Elastic Theory Method

8/17/2019 Elastic Theory Method

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REINFORCED CONCRETE BEAM DESIGNElastic Theory Method





The term plain concrete is used to describeany concrete mass used without anystrengthening materials. The physical

to stone and include the ability to withstandgreat pressure. Concrete is a combinationconstruction material made of cement, ash,

gravel, limestone, and granite. Some types of concrete include sand, chemical mixtures,and water.



A composite material that combines concretewith steel reinforcements

The combination of these materials provide a strong durable building material that could

cater both compressive and tensile strength.





ADVANTAGES DISADVANTAGES

1. Ability to be casted 1. Low Tensile Strength

2. Economical 2. Low Ductility

3. Durable 3. Volume Instability

4. Fire Resistance 4. Low strength-weight ration

5. Energy Efficient

6. On site Fabrication

7. Aesthetic Properties











Number of bars

Diameter

(mm) 1 2 3 4 5 6 7 8 9

6

8

28

50

57

101

85

151

113

201

142

252

170

302

198

352

226

402

255

453

12

16

20

25

32

40

113

201

314

491

804

1257

226

402

628

983

1608

2513

339

603

942

1474

2412

3770

452

804

1256

1966

3216

5027

565

1005

1570

2457

4020

6283

678

1206

1884

2946

4824

5740

791

1407

2198

3439

5628

8796

904

1608

2512

3932

6432

10053

1017

1809

2826

4423

7236

11310







Plain sections through the beam beforebending remain plain after bending.

The concrete above the neutral axis carries all

the compression The tensile steel carries all the tension The concrete shrinks in and thus grips the

steel bars firmly so that there is no slipbetween the steel and surrounding concrete.



Design of reinforced concrete structures started in thebeginning of this century following purely empiricalapproach.

Thereafter came the so called rigorous elastic theory where

t s assume t at concrete s e ast c an re n orc ng steebars and concrete act together elastically.

The load-deflection relation is linear and both concrete andsteel obey Hooke’s law.



The method is designated as working stress method as theloads for the design of structures are the service loads or theworking loads.

The failure of the structure will occur at a much higher load.

e rat o o t e a ure oa s to t e wor ng oa s s t efactor of safety.

Accordingly, the stresses of concrete and steel in a structuredesigned by the working stress method are not allowed toexceed some specified values of stresses known as

permissible stresses.



The permissible stresses are determined dividing thecharacteristic strength (fcu) of the material by therespective factor of safety.

The values of the factor of safet de end on the rade of the material and the type of stress. Thus, forconcrete in bending compression, the permissiblestress of grade M 20 is 7 N/mm2 , which is obtained bydividing the characteristic strength (fcu) of M 20concrete by a number 3 and then rationalising the

value to 7.

This permissible stress is designated by(Pcb @ Pst).



In the elastic theory, structures having different materials aremade equivalent to one common material. In the reinforcedconcrete structure, concrete and reinforcing steel are,therefore, converted into one material.

This is done by transformation using the modular ratio mwhich is the ratio of modulus of elasticity of steel andconcrete. Thus, m = Es/Ec. where Es is the modulus of elasticity of steel which is 200000 N/mm2 .

However, concrete has different modulus, as it is not aperfectly elastic material.



N=? j= ? R=?

P= percentage of steel d1 =Effective depth Ast = Area of steel



n = The distance

from the top face of

the beam to the NA

which indicates the

depth of concrete in

compression in a

beam is denoted by

d n







Referring to table,

515.205mm²

Number of bars

Diameter

(mm) 1 2 3 4 5 6 7 8 9

6 28 57 85 113 142 170 198 226 255

10

12

16

20

25

32

40

79

113

201

314

491

804

1257

157

226

402

628

983

1608

2513

236

339

603

942

1474

2412

3770

314

452

804

1256

1966

3216

5027

393

565

1005

1570

2457

4020

6283

471

678

1206

1884

2946

4824

5740

550

791

1407

2198

3439

5628

8796

628

904

1608

2512

3932

6432

10053

707

1017

1809

2826

4423

7236

11310

Use 5nos Y12 (565mm2 )



.

d = d1 + 1/2øBar + cd = 321mm + ½ (12mm) +25mm

= 352.5mm @ 355 mm

Spacing

150– [ (12 x 3) + (25 x 2)] = 32

2

= 32 ≥ 10 mm



A simple supported beam is to span 3.6m carrying a uniformload of 60 KN inclusive of self weight. The beam is to be 150mm wide and the stresses in steel and concrete respectivelyare to be 140 N/mm² and 10N/mm² (m=15)

eterm ne t e constant n , , an an c oose a su ta eeffective depth, overall depth and area of steel of the beam.









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