFE MANUAL: Slab Analysis and Design to EC2CSI ETABS & SAFE MANUAL: Slab Analysis and Design to EC2
CSI ETABS & SAFE MANUAL: Slab Analysis and Design to EC2
 
Design of slender columns as per IS 456-2000
Design of slender columns as per IS 456-2000Design of slender columns as per IS 456-2000
Design of slender columns as per IS 456-2000
 
Repair and strengthening of reinforced concrete beam column joints
Repair and strengthening of reinforced concrete beam column jointsRepair and strengthening of reinforced concrete beam column joints
Repair and strengthening of reinforced concrete beam column joints
 
Design of floor slab
Design of floor slabDesign of floor slab
Design of floor slab
 
Tower design-Chapter 2-pile caps design
Tower design-Chapter 2-pile caps designTower design-Chapter 2-pile caps design
Tower design-Chapter 2-pile caps design
 
Steel building design worked example
Steel building design worked exampleSteel building design worked example
Steel building design worked example
 
limit state method
limit state methodlimit state method
limit state method
 
Design of reinforced concrete beam
Design of reinforced concrete beamDesign of reinforced concrete beam
Design of reinforced concrete beam
 
Pile foundation design
Pile foundation designPile foundation design
Pile foundation design
 
Shear wall and its design guidelines
Shear wall and its design guidelinesShear wall and its design guidelines
Shear wall and its design guidelines
 
ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8
ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8 ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8
ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8
 
Introduction to Capacity-based Seismic Design
Introduction to Capacity-based Seismic DesignIntroduction to Capacity-based Seismic Design
Introduction to Capacity-based Seismic Design
 
BIAXIAL COLUMN DESIGN
BIAXIAL COLUMN DESIGNBIAXIAL COLUMN DESIGN
BIAXIAL COLUMN DESIGN
 
Final Report (Steel Bridge Design)
Final Report (Steel Bridge Design)Final Report (Steel Bridge Design)
Final Report (Steel Bridge Design)
 
Simplified design of reinforced concrete buildings
Simplified design of reinforced concrete buildings Simplified design of reinforced concrete buildings
Simplified design of reinforced concrete buildings
 
Construction process''column,beam,slab''
Construction process''column,beam,slab''Construction process''column,beam,slab''
Construction process''column,beam,slab''
 
Bs8110 design notes
Bs8110 design notesBs8110 design notes
Bs8110 design notes
 
CE 72.52 - Lecture 8a - Retrofitting of RC Members
CE 72.52 - Lecture 8a - Retrofitting of RC MembersCE 72.52 - Lecture 8a - Retrofitting of RC Members
CE 72.52 - Lecture 8a - Retrofitting of RC Members
 
BALANCED CANTILEVER BRIDGE
BALANCED CANTILEVER BRIDGEBALANCED CANTILEVER BRIDGE
BALANCED CANTILEVER BRIDGE
 

Similar to Reinforced Concrete Design (2)

10 Reinforced concrete design
10   Reinforced concrete design10   Reinforced concrete design
10 Reinforced concrete design
MD RUKHASAR ALAM
 
Design of short columns using helical reinforcement
Design of short columns using helical reinforcementDesign of short columns using helical reinforcement
Design of short columns using helical reinforcement
shivam gautam
 
Presentation on rectangular beam design by USD method
Presentation on rectangular beam design by USD methodPresentation on rectangular beam design by USD method
Presentation on rectangular beam design by USD method
000041
 
Reinforced concrete beams
Reinforced concrete beamsReinforced concrete beams
Reinforced concrete beams
Shivkumar Yadav
 
B.tech admission in india
B.tech admission in indiaB.tech admission in india
B.tech admission in india
Edhole.com
 
Rcc
RccRcc
10.01.03.041
10.01.03.04110.01.03.041
10.01.03.041
0041ezaz
 
10.01.03.041
10.01.03.04110.01.03.041
10.01.03.041
0041ezaz
 
B.tech admission in india
B.tech admission in indiaB.tech admission in india
B.tech admission in india
Edhole.com
 
Column design.ppt
Column design.pptColumn design.ppt
Column design.ppt
Samirsinh Parmar
 
Flexural design of beam...PRC-I
Flexural design of beam...PRC-IFlexural design of beam...PRC-I
Flexural design of beam...PRC-I
Irfan Malik
 
