# Types of problem in T Beam | Working Stress Method

Learn : Types of problem in T Beam :  Procedure for Determining the Moment of Resistance of the Given Section in T beam,Find Stresses in Steel and Concrete in T beam,To design the section for given loads.Design of T beam

## TYPES OF PROBLEM IN T BEAM

1. To determine the moment of resistance of the given section in T beam.
2. To Find Stresses in Steel and Concrete in T beam.
3. To design of T beam.

### Procedure for Determining the Moment of Resistance of the Given Section in T beam

Given : Dimensions of the section i.e., bw,  bf,  Df,  d.

Area of steel Ast

Material – grade of concrete and steel

(i)        Determine σcbc and σst from the Tables 2.1 and 2.2 for given grades of concrete and steel Calculater modular ratio (m)

$m=\frac{280}{3\sigma_{cbc}}$

(ii)       Determine critical neutral axis (nc)

$\frac{m.\sigma_{cbc}}{\sigma_{st}}=\frac{n_{c}}{d-n_{c}}$

(iii)     Determine actual neutral axis (n) : To reduce the trial of calculations, it is better to assume n>Df.

$\therefore b_{f}.D_{f}\left ( n-\frac{D_{f}}{2} \right )=m.A_{st}(d-n)$

If n comes out to be less than Df on solving the above equation, then use following equation to calculate n.

$\therefore b_{f}\times \frac{n^{2}}{2}=m.A_{st}(d-n)$

(iv)      Compare n and nc Moment of Resistance of the Given Section in T beam

(i)        If n<nc, then under reinforced section

(ii)       If n>nc, then over reinforced section

(v)       Determine moment of resistance using appropriate formula after determining the stress in following ways.

(a)       For under reinforced section, σst is known and σcbc can be calculated as follows :

$\therefore \frac{m.\sigma_{cbc}}{\sigma_{st}}=\frac{n}{d-n}$

(b)       Determine σc and ȳ

$\sigma’_{c}=\sigma_{cbc}\left ( \frac{n-D_{f}}{n} \right )$

$\bar y=\left ( \frac{\sigma_{cbc}+2\sigma’_{c}}{\sigma_{cbc}+\sigma’_{c}} \right )\frac{D_{f}}{3}$

(c)       For over reinforced section, σcbc is known hence calculating σc.

$\sigma’_{c}=\sigma_{cbc}\left ( \frac{n-D_{f}}{n} \right )$

### Problem to Find Stresses in Steel and Concrete in T beam

Given :

Dimension of the beam

Area of steel

Maximum B.M. or load on the beam

Determine actual neutral axis

Write σcbcin terms of σc

$\sigma’_{c}=\sigma_{cbc}\left ( \frac{n-D_{f}}{n} \right )$

Find ȳ

$\bar y=\left ( \frac{\sigma_{cbc}+2\sigma’_{c}}{\sigma_{cbc}+\sigma’_{c}} \right )\times\frac{D_{f}}{3}$

Find moment of resistance (Mr)

$M_{r}=b_{f}.D_{f}\left ( \frac{\sigma_{cbc}+\sigma’_{c}}{2} \right )(d-\bar y)$

Equate moment of resistance to maximum bending moment and find σcbc

Find σst

$\frac{m.\sigma_{cbc}}{\sigma_{st}}=\frac{n}{d-n}$.

### Design of T Beam

In Design of T beam of problem, the dimensions of the beam and the area of steel is to be determined.

Given : Maximum bending moment or loading

Materials i.e., grade of concrete and steel span of the beam.

1. Calculate design constants (m, k.j)
2. Assume total depth of the beam as $\frac{1}{12} to \frac{1}{15}$ of the span and calculate effective depth.
3. Determine the maximum bending moment coming on the beam due to given loads.
4. Determine area of steel required.

$A_{st}=\frac{M}{\sigma_{st}jd}$

1. Check the trial section as follows :

(i)        Determine actual neutral axis depth (n)

(ii)       Write σc in terms of σcbc and find ȳ.

(iii)     Write Mc in terms of σcbc.

(iv)      Equating M and Mr and calculate σcbcand σst

(v)       If the values of σcbc and σst are less than the permissible stresses, then design is OK, but if not, then revise the trial section and repeat steps from 2 to 5.

1. Design for shear
2. Check for development length.