--- title: "Isolated footing 400x400, service moment 120 kNm" subject: "Design of RCC Structure" chapter: 11 key: "semester_7/design_of_rcc_structure:isolated-footing-400x400-service-moment-120" source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/isolated-footing-400x400-service-moment-120 site: BCT Engineering --- # Isolated footing 400x400, service moment 120 kNm Design of RCC Structure · Chapter 11: Design of Footings - Asked in: 2081 Bhadra, 12 marks - Video: [Design of a Square Footing](https://www.youtube.com/watch?v=jYCc0QFKwR4) — 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/isolated-footing-400x400-service-moment-120 - Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-11 ## Question Design an isolated footing for a column of size 400 mm x 400 mm with 8-25 mm diameter bars as longitudinal reinforcement in order to carry a service axial load of 1200 kN and service moment of 120 kNm. Take the safe bearing capacity of soil as 150 kN/m$^2$. Use M20 concrete and Fe 415 steel. ## Short answer Adopt a 4.2 m x 2.4 m footing, overall depth 800 mm (d=740 mm). Long-direction reinforcement: 16 mm bars @140 mm c/c; short-direction: central band 16 mm @160 mm c/c and outer strips 16 mm @180 mm c/c. One-way and punching shear checks are satisfied. ## Answer #### Data and assumptions - Column 400 mm × 400 mm (long side $a=400$ mm along the footing length); footing concrete M20, steel Fe415; column concrete M20; column bars 8-25 mm. - Service load $P = 1200$ kN, service moment $M = 120$ kN·m. - Allowable (safe) bearing capacity of soil = 150 kN/m². - Clear cover 50 mm for the footing (IS 456 cl. 26.4.2.2); effective depth $d = D - 60$ mm (cover + half bar). Load factor 1.5. #### Size of footing Weight of footing and backfill is taken as 10% of the column load. $$ A_{req} = \frac{1.1\,P}{q_a} = \frac{1.1 \times 1200.0}{150} = 8.80\ \text{m}^2 $$ Eccentricity $e = M/P = 120.0/1200.0 = 0.100$ m, which is less than $L/6$, so there is no tension under the base. The size is chosen so that $$ q_{max} = 1.1\frac{P}{BL}\left(1 + \frac{6e}{L}\right) \le q_a $$ Try $L \times B = 4.2 \times 2.4$ m ($A = 10.08$ m²): $q_{max} = 149.7$ kN/m² $\le 150.0$ and $q_{min} = 112.2$ kN/m² $> 0$. **Safe.** #### Factored soil pressure $P_u = 1.5 \times 1200.0 = 1800.0$ kN, $M_u = 180.0$ kN·m. $p_u = \dfrac{P_u}{BL}\left(1 \pm \dfrac{6e}{L}\right)$: $p_{u,max} = 204.1$ kN/m², $p_{u,min} = 153.1$ kN/m² (average 178.6 kN/m²). Self-weight does not cause bending in the footing, so it is excluded. #### Bending moments and reinforcement Cantilever projections from the column face: along $L$: $(4200 - 400)/2 = 1900$ mm; along $B$: $(2400 - 400)/2 = 1000$ mm. Along $L$ (critical section at the column face on the side of maximum pressure): the pressure is 181.0 kN/m² at the face and 204.1 kN/m² at the edge, so per metre width $M = 181.0 \times \dfrac{1.9^2}{2} + (204.1 - 181.0) \times \dfrac{1.9^2}{3} = 326.7 + 27.8 = 354.5$ kN·m/m, and $M_{u,L} = 354.5 \times 2.4 = 850.8$ kN·m. Along $B$ (average pressure): $M_{u,B} = 375.0$ kN·m. Required depth for flexure: $M_{u,lim} = 0.138 f_{ck} b d^2$ is far larger than the moment for $d = 740$ mm, so the depth is governed by shear (one-way or punching). Trial **$D = 800$ mm, $d = 740$ mm**, found by the shear checks below. $A_{st} = \dfrac{0.5 f_{ck}}{f_y}\left[1 - \sqrt{1 - \dfrac{4.6 M_u}{f_{ck} b d^2}}\right] b d$; minimum steel = 0.12% of $bD$. | Direction | $M_u$ (kN·m) | $A_{st}$ req (mm²) | Provide | $A_{st}$ prov (mm²) | |---|---|---|---|---| | Along $L$ (width $B$) | 850.8 | 3315 | 16 mm @ 140 c/c | 3447 | | Along $B$ (width $L$) | 375.0 | 4032 (minimum) | 16 mm, banded (below) | 5027 | For the rectangular