--- title: "Footing, 1250 kN column load, depth 1.8 m" subject: "Design of RCC Structure" chapter: 11 key: "semester_7/design_of_rcc_structure:footing-1250-kn-column-load-depth" source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/footing-1250-kn-column-load-depth site: BCT Engineering --- # Footing, 1250 kN column load, depth 1.8 m Design of RCC Structure · Chapter 11: Design of Footings - Asked in: 2076 Chaitra, 13 marks - Video: [RCD:- Single column footing design](https://www.youtube.com/watch?v=6AGlI_T_mQg) — Engr Suliman Khan - 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/footing-1250-kn-column-load-depth - Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-11 ## Question Design a RC footing to carry a column load of 1250 kN from 400 x 400 mm square column having 20 mm diameter bar as longitudinal steel. The bearing capacity of soil is 140 kN/m$^2$. Consider the depth of foundation as 1.8 m. Take unit weight of earth as 18 kN/m$^3$. Use M20 concrete mix and Fe415 grade steel. Also sketch the reinforcements in plan and section. ## Short answer Net safe bearing capacity 107.6 kN/m² gives required area 11.62 m², so 3.5 m square footing. Factored pressure 153.1 kN/m²; depth D=550 mm (d=490 mm) governed by shear. Reinforcement 16 mm @ 180 c/c both ways; shear safe. Bearing stress 11.72 MPa exceeds 9 MPa, excess 435 kN carried by column dowels. ## 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 6-20 mm. - Service load $P = 1250$ kN. - Allowable (safe) bearing capacity of soil = 140 kN/m² at 1.8 m depth, soil unit weight 18 kN/m³. - Bearing capacity is taken as the gross value at the foundation level. - 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 Net safe bearing capacity = $q - \gamma D_f = 140 - 18 \times 1.8 = 107.60$ kN/m² (this takes care of the weight of footing and backfill). $$ A_{req} = \frac{P}{q_{net}} = \frac{1250.0}{107.60} = 11.62\ \text{m}^2 $$ Provide a square footing $L \times B = 3.5 \times 3.5$ m, area = 12.25 m² $\ge$ 11.62 m². #### Factored soil pressure $P_u = 1.5 \times 1250.0 = 1875.0$ kN. $p_u = \dfrac{P_u}{BL} = \dfrac{1875.0}{3.5 \times 3.5} = 153.1$ kN/m². #### Bending moments and reinforcement Cantilever projections from the column face: along $L$: $(3500 - 400)/2 = 1550$ mm; along $B$: $(3500 - 400)/2 = 1550$ mm. $M_u = p_u \times (\text{width}) \times \dfrac{(\text{projection})^2}{2}$: $M_{u,L} = 643.5$ kN·m, $M_{u,B} = 643.5$ kN·m. Required depth for flexure: $M_{u,lim} = 0.138 f_{ck} b d^2$ is far larger than the moment for $d = 490$ mm, so the depth is governed by shear (one-way or punching). Trial **$D = 550$ mm, $d = 490$ 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 $B$) | 643.5 | 3815 | 16 mm @ 180 c/c | 3910 | | Along $B$ (width $L$) | 643.5 | 3815 | 16 mm @ 180 c/c | 3910 | #### Check for one-way shear (at distance $d$ from the column face) - Along $L$ side: $V_u = 567.9$ kN, $\tau_v = \dfrac{V_u}{B d} = 0.331$ MPa; $p_t = 0.228\%$, $\tau_c = 0.345$ MPa (IS 456 Table 19, SP 16 formula). $\tau_v < \tau_c$, safe. - Along $B$ side: $V_u = 567.9$ kN, $\tau_v = 0.331$ MPa; $p_t = 0.228\%$, $\tau_c = 0.345$ MPa. Safe. #### Check for two-way (punching) shear (at $d/2$ from the column face) - Perimeter $b_o = 2[(a + d) + (c + d)] = 2[(400+490) + (400+490)] = 3560$ mm - $V_u = P_u - p_u (a+d)(c+d) = 1875.0 - 153.1 \times 0.890 \times 0.890 = 1753.8$ kN (average pressure; the effect of moment transfer is neglected). - $\tau_v = \dfrac{V_u}{b_o d} = 1.005$ 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): 1500 mm along $L$, 1500 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 $= P_u/A_2 = 11.72$ 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 $<$ $P_u = 1875$ kN, so the excess 435 kN must be carried by dowels: $A_{s,dow} = \dfrac{435000}{0.87 f_y} = 1205$ mm²; the column bars (6-20 mm, 1885 mm²) are continued into the footing as dowels, which is adequate. Dowel length in compression $L_{dc} = \dfrac{0.87 f_y\phi}{4 \times 1.25\,\tau_{bd}} = 752$ mm (and the same lap with the column bars). Available depth in footing = 550 - 50 - 32 = 468 mm $< L_{dc}$; dowels are bent at the bottom with 90° bends. #### Detailing ```text PLAN ELEVATION +------------------+ col | # # # # # # | | | | # +------+ # # | _|_|__ | # | col | # # | |_____| <- D = 550 mm | # +------+ # # | bars both ways | # # # # # # | +------------------+ L = 3.5 m, B = 3.5 m ``` - Bottom mesh: 16 mm @ 180 c/c along $L$ (lower layer), 16 mm @ 180 c/c along $B$ (upper layer), 50 mm clear cover; dowels 6-20 mm. **Answer:** Footing 3.5 m × 3.5 m × 550 mm thick; 16 mm @ 180 c/c along the length and 16 mm @ 180 c/c along the width. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is the area found as P/q_net with q_net = 140 - 18 x 1.8 = 107.6 kN/m^2? A. Because the soil unit weight reduces the load on the column B. Because overburden (footing and backfill) weight at 1.8 m depth already uses up part of the 140 kN/m^2 C. Because the bearing capacity is increased by depth D. Because the factored load is used for sizing Answer: B. The weight of soil/footing above the base, gamma x D_f, is subtracted from the gross capacity, leaving the net capacity available for the column load. (Key point: Net safe bearing capacity) 2. At what location is one-way shear checked, and what is the result here? A. At the column face; tau_v = 0.331 MPa is greater than tau_c B. At distance d from the column face; tau_v = 0.331 MPa < tau_c = 0.345 MPa, safe C. At d/2 from the column face; it fails D. At the footing edge; it is not required Answer: B. One-way (beam) shear is checked at d from the column face and compared with tau_c from Table 19 using p_t; 0.331 < 0.345 is safe. (Key point: One-way shear check) 3. For two-way shear with d = 490 mm and a 400 x 400 column, what is the critical perimeter b_o? A. 4 x 400 = 1600 mm B. 2[(400+490)+(400+490)] = 3560 mm, at d/2 from the column face C. 4 x 490 = 1960 mm D. 2 x (400+490) = 1780 mm Answer: B. The critical section is at d/2 around the column, so each side is a + d = 890 mm and b_o = 4 x 890 = 3560 mm. (Key point: Punching shear perimeter) 4. Bearing capacity is 1440 kN but P_u = 1875 kN. How is the excess handled? A. Footing depth is doubled B. The excess 435 kN is carried by dowels, A_s = 435000/(0.87 f_y) = 1205 mm^2, and the column bars (1885 mm^2) are continued as dowels C. The excess is ignored because soil carries it D. Bearing area is increased to 18 MPa Answer: B. Load beyond bearing capacity must pass through steel; required dowel area is 1205 mm^2, which the 6-20 mm column bars (1885 mm^2) exceed. (Key point: Dowels for excess load) ## Related in Design of RCC Structure - [Rectangular footing, 600x600 column, 1150 kN](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Arectangular-footing-600x600-column-1150-kn) — Design of RCC Structure, chapter 11 - [RC wall footing, 1000 kN total load](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Arc-wall-footing-1000-kn-total) — 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× - [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× - [Footing with load transfer check, 1000 kN](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Afooting-with-load-transfer-check-1000) — Design of RCC Structure, chapter 11 - [Footing for 400x300 column, reversible moment](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Afooting-for-400x300-column-reversible-moment) — Design of RCC Structure, chapter 11 ## Related in other subjects - [Square footing under eccentric load, min depth](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Asquare-footing-eccentric-2000kn) — Foundation Engineering, chapter 6 - [Allowable load of 400 mm pile, layered soil](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apile-400mm-layered-soil-chart) — Foundation Engineering, chapter 8 - [Square footing size in clay, 750 kN](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Asquare-footing-clay-750kn) — Foundation Engineering, chapter 6 - [Factors affecting foundation design, improving bearing capacity](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Afactors-design-improve-bc) — Building Technology, chapter 2