---
title: "Bent-up bars shear, 550 mm effective depth"
subject: "Design of RCC Structure"
chapter: 5
key: "semester_7/design_of_rcc_structure:bent-up-bars-shear-550-mm"
source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/bent-up-bars-shear-550-mm
site: BCT Engineering
---

# Bent-up bars shear, 550 mm effective depth

Design of RCC Structure · Chapter 5: Design for Shear and Torsion

- Asked in: 2076 Chaitra, 10 marks
- Video: [Design for Shear Reinforcement in Beams - Problems](https://www.youtube.com/watch?v=9esi2xeKCNM) — Stan Academy
- 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/bent-up-bars-shear-550-mm
- Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-5

## Question

A RC beam has an effective depth of 550 mm and a breadth of 300 mm. It contains 4 no. of 20 mm dia bars out of which two bars are to be bent up at 45$^\circ$ near end of the support. Calculate the shear resistance of bent up bars and the additional stirrups needed if the factored shear force due to uniformly distributed load is 425 kN at the support. The span of the beam is 6 m. Use M20 concrete and Fe415 grade (TOR) steel.

## Short answer

At d from support, Vud=347.1 kN and Vus=277.3 kN. Bent-up bars give 160.4 kN but are limited to 138.7 kN; balance is 138.7 kN. Provide 10 mm 2-legged stirrups at 220 mm c/c near the supports.

## Answer

**Given:** $b=300$ mm, $d=550$ mm, 4-20 mm bars (2 bent up at 45$^\circ$), $V_u=425$ kN at the support, $L=6$ m, M20, Fe415.

**Step 1: Shear force.** Reaction $=w_uL/2=425$ kN, so $w_u=\dfrac{2\times425}{6}=141.67$ kN/m. At $d$ from the face of support:

$$
V_{u,d}=425-141.67\times0.55=347.1\ \text{kN}
$$

Check: $\tau_v=\dfrac{425\times10^3}{300\times550}=2.576$ N/mm$^2<\tau_{c,max}=2.8$ N/mm$^2$, so the section is adequate.

**Step 2: Concrete strength.** Straight bars: 2-20, $A_{st}=628.3$ mm$^2$.

$$
p_t=\frac{100\times628.3}{300\times550}=0.381\%,\quad\tau_c=0.423\ \text{N/mm}^2,\quad V_c=69.8\ \text{kN}
$$

$V_{us}=V_{u,d}-V_c=347.1-69.8=277.3$ kN.

**Step 3: Shear resistance of the bent-up bars** ($A_{sb}=2\times314.16=628.3$ mm$^2$):

$$
V_{us,bent}=0.87f_yA_{sb}\sin45^\circ=0.87\times415\times628.3\times0.7071=160.4\ \text{kN}
$$

By IS 456 cl. 40.4 this should not exceed half of the total shear reinforcement load: $0.5\times277.3=138.7$ kN. Hence bent-up bars are credited with 138.7 kN.

**Step 4: Additional stirrups** for $V_{us}=277.3-138.7=138.7$ kN, using 10 mm 2-legged stirrups ($A_{sv}=157.1$ mm$^2$):

$$
s_v=\frac{0.87\times415\times157.1\times550}{138.7\times10^3}=225\ \text{mm}
$$

Limits: $0.75d=412$ mm, 300 mm, $\dfrac{0.87f_yA_{sv}}{0.4b}=473$ mm. 

**Answer:** Shear resistance of bent-up bars $=160.4$ kN (limited to 138.7 kN by the code); additional stirrups: 10 mm 2-legged @ 220 mm c/c near the supports.

## Check yourself

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

1. How is wu found from Vu = 425 kN at the support?
   A. 425/6
   B. 425x6/2
   C. 425/3 x 6
   D. wu = 2x425/6 = 141.67 kN/m
   Answer: D. Reaction is wuL/2. (Key point: UDL from reaction)

2. What is the shear at the critical section?
   A. 347.1 kN = 425 - 141.67x0.55
   B. 425 kN
   C. 425 + 77.9 kN
   D. 141.67 kN
   Answer: A. Critical section at d from the face. (Key point: Design shear)

3. Bent bars give 160.4 kN. What is credited?
   A. 160.4 kN
   B. 138.7 kN, half of Vus = 277.3 kN
   C. 277.3 kN
   D. 69.8 kN
   Answer: B. Limit is 50% of Vus. (Key point: Bent bar credit)

4. What stirrups carry the balance?
   A. 8 mm at 300 mm
   B. None
   C. Balance 138.7 kN gives 10 mm 2L at about 220 mm c/c
   D. 10 mm at 412 mm
   Answer: C. sv = 0.87fy Asv d/Vus = 225 mm, rounded to 220. (Key point: Stirrups)

## Close variants set in other exams

- [Bent-up bars, 600 mm effective depth](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Abent-up-bars-600-mm-effective) — Design of RCC Structure, chapter 5, asked 2×
- [Bent-up bars and stirrups, 5-25 mm bars](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Abent-up-bars-and-stirrups-5) — Design of RCC Structure, chapter 5, asked 2×

## Related in Design of RCC Structure

- [Shear at bent-up section, 8 mm stirrups](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Ashear-at-bent-up-section-8) — Design of RCC Structure, chapter 5
- [Bent-up bars in shear strength](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Abent-up-bars-in-shear-strength) — Design of RCC Structure, chapter 5
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