Columns lecture#1
Columns lecture#1Columns lecture#1
Columns lecture#1
Irfan Malik
 
Column
ColumnColumn
Struktur Rabgka Bangunan Bangunan Baja _13776666.ppt
Struktur Rabgka Bangunan Bangunan Baja _13776666.pptStruktur Rabgka Bangunan Bangunan Baja _13776666.ppt
Struktur Rabgka Bangunan Bangunan Baja _13776666.ppt
Gidion Turuallo
 
Lec 17
Lec 17Lec 17
Lec 17-flexural analysis and design of beamns1
Lec 17-flexural analysis and design of beamns1Lec 17-flexural analysis and design of beamns1
Lec 17-flexural analysis and design of beamns1
Civil Zone
 
Doubly reinforced beams...PRC-I
Doubly reinforced beams...PRC-IDoubly reinforced beams...PRC-I
Doubly reinforced beams...PRC-I
Irfan Malik
 
L01_Unit Info & Design Revision(2).pdf
L01_Unit Info & Design Revision(2).pdfL01_Unit Info & Design Revision(2).pdf
L01_Unit Info & Design Revision(2).pdf
NelsonLee79
 
Composite Design.pdf
Composite Design.pdfComposite Design.pdf
Composite Design.pdf
Amin Zuraiqi
 
B.tech admission in india
B.tech admission in indiaB.tech admission in india
B.tech admission in india
Edhole.com
 

Similar to Reinforced Concrete Design (2) (20)

10 Reinforced concrete design
10   Reinforced concrete design10   Reinforced concrete design
10 Reinforced concrete design
 
Design of short columns using helical reinforcement
Design of short columns using helical reinforcementDesign of short columns using helical reinforcement
Design of short columns using helical reinforcement
 
Presentation on rectangular beam design by USD method
Presentation on rectangular beam design by USD methodPresentation on rectangular beam design by USD method
Presentation on rectangular beam design by USD method
 
Reinforced concrete beams
Reinforced concrete beamsReinforced concrete beams
Reinforced concrete beams
 
B.tech admission in india
B.tech admission in indiaB.tech admission in india
B.tech admission in india
 
Rcc
RccRcc
Rcc
 
10.01.03.041
10.01.03.04110.01.03.041
10.01.03.041
 
10.01.03.041
10.01.03.04110.01.03.041
10.01.03.041
 
B.tech admission in india
B.tech admission in indiaB.tech admission in india
B.tech admission in india
 
Column design.ppt
Column design.pptColumn design.ppt
Column design.ppt
 
Flexural design of beam...PRC-I
Flexural design of beam...PRC-IFlexural design of beam...PRC-I
Flexural design of beam...PRC-I
 
Columns lecture#1
Columns lecture#1Columns lecture#1
Columns lecture#1
 
Column
ColumnColumn
Column
 
Struktur Rabgka Bangunan Bangunan Baja _13776666.ppt
Struktur Rabgka Bangunan Bangunan Baja _13776666.pptStruktur Rabgka Bangunan Bangunan Baja _13776666.ppt
Struktur Rabgka Bangunan Bangunan Baja _13776666.ppt
 
Lec 17
Lec 17Lec 17
Lec 17
 
Lec 17-flexural analysis and design of beamns1
Lec 17-flexural analysis and design of beamns1Lec 17-flexural analysis and design of beamns1
Lec 17-flexural analysis and design of beamns1
 
Doubly reinforced beams...PRC-I
Doubly reinforced beams...PRC-IDoubly reinforced beams...PRC-I
Doubly reinforced beams...PRC-I
 
L01_Unit Info & Design Revision(2).pdf
L01_Unit Info & Design Revision(2).pdfL01_Unit Info & Design Revision(2).pdf
L01_Unit Info & Design Revision(2).pdf
 
Composite Design.pdf
Composite Design.pdfComposite Design.pdf
Composite Design.pdf
 
B.tech admission in india
B.tech admission in indiaB.tech admission in india
B.tech admission in india
 

