deformation of concrete structures1. concrete structures : stresses and deformation by a. ghali and...
TRANSCRIPT
![Page 1: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/1.jpg)
Deformation of Concrete Structures
Fall 2010
Dept of Architecture
![Page 2: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/2.jpg)
1st week
Overview of design codes
![Page 3: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/3.jpg)
Course Preview
• Code provisions - Fib - Euro - ACI • Basics in Deformation • Axial deformation • Flexural deformation • Creep and Shrinkage • Shear deformation of Plane stress elements
![Page 4: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/4.jpg)
Text book and References
1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre
2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay
3.Ductility of Reinforced Concrete Structures CEB Bulletin 242
4. Strength and Deformation of Structural Concrete by Kaufmann
![Page 5: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/5.jpg)
Objectives of Course
1. Understanding of Concepts in Design Codes
2. Basic Concepts of Deformation of Concrete Structures: Axial and Bending
3. Ductility
4. Plane stress elements in shear
5. Mechanisms based Deformation Capacity Estimation
![Page 6: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/6.jpg)
Code Provisions-Fib
• 7.6 Verification of Serviceability of RC and PC structures
7.6.1 Requirement
7.6.2 Design Criteria
7.6.3 Stress limitation
7.6.4 Limit state of cracking
7.6.5 Limit state of deformation
![Page 7: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/7.jpg)
7.6.1 Requirement
• Stresses
• Crack width
• Deformation
• vibrations
![Page 8: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/8.jpg)
7.6.2 Design criteria
• Characteristic value
• Combination value
• Frequent value
• Quasi-permanent value
![Page 9: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/9.jpg)
![Page 10: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/10.jpg)
7.6.3 stress limitation
• Tensile stresses in concrete
• Compressive stresses in concrete
• Tensile stresses in the steel
![Page 11: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/11.jpg)
![Page 12: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/12.jpg)
![Page 13: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/13.jpg)
7.6.4 Limit state of cracking
• Requirement
• Design criteria vs. cracking
• Limitation of crack width
• Calculation of crack width in RC members
![Page 14: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/14.jpg)
![Page 15: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/15.jpg)
7.6.5 Limit states of deformation
• General
• Deformations due to bending with or w/o axial force
• Instantaneous deflection
• Long-term deflections
![Page 16: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/16.jpg)
![Page 17: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/17.jpg)
![Page 18: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/18.jpg)
Euro code
Section 7 Serviceability limit state
7.1 General
7.2 Stress limitation
7.3 Crack control
7.4 Deflection control
![Page 19: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/19.jpg)
![Page 20: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/20.jpg)
![Page 21: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/21.jpg)
![Page 22: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/22.jpg)
Deformation of cracked concrete in
tension
![Page 23: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/23.jpg)
1r ct c s ctN f A nA f A
1) N before cracking lower than the following value
s
c
En
E
rsr
s
N
A
Stress in steel
![Page 24: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/24.jpg)
rN N
2) After cracking
2s
s
N
A
Stress in steel at a crack
2
1s
s s
N
A E
1 1
1
s c
c c s c
N N
E A nA E A
Axial force
N
rN
(state 1)
(state 2)
2
1s
s s
N
A E
1
1
1s
c
N
A E
maxs
ssm
Stress in steel in state 2
s2
sr
Strain in steel
lsml l
N
N
![Page 25: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/25.jpg)
2s s sm
Fully cracked Mean steel strain
Assume strain difference has hyperbolic variation with stress in steel
max
2
srs s
s
max 2 1
2
srs s s
s
m 2s s s
2 max
2
srs s
s
2
2 2 1
2
srs s s
s
2 2
1 2
2 2
1sr srs s
s s
![Page 26: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/26.jpg)
Let
1 21sm s s
2
2
1 sr
s
2
1 2
2
1 sr
s
1 : bond effect
2 : loading characteristics
![Page 27: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/27.jpg)
![Page 28: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/28.jpg)
![Page 29: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/29.jpg)
![Page 30: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/30.jpg)
![Page 31: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/31.jpg)
![Page 32: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/32.jpg)
![Page 33: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/33.jpg)
![Page 34: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/34.jpg)
![Page 35: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/35.jpg)
![Page 36: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/36.jpg)
![Page 37: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/37.jpg)
![Page 38: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/38.jpg)
![Page 39: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/39.jpg)
![Page 40: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/40.jpg)
![Page 41: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/41.jpg)
![Page 42: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/42.jpg)
![Page 43: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/43.jpg)
![Page 44: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/44.jpg)
![Page 45: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/45.jpg)
![Page 46: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/46.jpg)
![Page 47: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/47.jpg)
![Page 48: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/48.jpg)
![Page 49: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/49.jpg)
![Page 50: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/50.jpg)
![Page 51: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/51.jpg)
![Page 52: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/52.jpg)
![Page 53: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/53.jpg)
![Page 54: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/54.jpg)
![Page 55: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/55.jpg)
![Page 56: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/56.jpg)
![Page 57: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/57.jpg)
![Page 58: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/58.jpg)
![Page 59: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/59.jpg)
![Page 60: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/60.jpg)
![Page 61: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/61.jpg)
![Page 62: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/62.jpg)
![Page 63: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/63.jpg)
![Page 64: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/64.jpg)
![Page 65: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/65.jpg)
![Page 66: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/66.jpg)
ACI code provisions (318-08)
Chap. 9.5 control of deflection
Chap. 10.6 Distribution of flexural reinforcement in beams and one-way slabs
![Page 67: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/67.jpg)
Basics in deformation
- Axial deformation
- Cracks
- Tension stiffening
- Bond
- Virtual work method
- Uncracked and cracked sections
![Page 68: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/68.jpg)
1r ct c s ctN f A nA f A
1) N before cracking lower than the following value
s
c
En
E
rsr
s
N
A
Stress in steel
![Page 69: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/69.jpg)
rN N
2) After cracking
2s
s
N
A
Stress in steel at a crack
2
1s
s s
N
A E
1 1
1
s c
c c s c
N N
E A nA E A
Axial force
N
rN
(state 1)
(state 2)
2
1s
s s
N
A E
1
1
1s
c
N
A E
maxs
ssm
Stress in steel in state 2
s2
sr
Strain in steel
lsml l
N
N
![Page 70: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/70.jpg)
2s s sm
Fully cracked Mean steel strain
Assume strain difference has hyperbolic variation with stress in steel
max
2
srs s
s
max 2 1
2
srs s s
s
m 2s s s
2 max
2
srs s
s
2
2 2 1
2
srs s s
s
2 2
1 2
2 2
1sr srs s
s s
![Page 71: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/71.jpg)
Let
1 21sm s s
2
2
1 sr
s
2
1 2
2
1 sr
s
1 : bond effect
2 : loading characteristics
![Page 72: Deformation of Concrete Structures1. Concrete Structures : Stresses and Deformation by A. Ghali and R Favre 2. Chap. 11 in Reinforced Concrete Structures by R Park and T. Paulay 3.Ductility](https://reader035.vdocument.in/reader035/viewer/2022071603/613d9fadd6303f41db6f07ce/html5/thumbnails/72.jpg)
Long-term deflection
1. Creep of concrete
2. Shrinkage
3. Relaxation of prestressing steel
4. Creep superposition
5. Aging Coefficient
6. Relaxation of concrete
7. Adjusted elasticity modulus