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Reinforced Concrete Design

General - RC design

 

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Section properties of reinforcing bars

Bar

Nominal diameter

Cross Section

Perimeter

Normal weight

No.

in

mm

in

mm

in

mm

in

mm

3

0.375

9.52

0.11

71

1.178

29.9

0.376

0.56

4

0.5

12.7

0.2

129

1.571

39.9

0.668

0.994

5

0.625

15.88

0.31

200

1.963

49.9

1.043

1.552

6

0.75

19.05

0.44

284

2.356

59.8

1.502

2.235

7

0.875

22.22

0.6

387

2.749

69.8

2.044

3.042

8

1.000

25.4

0.79

510

3.142

79.8

2.67

3.973

9

1.128

28.65

1.00

645

3.544

90.0

3.4

5.06

10

1.27

32.26

1.27

819

3.990

101.4

4.303

6.404

11

1.541

35.81

1.56

1006

4.43

112.5

5.313

7.907

14

1.693

43.00

2.25

1452

5.32

135.1

7.65

11.38

18

2.257

57.33

4.00

2581

7.09

180.1

13.6

20.24

 

Type of cements

Type

Name

Description

I

Normal

General purpose

II

Moderate

Moderate sulfate and heat resistance

III

High early strength

Fast strength development

IV

Low-heat

Generate low-heat during hydration

V

Sulfate-resisting

High sulfate resistance

 

Elastic modulus of concrete

The elastic modulus of concrete, Ec  (lb/in2)  is (ACI 318-05 Sec 8.5)

Ec = wc1.5 (33) Öfc                              lb/in2

Ec = wc1.5 (0.043) Öfc                         MPa

 

where wc is unit weight of concrete between 90 to 155 lb/ft3.   fc’ is compression strength of concrete in lb/in2.  

 

For normal weight concrete              Ec = 57000 Öfc     

 

Modulus of rapture

fr = 7.5 Ö fc                                        lb/in2.

fr = 0.62 Ö fc                                      MPa

Concrete strength

Elastic modulus

Modulus or rapture

psi

MPa

ksi

MPa

psi

MPa

3000

20.7

3156

21759

411

2.8

3500

24.1

3409

23503

444

3.1

4000

27.6

3644

25126

474

3.3

4500

31.0

3865

26650

503

3.5

5000

34.5

4074

28091

530

3.7

5500

37.9

4273

29462

556

3.8

6000

41.4

4463

30772

581

4.0

6500

44.8

4645

32029

605

4.2

7000

48.3

4821

33238

627

4.3

7500

51.7

4990

34405

650

4.5

8000

55.2

5154

35533

671

4.6

 

Load combinations from ASCE 7-10

Load combination or strength design (ASCE 7-10, sec, 2.3.2)

1. 1.4D

2. 1.2D+1.6L+0.5(Lr or S or R)

3. 1.2D+1.6(Lr or S or R)+(L or 0.5W)

4. 1.2D+1.0W+L+0.5(Lr or S or R)

5. 1.2D+1.0E+L+0.2S

6. 0.9D+1.0W

7. 0.9D+1.0E

Load combination for allowable stress design (ASCE 7-10, Sec. 2.4)

1. D

2. D+L

3. D+(Lr or S or R)

4. D+0.75L+0.75(Lror S or R)

5. D+ (0.6W or 0.7E)

6a. D+0.75L+0.75(0.6W)+0.75(Lr or S or R)

6b. D+0.75L+0.75(0.6E)+0.75S

7. 0.6D+0.6W

5. 0.6D+0.7E

 

Where D is dead load, L is live load, Lr is roof live load, W is strength design wind load, E is strength design seismic load,

R is rain load, S is snow load

 

Load combinations from ASCE 7-05

Load combination or strength design (ASCE 7-05, sec, 2.3.2)

1. 1.4(D+H)

2. 1.2(D+F+T)+1.6(L+H)+0.5(Lr or S or R)

3. 1.2D+1.6(Lr or S or R)+(0.5L or 0.8W)

4. 1.2D+1.6W+0.5L+0.5(Lr or S or R)

5. 1.2D+1.0E+0.5L+0.5(Lr or S or R)

6. 0.9D+1.6W+1.6H

7. 0.9D+1.0E+1.6H

Load combination for allowable stress design (ASCE 7-05, Sec. 2.4.1)

1. D

2. D+L+F+H+T+(Lr or S or R)

3. D+(W or 0.7E)+L+(Lr or S or R)

4. 0.6D+W+H

5. 0.6D+0.7E+H

 

Where W is serviced design wind load, E is strength desogm earthquake load, F is fluid pressure, R is rain load, S is snow load, T is temperature force.

 

Load combinations from ACI 318-05, ACI 318-08

Load combination or strength design (Sec 9-2)

1. 1.4(D+F)                                                                       (9-1)

2. 1.2(D+F+T)+1.6(L+H)+0.5(Lr or S or R)                     (9-2)

3. 1.2D+1.6(Lr or S or R)+(1.0L* or 0.8W)                      (9-3)

4. 1.2D+1.6W**+1.0L*+0.5(Lr or S or R)                        (9-4)

5. 1.2D+1.0E***+1.0L*+0.2S                                           (9-5)

6. 0.9D+1.6W**+1.6H                                                      (9-6)

7. 0.9D+1.0E***+1.6H                                                      (9-7)

 

*1.0L can be reduced to 0.5L except garages, public assembly and area that has 100 lb/ft2 of live load.

**1.6W can be reduced to 1.3W when wind load W is not reduced by directional factor (See ASCE 7-02 wind calculation)

*** Where seismic load, E is calculated based on service load, 1.4E shall be used instead of 1.0E.

 

Strength reduction factor, f, ACI 318-05, ACI 318-08

1. Tension-controlled sections, 0.9 (Sec. 9.3.2.1)

2. Compression-controlled sections (Sec. 9.3.2.2)

(a) Column with spiral reinforcement, 0.7

(b) Tie columns, 0.65.

3.  f is permitted to vary from 0.65 to 0.9 when the net tensile strain in extreme tension steel at nominal strength varies from compressive control strain to 0.005.

4. Shear and torsion, 0.75 (Sec. 9.3.2.3)

5. Bearing on concrete, 0.65 (Sec. 9.3.2.4)