Recently uploaded

AR 232 - TRENDS IN SOLID WASTE MANAGEMENT
AR 232 - TRENDS IN SOLID WASTE MANAGEMENTAR 232 - TRENDS IN SOLID WASTE MANAGEMENT
AR 232 - TRENDS IN SOLID WASTE MANAGEMENT
mpramos8
 
Call Girls Jaipur 📞 8445551418 🌟Door Step Delivery We Offering You 100% Genuine
Call Girls Jaipur 📞 8445551418 🌟Door Step Delivery We Offering You 100% GenuineCall Girls Jaipur 📞 8445551418 🌟Door Step Delivery We Offering You 100% Genuine
Call Girls Jaipur 📞 8445551418 🌟Door Step Delivery We Offering You 100% Genuine
parulsinha
 
Call Girls Jaipur Aaradhya 8445551418 Independent Escort Service Jaipur
Call Girls Jaipur Aaradhya 8445551418 Independent Escort Service JaipurCall Girls Jaipur Aaradhya 8445551418 Independent Escort Service Jaipur
Call Girls Jaipur Aaradhya 8445551418 Independent Escort Service Jaipur
TanyaAhuja34 $S2
 
Call Girls Ahmedabad( 🤑 7488326553 🤑) Vip Call Girl Ahmedabad
Call Girls Ahmedabad( 🤑 7488326553 🤑) Vip Call Girl AhmedabadCall Girls Ahmedabad( 🤑 7488326553 🤑) Vip Call Girl Ahmedabad
Call Girls Ahmedabad( 🤑 7488326553 🤑) Vip Call Girl Ahmedabad
babesbookhot
 
Delhi Call Girls 📞 9873940964 ❤️ Full enjoy at your Door Step Available 24x7
Delhi Call Girls 📞 9873940964 ❤️ Full enjoy at your Door Step Available 24x7Delhi Call Girls 📞 9873940964 ❤️ Full enjoy at your Door Step Available 24x7
Delhi Call Girls 📞 9873940964 ❤️ Full enjoy at your Door Step Available 24x7
yesp58846
 
🔥Call Girl Contact Number Chandigarh 💯Call Us 🔝 70230594 🔝💃Independent Chandi...
🔥Call Girl Contact Number Chandigarh 💯Call Us 🔝 70230594 🔝💃Independent Chandi...🔥Call Girl Contact Number Chandigarh 💯Call Us 🔝 70230594 🔝💃Independent Chandi...
🔥Call Girl Contact Number Chandigarh 💯Call Us 🔝 70230594 🔝💃Independent Chandi...
Ak47$A19
 
一比一原版美国加州大学戴维斯分校毕业证(ucdavis学位证)如何办理
一比一原版美国加州大学戴维斯分校毕业证(ucdavis学位证)如何办理一比一原版美国加州大学戴维斯分校毕业证(ucdavis学位证)如何办理
一比一原版美国加州大学戴维斯分校毕业证(ucdavis学位证)如何办理
twqryq79
 
🔥Cheap Rates Call Girls Bangalore 💯Call Us 🔝 9352988975 🔝💃Top Class Call Girl...
🔥Cheap Rates Call Girls Bangalore 💯Call Us 🔝 9352988975 🔝💃Top Class Call Girl...🔥Cheap Rates Call Girls Bangalore 💯Call Us 🔝 9352988975 🔝💃Top Class Call Girl...
🔥Cheap Rates Call Girls Bangalore 💯Call Us 🔝 9352988975 🔝💃Top Class Call Girl...
Sanjna Singh
 
Call Girls Jaipur Aaradhya 8445551418 Night Call Girls Jaipur
Call Girls  Jaipur Aaradhya 8445551418 Night Call Girls JaipurCall Girls  Jaipur Aaradhya 8445551418 Night Call Girls Jaipur
Call Girls Jaipur Aaradhya 8445551418 Night Call Girls Jaipur
vipgirlschennai
 
🔥VIP Call Girls Mumbai 🔝👉 9833363713 👈🔝High Calass Call Girl Mumbai
🔥VIP Call Girls Mumbai 🔝👉 9833363713 👈🔝High Calass Call Girl Mumbai🔥VIP Call Girls Mumbai 🔝👉 9833363713 👈🔝High Calass Call Girl Mumbai
🔥VIP Call Girls Mumbai 🔝👉 9833363713 👈🔝High Calass Call Girl Mumbai
Sifa Khan#i11
 
