**Different methods of design of RCC**

1.Working Stress Method

2.Limit State Method

3.Ultimate Load Method

4.Probabilistic Method of Design

**Limit state method of design**

- The object of the design based on the limit state concept is to achieve an acceptable probability, that a structure will not become unsuitable in it’s lifetime for the use for which it is intended,i.e. It will not reach a limit state
- A structure with appropriate degree of reliability should be able to withstand safely.
- All loads, that are reliable to act on it throughout it’s life and it should also satisfy the subs ability requirements, such as limitations on deflection and cracking.
- It should also be able to maintain the required structural integrity, during and after accident, such as fires, explosion & local failure.i.e. limit sate must be consider in design to ensure an adequate degree of safety and serviceability
- The most important of these limit states, which must be examine in design are as follows Limit state of collapse

- Flexure

- Compression

- Shear

- Torsion

This state corresponds to the maximum load carrying capacity.**Types of reinforced concrete beams**

a)Singly reinforced beam

b)Doubly reinforced beam

c)Singly or Doubly reinforced flanged beams

**Singly reinforced beam**

In singly reinforced simply supported beams or slabs reinforcing steel bars are placed near the bottom of the beam or slabs where they are most effective in resisting the tensile stresses.

x = Depth of Neutral axis

b = breadth of section

d = effective depth of section

The depth of neutral axis can be obtained by considering the equilibrium of the normal forces , that is,

Resultant force of compression = average stress X area

= 0.36 fck bx

Resultant force of tension = 0.87 fy At

Force of compression should be equal to force of tension,

**0.36 fck bx = 0.87 fy At**

The distance between the lines of action of two forces C & T is called the lever arm and is denoted by z.

Lever arm z = d – 0.42 x

z = d – 0.42

**z = d –(fy At/fck b)**

Moment of resistance with respect to concrete = compressive force x lever arm

**= 0.36 fck b x z**

Moment of resistance with respect to steel = tensile force x lever arm

**= 0.87 fy At z**

**Maximum depth of neutral axis**

- A compression failure is brittle failure.
- The maximum depth of neutral axis is limited to ensure that tensile steel will reach its yield stress before concrete fails in compression, thus a brittle failure is avoided.
- The limiting values of the depth of neutral axis xm for different grades of steel from strain diagram.

**Limiting value of tension steel and moment of resistance**

- Since the maximum depth of neutral axis is limited, the maximum value of moment of resistance is also limited.
- Mlim with respect to concrete = 0.36 fck b x z
- = 0.36 fck b xm (d – 0.42 xm)
- Mlim with respect to steel = 0.87 fck At (d – 0.42 xm)

**Limiting moment of resistance values, N mm**

**Design of a section**

**Design of rectangular beam to resist a bending moment equal to 45 kNm using (i) M15 mix and mild steel.**

The beam will be designed so that under the applied moment both materials reach their maximum stresses.

**Assume ratio of overall depth to breadth of the beam equal to 2.**

Breadth of the beam = b

Overall depth of beam = D

therefore , D/b = 2

**For a balanced design,**

Factored BM = moment of resistance with respect to concrete

= moment of resistance with respect to steel

= load factor X B.M

= 1.5 X 45

= 67.5 kNm

**For balanced section,**

Moment of resistance Mu = 0.36 fck b xm(d - 0.42 xm)

Grade for mild steel is Fe250

**For Fe250 steel,**

xm = 0.53d

**Mu = 0.36 fck b (0.53 d) (1 – 0.42 X 0.53) d**

= 2.22bd

Since D/b =2 or, d/b = 2 or, b=d/2

Mu = 1.11 d

Mu = 67.5 X 10 Nmm

d=394 mm and b= 200mm

Adopt D = 450 mm , b = 250 mm ,d = 415mm

=(0.85x250x415)/250

= 353 mm

353 mm < 962 mm

In beams the diameter of main reinforced bars is usually
selected between 12 mm and 25 mm.

Provide 2-20mm and 1-22mm bars giving total area

= 6.28 + 3.80

= 10.08 cm > 9.62 cm