Question

A isolated T-beam having cross-sectional dimensions shown in figure has a span of $6$ $m$. The grade of material used are $M25$ and $Fe500$ respectively.Moment of resistance of the beam is:

• A. $452$ $kN-m$
• B. $464$ $kN-m$
• C. $478$ $kN-m$
• D. $485$ $kN-m$

Answer 1

The correct option is C $478$ $kN-m$

Effective width of flange $=\frac{L_0}{\frac{L_0}{b}+4}+b_w\ngtr b_f$
$b_f=\frac{6000}{\frac{6000}{1200}+4}+300=966.67mm\ngtr 1200mm$
$\therefore b_f=966.67mm$
Let`s assume $x_u<120mm$
$0.362f_{ck}{b}_f.x_u=0.87f_y{A}_{st}$
$0.362\times 25\times 966.67x_u=0.87\times 500\times 4\times \frac{\pi }{4}\times {25}^2$
$x_u=97.6mm<120mm$, that means our assumption was right.
$\therefore M_R=0.87f_y{A}_{st}(d-0.416x_u)$
$=[0.87\times 500\times 4\times \frac{\pi }{4}\times {25}^2(600-0.416\times 97.6\left)\right]\times {10}^{-6}kN-m$
$=477.8kN-m$