DESIGN OF DOUBLY REINFORCED BEAM BY

BY LIMIT STATE METHOD

TYPES OF BEAMS

Doubly Reinforced beam Singly Reinforced beam

Need of doubly reinforced beam

NEED OF DOUBLY REINFORCED BEAM

In practice, very frequently, it is desirable or even

mandatory to have a section of restricted depth in order to comply with some architectural or structural requirements wherein the section has to carry a moment more than it can resist a balanced section. If the section is made arbitrarily made shallower than the balanced design, it results in over reinforced section and the concrete is over stressed, while steel is stressed to its permissible value. As it is mentioned in IS:456 do not permit the use of over reinforced section. In such cases it is preferable to design it as doubly reinforced beam where the reinforcement is also provided in compression to give additional strength to concrete.

MINIMUM AND MAXIMUM STEEL AS COMPRESSION STEEL IN BEAMS

The minimum area of steel in compression

= 0.4% of area in compression steel

The maximum area of steel in compression

=4% of the total sectional area of the beam

YIELD STRESS IN COMPRESSION STEEL

IS 456 ASSUMES THAT THE YIELD STRESS-STRAIN RELATIONSHIP FOR STEEL IN COMPRESSION AND TENSION REMAIN SAME

Design yield stress = 0.87ƒy

Z S

Z C

CC

d’C S

0.0035d’

0.002

b

X u

Є s

d

Є’ s

Action of doubly reinforced beam

T

STRAIN DIAGRAM STRESS DISTRIBUTION

T = CC = CS

MU = CCZC + CSZS

CS = Compressive force due to concrete

CC = Compressive force due to steel

ANALYSIS AND DESIGN OF DOUBLY REINFORCED BEAM

1. Choose value of x, the depth of neutral axis. Assuming compressive strain of 0.0035

2. Total tension in steel, T = ƒast Ast

3. Total compression in steel, C = 0.36ƒckbx

1. The total compression, C = CS + CC

2. Check- if T = C, the assumed neutral axis is satisfactory.

3. Moment of resistance of section

MU = CC(d-k2x) + CS (d-d΄)

Thank you