--- title: "Shear reinforcement and punching shear in footings" subject: "Design of RCC Structure" chapter: 5 key: "semester_7/design_of_rcc_structure:shear-reinforcement-and-punching-shear-in" source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/shear-reinforcement-and-punching-shear-in site: BCT Engineering --- # Shear reinforcement and punching shear in footings Design of RCC Structure · Chapter 5: Design for Shear and Torsion - Asked in: 2067 Asar (old course), 8 marks - Video: [Punching Shear | Two way Shear | Punching Shear in footing | Two way Shear in footing](https://www.youtube.com/watch?v=fkk6zg8aPOU) — Civil Engineering Mastery - 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/shear-reinforcement-and-punching-shear-in - Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-5 ## Question Write down the procedure for design of shear reinforcement. Also explain how the isolated footings are designed under punching shear. ## Short answer Beam: at d from support compute τv=Vu/(bd)≤τc,max; if τv≤τc provide minimum stirrups; else Vus=Vu−τcbd, sv=0.87fyAsvd/Vus≤0.75d,300mm. Footing: check punching at d/2 from column face; force Vu=qu[BL−(a+d)(b+d)], perimeter b0=2(a+b+2d); τv=Vu/(b0d)≤ksτc, τc=0.25√fck, ks=0.5+βc≤1. Increase depth if not satisfied. ## Answer #### Procedure for design of shear reinforcement (beam) 1. Compute factored shear $V_u$ at the critical section (distance $d$ from the support face). 2. Nominal shear stress $\tau_v=\dfrac{V_u}{bd}$; check $\tau_v\le\tau_{c,max}$. 3. Find $\tau_c$ from IS 456 Table 19 using $p_t=\dfrac{100A_{st}}{bd}$ and $f_{ck}$. 4. If $\tau_v\le\tau_c$, provide minimum stirrups: $\dfrac{A_{sv}}{b\,s_v}\ge\dfrac{0.4}{0.87f_y}$. 5. If $\tau_v>\tau_c$, shear carried by steel $V_{us}=V_u-\tau_cbd$, then $$ s_v=\frac{0.87f_yA_{sv}d}{V_{us}}\le\min(0.75d,\ 300\ \text{mm}) $$ 6. Provide closer spacing near supports and wider spacing where shear is small. #### Punching (two-way) shear in isolated footings A column punches through the footing along a truncated pyramid. IS 456 (cl. 31.6) checks it at a section at **$d/2$ from the face of the column** (critical perimeter $b_0$), in addition to one-way shear at $d$ from the face. ```text plan section +--------------+ col | +--------+ | ____|__|____ | | col | | d/2 \ / 45 | +--------+ | |<--->|____/__\____ | critical | critical perimeter +--------------+ ``` **Steps** 1. Factored upward soil pressure $q_u=P_u/(\text{footing area})$ (net, excluding self weight). 2. Punching shear force: $V_u=q_u\left[BL-(a+d)(b+d)\right]$ for a column $a\times b$. 3. Critical perimeter: $b_0=2[(a+d)+(b+d)]$. 4. Nominal punching shear stress: $\tau_v=\dfrac{V_u}{b_0\,d}$. 5. Permissible punching shear stress: $\tau_c'=k_s\tau_c$, where $k_s=0.5+\beta_c\le1$ ($\beta_c$ = short side/long side of column) and $\tau_c=0.25\sqrt{f_{ck}}$. 6. Condition: $\tau_v\le\tau_c'$. If not satisfied, increase the depth $d$ of the footing (shear reinforcement is not normally used in footings). 7. Also check one-way (beam) shear at distance $d$ from the column face with $\tau_c$ from Table 19 for the footing steel percentage. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Where is punching shear checked? A. At d from face B. At column face C. At footing edge D. At d/2 from column face Answer: D. Critical perimeter b0 at d/2 around the column. (Key point: Critical section) 2. How is Vu found? A. qu x [BL - (a+d)(b+d)] B. qu x BL C. qu x ab D. qu x d Answer: A. Upward net pressure outside the critical perimeter. (Key point: Punching force) 3. What is permissible punching stress? A. 0.25 fck B. ks tau_c with ks = 0.5 + beta_c <= 1, tau_c = 0.25 sqrt(fck) C. 0.87 fy D. ks = 2 Answer: B. beta_c is short/long column side ratio. (Key point: Permissible stress) 4. If tau_v exceeds permissible? A. Add stirrups normally B. Reduce column C. Increase footing depth D. Ignore Answer: C. Shear steel is not normally used in footings. (Key point: If fails) ## Related in Design of RCC Structure - [Design reinforcement under torsion, 400x750](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Adesign-reinforcement-under-torsion-400x750) — Design of RCC Structure, chapter 5 - [Design shear reinforcement of flanged beam](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Adesign-shear-reinforcement-of-flanged-beam) — Design of RCC Structure, chapter 5 - [Shear reinforcement, 300x500 beam, 370 kN](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Ashear-reinforcement-300x500-beam-370-kn) — Design of RCC Structure, chapter 5 - [Shear reinforcement, 250x500 beam, Fe500](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Ashear-reinforcement-250x500-beam-fe500) — Design of RCC Structure, chapter 5 - [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 - [Design of member for bending, shear, torsion](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Adesign-of-member-for-bending-shear) — Design of RCC Structure, chapter 5, asked 6× ## Related in other subjects - [General, local and punching shear failure](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Amodes-shear-failure) — Foundation Engineering, chapter 6, asked 4× - [Proportioning footings for uniform settlement](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aproportion-footings-uniform-settlement) — Foundation Engineering, chapter 6, asked 2× - [Factors for selection; strap and combined footings](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Afactors-strap-combined) — Foundation Engineering, chapter 1 - [Design procedure of sloping glacis weir bay](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Asloping-glacis-weir-bay-design-steps) — Irrigation and Drainage Engineering, chapter 5