RCC & Prestressed Concrete - Design of Beam & Design of Slabs Complete Study Notes

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

f_d = design value of strength

For steel

Singly Reinforced Beam

1. Limiting depth of the neutral axis (x_{u, lim})
   

Here d = effective depth of beam

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

Some special cases

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

Doubly Reinforced Section

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

1. Ultimate moment of resistance

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

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., X_u < D_f

(a) for Xu

(b) Ultimate moment of resistance

Case-2: When NA is in web area (X_u > D_f)

Case (a) when X_u > D_f 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

(b_f – b_w) D_f portion of flange is converted into (b_f – b_w)y_f section for which stress is taken constant throughout the section is 0.45 f_ck.

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, l_y = length of longer span

l_x = 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 (V_X)

At longer edge (V_y)

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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