### Design of T beam

The flange width for T beam will be selected previously in slab design. The web size will be determined based on the shear requirement. Sufficient area of the web will be chosen to provide a minimum shear capacity. Also, the width of the web can be selected to accommodate the reinforcing bars. The size may preselect based on formwork for architectural requirements or for deflection reasons. The size of the flange is big. Therefore the neutral axis will be located in the flange for the majority of T beams. The step of Designing T beam if the dimension of flange and web are known:

• Calculate Mu for the given loads. Don't forget to factor the given loads.

• Compute Mn, Mn=Mu/ϕ.

• Assuming a Lever Arm z Equal to the Larger of 0.9d or d − (hf/2)

• Compute the trial steel area
As=Mn/(fy*Z)

• Compute the value of a and z

a=(As*fy)/(0.85*fc'*b)

if the a is in the flange, the rectangular equations are applied
z=d-a/2

• calculate the revised value of steel, As with revised value of z

As=Mn/(fy*Z)

• check the value of a and Z again until the values are closed to the one calculated before.

• Checking Minimum Reinforcing
As,min=(3*√fc'/fy)*bw*d but not less than (200*bw*d)/fy

• verify if ϕ=0.9 or no.
if a>hf

• determine the value of "a" using the following equation
Mu=ϕ*(0.85*fc'*a*bw*(d-a/2)+0.85*fc'*(b-bw)*hf*(d-hf/2)) Figure 1

• compute the amount of steel required to balance the compression stress in flange
0.85fc' (b − bw) (hf ) = Asf fy

Asf=(0.85fc'*(b-bw)hf)/fy

• The design strength of the flange
Muf=ϕ*Asf*fy(d-hf/2)

• The remaining moment to be resisted by the web of the T beam and the steel required to balance that value are determined next.
Muw=Mu-Muf

Asw=As*bw*d*ρw

ρw=(0.85*fc'/fy)*(1-√(1-2Rn/0.85*fc')

Rn=Muw/(ϕ*b*d^2)