My Fashion PPT is my presentation on fashion and Trendss
My Fashion PPT is my presentation on fashion and TrendssMy Fashion PPT is my presentation on fashion and Trendss
My Fashion PPT is my presentation on fashion and Trendss
MedhaRana1
 
Independent Call Girls In Churchgate ( Mumbai ) 💯Call Us 🔝 9910780858 🔝💃Top C...
Independent Call Girls In Churchgate ( Mumbai ) 💯Call Us 🔝 9910780858 🔝💃Top C...Independent Call Girls In Churchgate ( Mumbai ) 💯Call Us 🔝 9910780858 🔝💃Top C...
Independent Call Girls In Churchgate ( Mumbai ) 💯Call Us 🔝 9910780858 🔝💃Top C...
pr971917
 
Ways to keep strategy alive throughout a project, in the smaller moments
Ways to keep strategy alive throughout a project, in the smaller momentsWays to keep strategy alive throughout a project, in the smaller moments
Ways to keep strategy alive throughout a project, in the smaller moments
Ariana Koblitz
 
一比一原版加拿大瑞尔森大学毕业证如何办理
一比一原版加拿大瑞尔森大学毕业证如何办理一比一原版加拿大瑞尔森大学毕业证如何办理
一比一原版加拿大瑞尔森大学毕业证如何办理
oydykuz
 
Call Girls Service Jaipur {8445551418} ❤️BHAWNA VIP Jaipur Call Girl UKHBET E...
Call Girls Service Jaipur {8445551418} ❤️BHAWNA VIP Jaipur Call Girl UKHBET E...Call Girls Service Jaipur {8445551418} ❤️BHAWNA VIP Jaipur Call Girl UKHBET E...
Call Girls Service Jaipur {8445551418} ❤️BHAWNA VIP Jaipur Call Girl UKHBET E...
ishu38418
 
Connaught Place Call Girls 📞 9711199171 ❤️ Full enjoy at your Door Step Avail...
Connaught Place Call Girls 📞 9711199171 ❤️ Full enjoy at your Door Step Avail...Connaught Place Call Girls 📞 9711199171 ❤️ Full enjoy at your Door Step Avail...
Connaught Place Call Girls 📞 9711199171 ❤️ Full enjoy at your Door Step Avail...
yesp58846
 
v1-replaced– AI Explanations as Two-Way Experiences
v1-replaced– AI Explanations as Two-Way Experiencesv1-replaced– AI Explanations as Two-Way Experiences
v1-replaced– AI Explanations as Two-Way Experiences
Design for Context
 
World trade center in kerala proposal- AR. DEEKSHITH MAROLI 724519251008 REPORT
World trade center in kerala proposal- AR. DEEKSHITH MAROLI 724519251008 REPORTWorld trade center in kerala proposal- AR. DEEKSHITH MAROLI 724519251008 REPORT
World trade center in kerala proposal- AR. DEEKSHITH MAROLI 724519251008 REPORT
deekshithmaroli666
 
Premium Call Girls In Mahipalpur ( Delhi ) 🔥 9711199012 ❄- Pick Your Dream Ca...
Premium Call Girls In Mahipalpur ( Delhi ) 🔥 9711199012 ❄- Pick Your Dream Ca...Premium Call Girls In Mahipalpur ( Delhi ) 🔥 9711199012 ❄- Pick Your Dream Ca...
Premium Call Girls In Mahipalpur ( Delhi ) 🔥 9711199012 ❄- Pick Your Dream Ca...
deepakvermat423724
 
Low_Rate↠Jaipur Call Girls Sindhi Camp (+918445551418) Escorts Service 24×7 H...
Low_Rate↠Jaipur Call Girls Sindhi Camp (+918445551418) Escorts Service 24×7 H...Low_Rate↠Jaipur Call Girls Sindhi Camp (+918445551418) Escorts Service 24×7 H...
Low_Rate↠Jaipur Call Girls Sindhi Camp (+918445551418) Escorts Service 24×7 H...
ishu38418
 

Recently uploaded (20)

AR 232 - TRENDS IN SOLID WASTE MANAGEMENT
AR 232 - TRENDS IN SOLID WASTE MANAGEMENTAR 232 - TRENDS IN SOLID WASTE MANAGEMENT
AR 232 - TRENDS IN SOLID WASTE MANAGEMENT
 
