# RCC : Design of Beam & Design of slabs

By Saurabh Kumar|Updated : August 30th, 2021

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## Design of Beam

### Design stress-strain curve at ultimate state

Design value of strength

For concrete

where,

Partial factor of safety for concrete = 1.5

fd = design value of strength

For steel

### Singly Reinforced Beam

1. Limiting depth of the neutral axis (xu, lim)

Here d = effective depth of beam

1. Actual depth of neutral axis (Xu)
2. Lever arm = d – 0.42 Xu
3. Ultimate moment of resistance

### Some special cases

1. When Xu < Xu,lim
It is an under-reinforced section
2. When Xu = Xu,lim
It is balanced section
3. When Xu > Xu,lim
It is over reinforced section. In this case, keep Xu limited to Xu,lim and moment of resistance of the section shall be limited to limiting moment of resistance, (Mu,lim)

### Doubly Reinforced Section

1. Limiting depth of neutral axis
2. For actual depth of neutral axis (Xu)

1. Ultimate moment of resistance

where fSC = stress in compression steel and it is calculated by strain at the location of compression steel (fSC)

### T-Beam

1. Effective width of flange
Discussed in WSM
2. Limiting depth of neutral axis

Singly reinforced T-Beam

Case-1: When NA is in flange area

i.e., Xu < Df

(a) for Xu

(b) Ultimate moment of resistance

Case-2: When NA is in web area (Xu > Df)

Case (a) when Xu > Df and

i.e., depth of flange in less than the depth of the rectangular portion of stress diagram.

1. For actual depth of neutral ais

1. Ultimate moment of resistance

Special Case (2): When Xu > Df and

i.e., depth of flange is more than depth of rectangular portion of stress diagram.

### As per IS 456 : 2000

(bf – bw) Df portion of flange is converted into (bf – bw)yf section for which stress is taken constant throughout the section is 0.45 fck.

As per IS 456 : 2000

1. For actual depth of neutral axis

DESIGN OF SLAB

### One way slab

(i) Ly/Lx ratio is less than 2

where, ly = length of longer span

lx = length of shorter span

(ii) Slab is supported only on two edges.

Design of One way slab

### Two way slab

(i)  Ly/Lx ratio is more than 2

(ii) Slab is supported on all edges.

Design of two way slab

1. Grasoff Ranking method
It is used for corners not held down position.
It is purely simply supported case.

(i)

(ii) Moment in x-direction

Moment in y-direction

(iii) Shear force

At shorter edge (VX)

At longer edge (Vy)

1. Design of slab with corner held down position

(a) Pigeauds method:

where, the values of  are read from table

(b) I.S. code method

The values of  read from table (page 91, IS : 456-2000)

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