---
title: "Limiting moment of T-beam"
subject: "Design of RCC Structure"
chapter: 4
key: "semester_7/design_of_rcc_structure:limiting-moment-of-t-beam"
source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/limiting-moment-of-t-beam
site: BCT Engineering
---

# Limiting moment of T-beam

Design of RCC Structure · Chapter 4: Design of beams: Behavior in Flexure

- Asked in: 2081 Baisakh, 6 marks
- Video: [Analysis of T- beam by LSM](https://www.youtube.com/watch?v=uK9-fzaeo7g) — Vijay Srivastava
- 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/limiting-moment-of-t-beam
- Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-4

## Question

Determine the limiting moment of resistance and limiting area of steel for a reinforced concrete T-beam having effective width of flange 1500 mm, effective depth of 590 mm, depth of flange 150 mm and width of web 240 mm. Use M20 grade concrete and Fe415 grade steel.

## Short answer

xu,max = 0.48d = 283.2 mm; Df/d > 0.2 so yf = 0.15xu,max + 0.65Df = 140 mm. Using T-beam formula, Mu,lim = 1056.52 kNm and Ast,lim = 5752 mm².

## Answer

**Given:** $b_f=1500$ mm, $b_w=240$ mm, $D_f=150$ mm, $d=590$ mm, M20, Fe415.

**Step 1: Limiting depth of neutral axis** (Fe415)

$$
x_{u,max}=0.48d=0.48\times590=283.2\ \text{mm}>D_f=150\ \text{mm}
$$

so the neutral axis lies in the web. Also $D_f/d=150/590=0.254>0.2$, therefore the flange is not thin and IS 456 Annex G-2.2 uses the equivalent flange thickness

$$
y_f=0.15x_{u,max}+0.65D_f=0.15\times283.2+0.65\times150=139.98\ \text{mm}
$$

**Step 2: Limiting moment of resistance**

$$
M_{u,lim}=0.36f_{ck}b_wx_{u,max}(d-0.416x_{u,max})+0.45f_{ck}(b_f-b_w)y_f\left(d-\frac{y_f}{2}\right)
$$

$$
\begin{aligned}
M_{u,web}&=0.36\times20\times240\times283.2\times(590-0.416\times283.2)=231.07\ \text{kN·m}\\
M_{u,flange}&=0.45\times20\times(1500-240)\times139.98\times\left(590-\frac{139.98}{2}\right)=825.45\ \text{kN·m}
\end{aligned}
$$

$$
M_{u,lim}=231.07+825.45=1056.52\ \text{kN·m}
$$

**Step 3: Limiting area of steel** (from $C=T$)

$$
A_{st,lim}=\frac{0.36f_{ck}b_wx_{u,max}+0.45f_{ck}(b_f-b_w)y_f}{0.87f_y}=5752\ \text{mm}^2
$$

**Answer:** $M_{u,lim}=1056.52$ kN·m and $A_{st,lim}=5752$ mm$^2$.

## Check yourself

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

1. Why does the limiting NA lie in the web?
   A. xu,max = 283.2 mm > Df = 150 mm
   B. xu,max < Df
   C. bw is small
   D. fck is low
   Answer: A. Since the limiting depth exceeds the flange thickness, the web is partly in compression. (Key point: NA position)

2. Df/d = 0.254 > 0.2. What does this imply?
   A. Use yf = 0.15 xu,max + 0.65 Df instead of Df
   B. Ignore the flange
   C. Use rectangular design
   D. Use xu = Df
   Answer: A. The flange is thick, so the equivalent thickness yf = 139.98 mm is used. (Key point: Df/d check)

3. What are the two parts of Mu,lim?
   A. Web rectangle 0.36 fck bw xu,max (d - 0.416 xu,max) and flange part 0.45 fck (bf - bw) yf (d - yf/2)
   B. Only the web part
   C. Only the flange part
   D. 0.138 fck bf d^2
   Answer: A. They sum to 231.07 + 825.45 = 1056.52 kN·m. (Key point: Moment parts)

4. How is Ast,lim obtained?
   A. From C = T, dividing compression forces by 0.87 fy
   B. From 0.85 b d / fy
   C. From 4% of bD
   D. From Mu/(fy d)
   Answer: A. Total compression force of web and flange divided by 0.87 fy gives 5752 mm^2. (Key point: Ast,lim)

## 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
- [Ultimate moment of L-beam, doubly reinforced](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aultimate-moment-of-l-beam-doubly) — Design of RCC Structure, chapter 4
- [Moment of resistance of doubly reinforced beam](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Amoment-of-resistance-of-doubly-reinforced) — Design of RCC Structure, chapter 4
- [WSM moment of resistance, 4.2 m beam](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Awsm-moment-of-resistance-4-2) — Design of RCC Structure, chapter 2
- [WSM moment of resistance, 300x550 beam](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Awsm-moment-of-resistance-300x550-beam) — Design of RCC Structure, chapter 2
- [Bent-up bars shear, 550 mm effective depth](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Abent-up-bars-shear-550-mm) — Design of RCC Structure, chapter 5, asked 3×

## Related in other subjects

- [Symmetrical I-beam: moment, flange and web share](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Asymmetrical-i-beam-max-moment-flange) — Strength of Materials, chapter 7
- [Principal stresses at web-flange junction](https://www.bctengineer.com/question.md?key=semester_4%2Fstrength_of_materials_mechanical%3Aprincipal-stresses-web-flange-junction) — Strength of Materials, chapter 9
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- [Simply supported I-beam: stress at flange-web junction](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Ai-beam-flange-web-junction-stress) — Strength of Materials, chapter 7