Call Girls Jaipur 📞 8445551418 🌟Door Step Delivery We Offering You 100% Genuine
Call Girls Jaipur 📞 8445551418 🌟Door Step Delivery We Offering You 100% GenuineCall Girls Jaipur 📞 8445551418 🌟Door Step Delivery We Offering You 100% Genuine
Call Girls Jaipur 📞 8445551418 🌟Door Step Delivery We Offering You 100% Genuine
 
Call Girls Jaipur Aaradhya 8445551418 Independent Escort Service Jaipur
Call Girls Jaipur Aaradhya 8445551418 Independent Escort Service JaipurCall Girls Jaipur Aaradhya 8445551418 Independent Escort Service Jaipur
Call Girls Jaipur Aaradhya 8445551418 Independent Escort Service Jaipur
 
Call Girls Ahmedabad( 🤑 7488326553 🤑) Vip Call Girl Ahmedabad
Call Girls Ahmedabad( 🤑 7488326553 🤑) Vip Call Girl AhmedabadCall Girls Ahmedabad( 🤑 7488326553 🤑) Vip Call Girl Ahmedabad
Call Girls Ahmedabad( 🤑 7488326553 🤑) Vip Call Girl Ahmedabad
 
Delhi Call Girls 📞 9873940964 ❤️ Full enjoy at your Door Step Available 24x7
Delhi Call Girls 📞 9873940964 ❤️ Full enjoy at your Door Step Available 24x7Delhi Call Girls 📞 9873940964 ❤️ Full enjoy at your Door Step Available 24x7
Delhi Call Girls 📞 9873940964 ❤️ Full enjoy at your Door Step Available 24x7
 
🔥Call Girl Contact Number Chandigarh 💯Call Us 🔝 70230594 🔝💃Independent Chandi...
🔥Call Girl Contact Number Chandigarh 💯Call Us 🔝 70230594 🔝💃Independent Chandi...🔥Call Girl Contact Number Chandigarh 💯Call Us 🔝 70230594 🔝💃Independent Chandi...
🔥Call Girl Contact Number Chandigarh 💯Call Us 🔝 70230594 🔝💃Independent Chandi...
 
一比一原版美国加州大学戴维斯分校毕业证(ucdavis学位证)如何办理
一比一原版美国加州大学戴维斯分校毕业证(ucdavis学位证)如何办理一比一原版美国加州大学戴维斯分校毕业证(ucdavis学位证)如何办理
一比一原版美国加州大学戴维斯分校毕业证(ucdavis学位证)如何办理
 
🔥Cheap Rates Call Girls Bangalore 💯Call Us 🔝 9352988975 🔝💃Top Class Call Girl...
🔥Cheap Rates Call Girls Bangalore 💯Call Us 🔝 9352988975 🔝💃Top Class Call Girl...🔥Cheap Rates Call Girls Bangalore 💯Call Us 🔝 9352988975 🔝💃Top Class Call Girl...
🔥Cheap Rates Call Girls Bangalore 💯Call Us 🔝 9352988975 🔝💃Top Class Call Girl...
 
Call Girls Jaipur Aaradhya 8445551418 Night Call Girls Jaipur
Call Girls  Jaipur Aaradhya 8445551418 Night Call Girls JaipurCall Girls  Jaipur Aaradhya 8445551418 Night Call Girls Jaipur
Call Girls Jaipur Aaradhya 8445551418 Night Call Girls Jaipur
 
🔥VIP Call Girls Mumbai 🔝👉 9833363713 👈🔝High Calass Call Girl Mumbai
🔥VIP Call Girls Mumbai 🔝👉 9833363713 👈🔝High Calass Call Girl Mumbai🔥VIP Call Girls Mumbai 🔝👉 9833363713 👈🔝High Calass Call Girl Mumbai
🔥VIP Call Girls Mumbai 🔝👉 9833363713 👈🔝High Calass Call Girl Mumbai
 
My Fashion PPT is my presentation on fashion and Trendss
My Fashion PPT is my presentation on fashion and TrendssMy Fashion PPT is my presentation on fashion and Trendss
My Fashion PPT is my presentation on fashion and Trendss
 
Independent Call Girls In Churchgate ( Mumbai ) 💯Call Us 🔝 9910780858 🔝💃Top C...
Independent Call Girls In Churchgate ( Mumbai ) 💯Call Us 🔝 9910780858 🔝💃Top C...Independent Call Girls In Churchgate ( Mumbai ) 💯Call Us 🔝 9910780858 🔝💃Top C...
Independent Call Girls In Churchgate ( Mumbai ) 💯Call Us 🔝 9910780858 🔝💃Top C...
 
