Reinforced Concrete Design

ACI Code 318-08

Course Outline

1. Properties of Reinforced Concrete

2. Flexural Analysis of Reinforced Concrete Beams

3. Flexural Design of Reinforced Concrete Beams

4. Development Length of Reinforcing Bars

5. Shear and Diagonal Tension

6. Torsion

7. Axially Loaded Columns

8. Members in Compression and Bending

9. Slender Columns

10. One-way Slabs

11. Two-ways Slabs

12. Stairs

13. Footings

Chapter 1

Properties of Reinforced Concrete

1. Properties of Reinforced Concrete

1.1 Factor affecting the strength of concrete

1.2 Compressive strength

1.3 Tensile strength of concrete

1.4 Flexural strength (Modulus of rupture) of concrete

1.5 Shear strength

1.6 Modulus of elasticity of concrete

1.7 Steel reinforcement

1.1 Factor affecting the strength of concrete Water-cement ratio: for complete hydration

W/C = 0.25 is needed. Properties and proportions of concrete

constituents: An increase in cement content in the mix and use well-graded aggregate increase the strength of concrete. Special admixtures are usually added to the mix to produce the desired quality and strength of concrete.

1. Properties of Reinforced Concrete

1.1 Factor affecting the strength of concrete Method of mixing and curing: concrete mixer,

proper time of mixing, vibrator, curing (moisture and temperature). The longer period of moist storage, the greater the strength.

Age of the concrete:

1. Properties of Reinforced Concrete

,28( )4 0.85c c

tf t f

t

Age 7 days

14 days

28 days

3 months

6 months

1 year

2 years

3 years

Strength Ratio

0.67 0.86 1 1.17 1.23 1.27 1.31 1.35

1.1 Factor affecting the strength of concrete Loading condition: the compressive strength of

concrete (f’c) is usually obtained from static loading test, not including dynamic and creep effects.

Shape and dimension of tested specimen:

1. Properties of Reinforced Concrete

, , ,0.85 to 0.8 1.1c cyl c cube c prismf f f

Relative strength for various size of cylinders

1. Properties of Reinforced Concrete

Size of cylinder (mm) Relative compressive strength

50 x 100 1.09

75 x 150 1.06

150 x 300 1.00

200 x 400 0.96

300 x 600 0.91

450 x 900 0.86

600 x 1200 0.84

900 x 1800 0.82

1. Properties of Reinforced Concrete

1.1 Factor affecting the strength of concrete

1.2 Compressive strength

1.3 Tensile strength of concrete

1.4 Flexural strength (Modulus of rupture) of concrete

1.5 Shear strength

1.6 Modulus of elasticity of concrete

1.7 Steel reinforcement

1.2 Compressive strength

1.2 Compressive strength

1. Properties of Reinforced Concrete

1.1 Factor affecting the strength of concrete

1.2 Compressive strength

1.3 Tensile strength of concrete

1.4 Flexural strength (Modulus of rupture) of concrete

1.5 Shear strength

1.6 Modulus of elasticity of concrete

1.7 Steel reinforcement

1.3 Tensile strength of concrete

Where P compressive load, D and L are diameter and length of cylinder

Generally,

2sp

Pf

LD

10%sp cf f

1.4 Flexural strength (Modulus of rupture) of concrete

0.62 (MPa)r cf f

1.25 1.50 (MPa)r spf to f

1.5 Shear strength

Where: is a modification factor for type of concrete (ACI 8.6.1)

l = 1.0 Normal-weight concretel = 0.85 Sand-lightweight concretel = 0.75 for all-lightweight concrete

0.17 (MPa)t cf f

1.6 Modulus of elasticity of concrete

1.6 Modulus of elasticity of concrete

In practice, secant modulus at 50% of f ’c is used.

Or

cE

1.5 30.043 (MPa), = /c cE w f w kg m

=4780 (MPa) c cE f

1.7 Steel reinforcement

តារាងមុ�ខកាត់ដែ�កសសៃស(សមុ២)

Diameter Number of Bars

ϕ (mm) 1 2 3 4 5 6 7 8 9 10 12 13 14 15

6 0.28 0.57 0.85 1.13 1.41 1.70 1.98 2.26 2.54 2.83 3.39 3.68 3.96 4.24

8 0.50 1.01 1.51 2.01 2.51 3.02 3.52 4.02 4.52 5.03 6.03 6.53 7.04 7.54

10 0.79 1.57 2.36 3.14 3.93 4.71 5.50 6.28 7.07 7.85 9.42 10.21 11.00 11.78

12 1.13 2.26 3.39 4.52 5.65 6.79 7.92 9.05 10.18 11.31 13.57 14.70 15.83 16.96

14 1.54 3.08 4.62 6.16 7.70 9.24 10.78 12.32 13.85 15.39 18.47 20.01 21.55 23.09

16 2.01 4.02 6.03 8.04 10.05 12.06 14.07 16.08 18.10 20.11 24.13 26.14 28.15 30.16

18 2.54 5.09 7.63 10.18 12.72 15.27 17.81 20.36 22.90 25.45 30.54 33.08 35.63 38.17

20 3.14 6.28 9.42 12.57 15.71 18.85 21.99 25.13 28.27 31.42 37.70 40.84 43.98 47.12

22 3.80 7.60 11.40 15.21 19.01 22.81 26.61 30.41 34.21 38.01 45.62 49.42 53.22 57.02

25 4.91 9.82 14.73 19.63 24.54 29.45 34.36 39.27 44.18 49.09 58.90 63.81 68.72 73.63

30 7.07 14.14 21.21 28.27 35.34 42.41 49.48 56.55 63.62 70.69 84.82 91.89 98.96 106.03

32 8.04 16.08 24.13 32.17 40.21 48.25 56.30 64.34 72.38 80.42 96.51 104.55 112.59 120.64

38 11.34 22.68 34.02 45.36 56.71 68.05 79.39 90.73 102.07 113.41 136.09 147.43 158.78 170.12

Chapter 2

Flexural Analysis

of

Reinforced Concrete Beams

1. Introduction

• The analysis and design of a structural member may be regarded as the process of selecting the proper materials and determining the member dimensions such that the design strength is equal or greater than the required strength.

M M

V V

T

P P

n u

n u

n u

n u

T

Gravity load path in a floor slab a) one-way system;

b) two-way system

2. Design Assumptions1. Strain in concrete is the same as in reinforcing bars at

the same level, provided that the bond between the steel and concrete is adequate.

2. Strain in concrete is linearly proportional to the distance from the neutral axis (Fig 2.1).

3. The modulus of elasticity of all grades of steel is

4. Plane cross-sections continue to be plane after bending

5200000 2 10sE MPa MPa

Fig 2.1 Strain diagram

2. Design Assumptions

5. Tensile strength of concrete shall be neglected in axial and flexural calculations of reinforced concrete.

6.

2. Design Assumptions

7. Maximum usable strain at extreme concrete compression fiber shall be assumed equal to εu = 0.003.

2. Design Assumptions

3. Stress in reinforcement fs below the yield strength fy shall be taken as Es times the steel strain εs. For strains greater than fy/Es, stress in reinforcement shall be considered independent of strain and equal to fy.

• when εs ≤ εy (yield strain):

fs = Es εs

• when εs ≥ εy:

fs = Es εy = fy

3. Behavior of a simply supported reinforced concrete beam loaded to failure

Failure conditions at the positive sections in a continuous reinforced concrete beam

Failure conditions at the negative-moment sections in a continuous reinforced concrete beam

4. Type of flexural failure

Three types of flexural failure of a structural member can be expected depending on the percentage of steel used in the section.

1.Tension-control section: c = 0.003 & s 0.005

4. Type of flexural failure

2. Balance-control section:

4. Type of flexural failure

2. Compression-control section:

5. Strain Limits

Strain Limits Section Condition Concrete Strain Steel Strain Notes (fy = 400MPa)

Compression-controlled 0.003 t fy/Es t 0.002

Tension-controlled 0.003 t 0.005 t 0.005

Transition region 0.003 fy/Es t 0.005 0.002 t 0.005

Balanced strain 0.003 s = fy/Es s = 0.002

Transition region (flexure) 0.003 0.004 t 0.005 0.004 t 0.005

6. Load Factors