footing, the short-direction steel is placed in a central band of width $B = 2400$ mm in the proportion $\dfrac{2}{\beta+1} = \dfrac{2}{1.75+1} = 0.727$ (IS 456 cl. 34.3.1), where $\beta = L/B$. - Central band: $0.727 \times 4032 = 2932$ mm² → 16 mm @ 160 mm c/c (15 bars, 3016 mm²). - Each outer strip (900 mm wide): remaining steel 550 mm² or minimum 0.12% = 864 mm², whichever is more → 16 mm @ 180 mm c/c (5 bars, 1005 mm²). #### Check for one-way shear (at distance $d$ from the column face) - Along $L$ side: $V_u = 548.5$ kN, $\tau_v = \dfrac{V_u}{B d} = 0.309$ MPa; $p_t = 0.194\%$, $\tau_c = 0.315$ MPa (Table 19). $\tau_v < \tau_c$, safe. - Along $B$ side: $V_u = 195.0$ kN, $\tau_v = 0.063$ MPa; $p_t = 0.16\%$, $\tau_c \approx 0.29$ MPa. Safe. #### Check for two-way (punching) shear (at $d/2$ from the column face) - Perimeter $b_o = 2[(a + d) + (c + d)] = 2[(400+740) + (400+740)] = 4560$ mm - $V_u = P_u - p_u (a+d)(c+d) = 1800.0 - 178.6 \times 1.140 \times 1.140 = 1567.9$ kN (average pressure; the effect of moment transfer is neglected). - $\tau_v = \dfrac{V_u}{b_o d} = 0.465$ MPa; $k_s = 0.5 + \beta_c = 1.00$, $\tau_c' = k_s \times 0.25\sqrt{f_{ck}} = 1.118$ MPa. $\tau_v < \tau_c'$, **safe**. #### Development length $L_d = \dfrac{0.87 f_y \phi}{4\tau_{bd}}$, $\tau_{bd} = 1.92$ MPa (M20, deformed bars): 16 mm bars (both directions) → $L_d = 752$ mm. Available length from column face (less 50 mm end cover): 1850 mm along $L$, 950 mm along $B$. **Satisfied** in both directions. #### Bearing stress and transfer of load from column Column area $A_2 = 400\times400 = 0.160$ m². Bearing stress $= P_u/A_2 = 11.25$ MPa. Permissible bearing stress: column concrete $0.45 f_{ck} = 9.00$ MPa; footing concrete $0.45 f_{ck}\sqrt{A_1/A_2}$ with $\sqrt{A_1/A_2} \le 2$ gives up to 18.00 MPa. The lesser, 9.00 MPa, governs. Capacity of bearing = 1440 kN $<$ $P_u = 1800$ kN, so the excess 360 kN must be carried by dowels: $A_{s,dow} = \dfrac{360000}{0.87 f_y} = 997$ mm²; the column bars (8-25 mm, 3927 mm²) are continued into the footing as dowels - adequate. Dowel length in compression $L_{dc} = \dfrac{0.87 f_y\phi}{4 \times 1.25\,\tau_{bd}} = 940$ mm (and the same lap with the column bars). Available depth in footing = 800 - 50 - 32 = 718 mm $< L_{dc}$; dowels are bent at the bottom with 90° bends. #### Detailing ```text PLAN (4.2 m x 2.4 m; L horizontal) +--------------------------------------------+ | | | | | | | | | | | | | |--+---+---+---+---+---+---+---+---+---+---+-| | | | | | | | | | | | | | |--+---+---+---+-+----------+--+---+---+---+-| | | | | | | column | | | | | | |--+---+---+---+-+----------+--+---+---+---+-| | | | | | | | | | | | | | |--+---+---+---+---+---+---+---+---+---+---+-| | | | | | | | | | | | | | +--------------------------------------------+ <-0.9 m-><---central band 2.4 m---><-0.9 m-> - = 16 mm @ 140 c/c (along L) | = 16 mm along B: @ 160 c/c in central band, @ 180 c/c in outer strips ELEVATION | column | | | +----------------+----------+----------------+ | (dowels) | D = 800 mm | o o o o o o o o o o o o o o | bottom mesh, 50 mm cover +--------------------------------------------+ <----------------- 4200 mm ------------------> ``` - Bottom mesh: 16 mm @ 140 c/c along $L$ (lower layer); along $B$ (upper layer), 16 mm @ 160 c/c in the central 2.4 m band and 16 mm @ 180 c/c in each 0.9 m outer strip; 50 mm clear cover; dowels 8-25 mm. **Answer:** Footing 4.2 m × 2.4 m × 800 mm thick; 16 mm @ 140 c/c along the length; along the width, 16 mm @ 160 c/c in the central 2.4 m band and 16 mm @ 180 c/c in the outer strips. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For P = 1200 kN, M = 120 kNm, the footing 4.2 m x 2.4 m is accepted because: A. Its area is larger than 8.80 m^2 only B. q_max = 149.7 kN/m^2 is not more than 150 and q_min is positive C. q_min equals q_max D. The moment is neglected in the check Answer: B. The footing is safe when q_max = 1.1(P/BL)(1 + 6e/L) does not exceed the safe bearing capacity and q_min stays above zero. (Key point: Soil pressure with moment) 2. In the rectangular footing, what fraction of the short-direction steel is placed in the central band of width B? A. 0.5 B. 1/beta C. 2/(beta + 1) = 0.727 D. (beta + 1)/2 Answer: C. IS 456 cl. 34.3.1 puts 2/(beta+1) of the short-direction steel in the central band, with beta = L/B = 1.75. (Key point: Distribution of short-direction steel) 3. Bearing capacity (1440 kN) is less than Pu = 1800 kN. How is the excess handled? A. The excess 360 kN is carried by dowels of area 360000/(0.87 fy) = 997 mm^2 B. The footing area is increased C. The column grade is increased only D. Nothing is needed because the footing concrete is stronger Answer: A. Load beyond bearing capacity must go through reinforcement; the 8-25 mm column bars continued as dowels give 3927 mm^2, which is adequate. (Key point: Load transfer by bearing) 4. Dowel length needed (940 mm) exceeds the footing depth available (718 mm). What is done? A. The column size is increased B. Dowels are cut short C. Dowels are bent at the bottom with 90 degree bends D. Footing depth is ignored Answer: C. Where straight development is not available, the dowels are given 90 degree bends at the bottom to provide anchorage. (Key point: Dowel anchorage) ## Close variants set in other exams - [Isolated footing 450x450, service moment 110 kNm](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aisolated-footing-450x450-service-moment-110) — Design of RCC Structure, chapter 11, asked 2× ## Related in Design of RCC Structure - [Isolated footing 400x400, 1200 kN service](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aisolated-footing-400x400-1200-kn-service) — Design of RCC Structure, chapter 11 - [Footing 300x400 column, factored moment 120 kNm](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Afooting-300x400-column-factored-moment-120) — Design of RCC Structure, chapter 11 - [Isolated square footing, 600 kN and 50 kNm](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aisolated-square-footing-600-kn-and) — Design of RCC Structure, chapter 11, asked 2× - [Isolated footing 450x450, 1600 kN service](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aisolated-footing-450x450-1600-kn-service) — Design of RCC Structure, chapter 11 - [Isolated square footing, 650 kN service](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aisolated-square-footing-650-kn-service) — Design of RCC Structure, chapter 11, asked 2× - [Footing 350x350, 8-16 mm bars, reversible moment](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Afooting-350x350-8-16-mm-bars) — Design of RCC Structure, chapter 11 ## Related in other subjects - [Brick column design for 80 kN axial load](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Abrick-column-80kn-roof) — Concrete Technology and Masonry Structure, chapter 8 - [Check 25 cm x 25 cm Sal column, 200 kN + 20 kNm](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Atimber-column-sal-25x25-200kn-20knm) — Design of Steel and Timber Structure, chapter 11 - [Footing size from plate load test curve](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aplate-load-footing-size-3200kn) — Foundation Engineering, chapter 6 - [Built-up column with battens, 6 m, 1200 kN](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Abuiltup-battens-1200kn-6m) — Design of Steel and Timber Structure, chapter 6