Manual Beam Design

Beam design

1- Data 

L=3000mm

Dead load=6KN/m

Live Load=8KN/m

Finished load=0.75KN/m

Wall Support=230Mm

Concrete grade=M20, Steel grade=fe₄₁₅

2- Efectve span of beam 

Effective Span =c/c of the support

= 3230 mm

3- Size of beam 

Effective depth=Span/12

=269.16mm , Say 270mm

Breadth=1/2d =135mm

Clear cover=25mm,Use 16 mm ø

D=303 mm, Say 310 mm

D=310mm

d = 277mm, Say 280mm

d=280mm

4- Load calculations 

Self Weight =1× 0.31× 0.135× 25=1.046KN/m

Live Load = 8KN/m

Dead Load =6KN/m

Finished load =0.75KN/m

T0tal Load =15.796KN/m

Factored Load =23.694KN/m, Factored BM=Wl²/8 = 30.89KN/m

5- To get AST 

Ast(Required) = 388.33mm²

Numbers of rods = 2nos

Provide 2nos of 16mmø rods

6- Check for minimum and maximum AST 

AST_min=(0.85/F_y) bd =77.421mm²

AST_max=0.04 bd=1512mm²

7- Check for shear 

Nominal shear stress < permissible shear stress

ڂ_v =K ڂ_c ڂ & _v=V_u/bd

V_u=38.26KN , ڂ_v=1.012N/mm²

Permissible shear stress (K ڂ_c)

100Ast/bd=1.026N/mm²

Refer From Table 19 for I.S. 456

ڂ_c = 0.625, ڂ_cmax=2.8 N/mm²

ڂ _v > ڂ_c > ڂ_cmax

K ڂ_c=1×0.625=0.652N/mm²

8- Shear reinforcement 

V_us =V_u – ڂ_cbd

V_us =14.625× 10³ N

Provided 8mmø rods @ 2 legged Stirrups

1) S_v= ( 0.87 F_y Asv d/ V_us)

=694.41mm, Say 690 mm

2) S_v= ( 0.8 7 F_y Asv / bd)

=96.01mm < Say 100mm

3) 0.75 d= 210mm

4) 450mm

Provide 8mmø rods & 2 Legged Stirrups @ 100mm c/c

9- Check for deflection 

F_S=O.58 f_y

F_s=240.7N/mm² [M.F=2, BV=20]

Effective depth=Span/(BV×MF)

=80.75mm

80.75mm < 280mm

Hence it is safe