WSM moment of resistance of T-section

Given (from figure): flange width $b_f=2000$ mm, web width $b_w=250$ mm, 3-20 mm dia tension bars, $A_{st}=3\times\frac{\pi}{4}(20)^2=942.5$ mm$^2$. Overall depth 350 mm with 50 mm cover below bars, so effective depth $d=300$ mm. The flange thickness is not legible; assume $D_f=100$ mm (the result is the same for any $D_f>x$ found below). $\sigma_{cbc}=7$, $\sigma_{st}=140$ N/mm$^2$, $m=13.33$.

Step 1: Neutral axis (assuming it lies in the flange, so the section acts as a rectangle of width 2000 mm)

$$\frac{b_f x^2}{2}=mA_{st}(d-x)\ \Rightarrow\ \frac{2000x^2}{2}=13.33\times942.5(300-x)$$ $$x=55.43\ \text{mm}<D_f=100\ \text{mm}$$

The assumption is correct (neutral axis is in the flange).

Step 2: Critical neutral axis

$$k=\frac{13.33\times7}{13.33\times7+140}=0.400,\quad x_c=kd=0.400\times300=120\ \text{mm}$$

Since $x=55.43<x_c$, the section is under-reinforced and steel governs.

Step 3: Moment of resistance

$$M_r=\sigma_{st}A_{st}\left(d-\frac{x}{3}\right)=140\times942.5\times\left(300-\frac{55.43}{3}\right)=37.15\ \text{kN·m}$$

Concrete stress at this moment: $\sigma_c=\dfrac{\sigma_{st}x}{m(d-x)}=2.38$ N/mm$^2$ $<7$, safe.

Answer: $M_r=37.15$ kN·m.