Ways to keep strategy alive throughout a project, in the smaller moments
Ways to keep strategy alive throughout a project, in the smaller momentsWays to keep strategy alive throughout a project, in the smaller moments
Ways to keep strategy alive throughout a project, in the smaller moments
 
一比一原版加拿大瑞尔森大学毕业证如何办理
一比一原版加拿大瑞尔森大学毕业证如何办理一比一原版加拿大瑞尔森大学毕业证如何办理
一比一原版加拿大瑞尔森大学毕业证如何办理
 
Call Girls Service Jaipur {8445551418} ❤️BHAWNA VIP Jaipur Call Girl UKHBET E...
Call Girls Service Jaipur {8445551418} ❤️BHAWNA VIP Jaipur Call Girl UKHBET E...Call Girls Service Jaipur {8445551418} ❤️BHAWNA VIP Jaipur Call Girl UKHBET E...
Call Girls Service Jaipur {8445551418} ❤️BHAWNA VIP Jaipur Call Girl UKHBET E...
 
Connaught Place Call Girls 📞 9711199171 ❤️ Full enjoy at your Door Step Avail...
Connaught Place Call Girls 📞 9711199171 ❤️ Full enjoy at your Door Step Avail...Connaught Place Call Girls 📞 9711199171 ❤️ Full enjoy at your Door Step Avail...
Connaught Place Call Girls 📞 9711199171 ❤️ Full enjoy at your Door Step Avail...
 
v1-replaced– AI Explanations as Two-Way Experiences
v1-replaced– AI Explanations as Two-Way Experiencesv1-replaced– AI Explanations as Two-Way Experiences
v1-replaced– AI Explanations as Two-Way Experiences
 
World trade center in kerala proposal- AR. DEEKSHITH MAROLI 724519251008 REPORT
World trade center in kerala proposal- AR. DEEKSHITH MAROLI 724519251008 REPORTWorld trade center in kerala proposal- AR. DEEKSHITH MAROLI 724519251008 REPORT
World trade center in kerala proposal- AR. DEEKSHITH MAROLI 724519251008 REPORT
 
Premium Call Girls In Mahipalpur ( Delhi ) 🔥 9711199012 ❄- Pick Your Dream Ca...
Premium Call Girls In Mahipalpur ( Delhi ) 🔥 9711199012 ❄- Pick Your Dream Ca...Premium Call Girls In Mahipalpur ( Delhi ) 🔥 9711199012 ❄- Pick Your Dream Ca...
Premium Call Girls In Mahipalpur ( Delhi ) 🔥 9711199012 ❄- Pick Your Dream Ca...
 
Low_Rate↠Jaipur Call Girls Sindhi Camp (+918445551418) Escorts Service 24×7 H...
Low_Rate↠Jaipur Call Girls Sindhi Camp (+918445551418) Escorts Service 24×7 H...Low_Rate↠Jaipur Call Girls Sindhi Camp (+918445551418) Escorts Service 24×7 H...
Low_Rate↠Jaipur Call Girls Sindhi Camp (+918445551418) Escorts Service 24×7 H...
 

