---
title: "Ultimate moment of T-beam (2250 mm flange)"
subject: "Design of RCC Structure"
chapter: 4
key: "semester_7/design_of_rcc_structure:ultimate-moment-of-t-beam-2250"
source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/ultimate-moment-of-t-beam-2250
site: BCT Engineering
---

# Ultimate moment of T-beam (2250 mm flange)

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

- Asked in: 2073 Shrawan, 14 marks
- Video: [Design Moment Strength Calculation of a RC T-beam - Reinforced Concrete](https://www.youtube.com/watch?v=HSjMacgA3Bc) — structurefree
- 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/ultimate-moment-of-t-beam-2250
- Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-4

## Question

Find the ultimate moment resisting capacity of a beam as shown in figure. Consider M 20 and Fe415 grade of concrete and steel. [Figure: T-beam with flange width 2250 mm, flange depth 150 mm, web width 250 mm, overall depth 450 mm, reinforced with 4-25 mm dia bars]

## Short answer

Neutral axis lies in flange at 43.76 mm; the section acts as a rectangular beam of width 2250 mm. Ultimate moment capacity is 270.54 kN·m.

## Answer

**Given (from figure):** $b_f=2250$ mm, $D_f=150$ mm, $b_w=250$ mm, $D=450$ mm, 4-25 mm bars, $A_{st}=4\times\frac{\pi}{4}(25)^2=1963.5$ mm$^2$; M20, Fe415. Effective cover is not given; assume 50 mm, so $d=450-50=400$ mm.

**Step 1: Position of neutral axis.** Assume it lies in the flange ($x_u\le D_f$):

$$
x_u=\frac{0.87f_yA_{st}}{0.36f_{ck}b_f}=\frac{0.87\times415\times1963.5}{0.36\times20\times2250}=43.76\ \text{mm}
$$

$x_u=43.76$ mm $<D_f=150$ mm, so the assumption holds. The section behaves as a rectangular beam of width 2250 mm.

**Step 2: Check for under-reinforcement**

$$
x_{u,max}=0.48d=0.48\times400=192.0\ \text{mm}>x_u
$$

The section is under-reinforced (ductile).

**Step 3: Ultimate moment capacity**

$$
\begin{aligned}
M_u&=0.87f_yA_{st}(d-0.42x_u)\\
&=0.87\times415\times1963.5\times(400-0.42\times43.76)\\
&=270.54\ \text{kN·m}
\end{aligned}
$$

**Answer:** $M_u=270.54$ kN·m.

## Check yourself

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

1. How is xu found, assuming the NA lies in the flange?
   A. xu = 0.87 fy Ast / (0.36 fck bf)
   B. xu = 0.87 fy Ast / (0.36 fck bw)
   C. xu = Df
   D. xu = 0.48 d
   Answer: A. C = T for a rectangular block of width bf gives xu = 43.76 mm. (Key point: NA position)

2. Why is xu = 43.76 mm compared with Df = 150 mm?
   A. To find web shear
   B. If xu <= Df the section behaves as a rectangular beam of width bf
   C. To fix the cover
   D. To compute the flange width
   Answer: B. xu < Df confirms the assumption, so rectangular beam formulas with bf are valid. (Key point: Check of assumption)

3. The cover was not given. What was done?
   A. d was taken as the overall depth 450 mm
   B. d was taken as 2250 mm
   C. Cover was assumed as 50 mm, so d = 450 - 50 = 400 mm
   D. Cover was assumed as 25 mm so d = 425 mm
   Answer: C. Missing data is assumed: effective cover 50 mm gives d = 400 mm. (Key point: Assumed effective depth)

4. Which expression gives Mu = 270.54 kN·m?
   A. 0.36 fck bf xu^2
   B. 0.87 fy Ast (d - 0.48 d)
   C. 0.138 fck bf d^2
   D. 0.87 fy Ast (d - 0.42 xu)
   Answer: D. Under-reinforced, NA in flange: Mu is the tension force times the lever arm d - 0.42xu. (Key point: Ultimate moment)

## Related in Design of RCC Structure

- [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
- [Shear reinforcement of T-beam, 250 kN](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Ashear-reinforcement-of-t-beam-250) — Design of RCC Structure, chapter 5
- [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
- [Limiting moment of T-beam](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Alimiting-moment-of-t-beam) — Design of RCC Structure, chapter 4
- [Design T-beam with 150 mm slab](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Adesign-t-beam-with-150-mm) — Design of RCC Structure, chapter 4
- [WSM moment of resistance, 250x450 beam](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Awsm-moment-of-resistance-250x450-beam) — Design of RCC Structure, chapter 2

## 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
- [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
- [Reinforced concrete column stresses in steel and concrete](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Arc-column-8-bars) — Strength of Materials, chapter 3