---
title: "WSM moment of resistance of T-section"
subject: "Design of RCC Structure"
chapter: 2
key: "semester_7/design_of_rcc_structure:wsm-moment-of-resistance-of-t"
source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/wsm-moment-of-resistance-of-t
site: BCT Engineering
---

# WSM moment of resistance of T-section

Design of RCC Structure · Chapter 2: Working Stress Method of Design

- Asked in: 2067 Asar (old course), 8 marks
- Video: [Depth of neutral Axis and Moment of resistance | Civil Engineering](https://www.youtube.com/watch?v=YW9yMhVQzf8) — cwill structures
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/wsm-moment-of-resistance-of-t
- Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-2

## Question

Determine the moment of resistance of the section shown below. Take $\sigma_{cbc}$ = 7 N/mm$^2$ and $\sigma_{st}$ = 140 N/mm$^2$. [Figure: T-section with flange width 2000 mm, web width 250 mm, 3-20 mm dia. tension bars; dimensions 300 mm and 50 mm marked on the right side of the web (as printed, 300 mm is the depth and 50 mm the cover below the bars)]

## Short answer

Moment of resistance is 37.15 kN·m. Neutral axis lies in flange, section under-reinforced, steel governs.

## Answer

**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.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How is the neutral axis first located for the T-section?
   A. Assume it lies in the web and use web width 250 mm
   B. Assume it lies in the flange and treat the section as a rectangle of width 2000 mm
   C. Take x = d/2
   D. Take x equal to the critical depth
   Answer: B. A wide flange usually keeps the NA inside it, so the section acts as a 2000 mm wide rectangle; the result is then checked against D_f. (Key point: Assumption for NA)

2. Why is the section under-reinforced?
   A. x = 55.43 mm is less than the critical depth x_c = 120 mm
   B. x = 55.43 mm is greater than D_f
   C. Ast is less than 1000 mm^2
   D. sigma_c exceeds 7 N/mm^2
   Answer: A. When the actual NA depth is smaller than kd, steel reaches 140 N/mm^2 first, so steel governs the moment. (Key point: Under-reinforced check)

3. Which expression gives the moment of resistance here?
   A. sigma_cbc * b * x * (d - x/3)
   B. sigma_st * Ast * (d - x/3)
   C. sigma_st * Ast * d
   D. 0.5 * sigma_cbc * b * x^2
   Answer: B. For an under-reinforced section, steel force times the lever arm d - x/3 gives Mr = 140 x 942.5 x (300 - 55.43/3) = 37.15 kN·m. (Key point: Moment formula)

## Related in Design of RCC Structure

- [Ultimate moment of T-beam (2250 mm flange)](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aultimate-moment-of-t-beam-2250) — Design of RCC Structure, chapter 4
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## Related in other subjects

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