Reinforced Concrete Design (2)

  • 2. Compressive Strength of Concrete • fcr is the average cylinder strength • f’c compressive strength for design • f’c ~2500 psi - 18,000 psi, typically 3000 - 6000 psi • Ec estimated as: where w = weight of concrete, lb/ft3 f’c in psi E in psi for normal weight concrete ~145 lb/ft3 E w fc c= 3 3 1 5. ' E fc c= 5 7 0 0 0, '
  • 3. Concrete Stress-Strain Curve For short term loading. Over time concrete will creep and shrink.
  • 4. Concrete Strain Strain in concrete will be caused by loading, creep, shrinkage, and temperature change. For scale, consider a 20’ section of concrete, f’c = 4000 psi, under a stress, fc = 1800 psi. Determine the change in length.
  • 5. Tensile Strength of Concrete • Tensile strength of concrete is about • ~300 – 600 psi • Tensile strength of concrete is ignored in design • Steel reinforcement is placed where tensile stresses occur Where do tensile stresses occur? f c' 1 0
  • 6. Tensile Stresses Restrained shrinkage slab on grade shrinkage strain, ε = 0.0006 σ = εE = 0.0006 x 3600 ksi = 2.16 ksi Flexural member compression tension
  • 7. Reinforcing Steel • Deformed steel reinforcing bars • Welded wire fabric • 7-strand wire (for pre-stressing)
  • 8. Deformed Steel Reinforcing Bars Rebar • Grade 60 (most common in US) • Sizes #3 → #18 (number indicates diameter in ⅛ inch)
  • 9. Welded Wire Fabric Readily available fabrics Designation: longitudinal wire spacing x transverse wire spacing – cross-sectional areas of longitudinal wire x transverse wires in hundredths of in2
  • 11. Reinforce Concrete Design Two codes for reinforced concrete design: • ACI 318 Building Code Requirements for Structural Concrete • AASHTO Specifications for Highway Bridges We will design according to ACI 318 which is an ‘LRFD’ design. Load and resistance factors for ACI 318 are given on page 7, notes.
  • 12. Short Reinforced Concrete Compression Members • Short - slenderness does not need to be considered – column will not buckle • Only axial load L Cross-sectional Areas: As = Area of steel Ac = Area of concrete Ag = Total area Fs = stress in steel Fc = stress in concrete From Equilibrium: P = Acfc + Asfs P L P If bond is maintained εs = εc
  • 13. Short Concrete Columns For ductile failure – must assure that steel reinforcement will yield before concrete crushes. – Strain in steel at yield ~0.002 – ε = 0.002 corresponds to max. stress in concrete. – Concrete crushes at a strain ~ 0.003 Equilibrium at failure: P = AsFy +Acf’c
  • 14. Reinforcement Ratio • ρ = As/Ag • ACI 318 limits on ρ for columns: 0.01≤ρ≤0.08 (practical ρmax = 0.06) • Substitute ρ=As/Ag and Ag=As+Ac into equilibrium equation: P = Ag[ρfy +f’c(1- ρ)]
  • 15. Short Concrete Columns P = Ag[ρfy +f’c(1- ρ)] Safety Factors • Resistance factor, Ф = 0.65 (tied), Ф = 0.70 (spiral) • When fc>0.85f’c, over time, concrete will collapse • Stray moment factor for columns, K1 – K1=0.80 for tied reinforcement – K1=0.85 for spiral reinforcement ФPn = Ф K1 Ag[ρfy +0.85f’c(1- ρ)]
  • 16. Short Column Design Equation ФPn = Ф K1 Ag[ρfy +0.85f’c(1- ρ)] for design, Pu ≤ ФPn         − − ≥ c g u cy f AK P ff '85.0 )'85.0( 1 1φ ρ [ ])1('85.01 ρρφ −+ ≥ cy u g ffK P A
  • 17. Transverse Reinforcement Used to resist bulge of concrete and buckling of steel
  • 18. Concrete Cover Used to protect steel reinforcement and provide bond between steel and concrete
  • 19. Short Concrete Column Example Design a short, interior, column for a service dead load of 220 kips and a service live load of 243 kips. Consider both a circular and a square cross section. Assume that this column will be the prototype for a number of columns of the same size to take advantage of the economy to be achieved through repetition of formwork. Also assume that this column will be the most heavily loaded (“worst first”). Available materials are concrete with f’c = 4 ksi and grade 60 steel.
  • 21.
  • 22.
  • 23.
  • 24.
  • 25. Design of Spiral Reinforcement • Asp = cross sectional area of spiral bar • Dcc = center to center diameter of spiral coil • Acore = area of column core to outside of spiral coils • Pitch = vertical distance center to center of coils with the limit: 1” ≤ clear distance between coils ≤ 3” )('45.0 coregc yccsp AAf fDA − ≤ π Pitch of spiral
  翻译: