RC wall footing, 1000 kN total load

Data and assumptions

• Wall 300 mm thick and 4 m long carrying a total service load of 1000 kN, so the load per metre run is $w = 1000/4 = 250$ kN/m. M20 concrete, Fe415 steel, $q_a = 150$ kN/m². The footing is designed for a 1 m length of wall. Cover 50 mm.

Width of footing

$$B = \frac{1.1\,w}{q_a} = \frac{1.1 \times 250}{150} = 1.833\ \text{m} \Rightarrow \text{provide } B = 1.85\ \text{m}$$

(10% is added for the weight of the footing and backfill.)

Factored pressure and bending moment

$w_u = 1.5 \times 250 = 375$ kN/m, $p_u = \dfrac{w_u}{B} = \dfrac{375}{1.85} = 202.70$ kN/m² Projection beyond the wall face $= (1850 - 300)/2$ $= 775$ mm.

$$M_u = \frac{p_u\, a^2}{2} = \frac{202.70 \times 0.775^2}{2} = 60.87\ \text{kN·m per metre}$$

Depth

The depth is governed by one-way shear at $d$ from the wall face (checked below); trial $D = 375$ mm, $d = 375 - 50 - 6 = 319$ mm (conservative). Flexure check: $M_{u,lim} = 0.138 f_{ck} b d^2 = 280.9$ kN·m $> 60.87$ kN·m, so the depth is adequate and the section is under-reinforced.

Reinforcement

$A_{st} = 548$ mm²/m from $M_u$ (minimum 0.12% of $bD$ = 450 mm²/m). Adopt 548 mm²/m → provide 10 mm @ 140 mm c/c across the width (561 mm²/m, $p_t = 0.176\%$). Distribution steel along the wall (0.12% of $bD$) = 450 mm²/m → 8 mm @ 110 mm c/c (457 mm²/m).

Check for shear

$V_u = p_u (a - d) = 202.70 \times (0.775 - 0.319) = 92.43$ kN/m; $\tau_v = \dfrac{92432}{1000 \times 319} = 0.290$ MPa < $\tau_c = 0.30$ MPa (M20, $p_t = 0.176\%$, Table 19). Safe.

Development length

$L_d = \dfrac{0.87 \times 415 \times 10}{4 \times 1.92} = 470$ mm; available length $= 775 - 50 = 725$ mm. Satisfied.

Detailing

SECTION ACROSS WALL
        |  wall 300  |
        |            |
   _____|            |_____
  |                       |  D = 375 mm
  |_______________________|
   o o o o o o o o o o o o   <- 10 mm @ 140 c/c
  <---------- 1.85 m ------->

Distribution bars of 8 mm @ 110 mm c/c are tied above the main bars, parallel to the wall.

Answer: Strip footing 1.85 m wide and 375 mm thick; main bars 10 mm @ 140 mm c/c across the wall, distribution bars 8 mm @ 110 mm c/c.