Equations · Footings

Each equation of Rischio's footing calculation, from the eccentricity to the settlement, with the name and unit of every term.

The same steps, in the same order, as the calculation report.

1Loads and geometry

Eccentricity along the width
$e_B = M_B / V$
where $V$ vertical load (kN)
Effective width
$B' = \min(B - 2 e_B,\; L - 2 e_L)$
where $B$ width (m); $e_B$ eccentricity along the width (m); $L$ length (m); $e_L$ eccentricity along the length (m)
Eccentricity along the length
$e_L = M_L / V$
where $V$ vertical load (kN)
Effective length
$L' = \max(B - 2 e_B,\; L - 2 e_L)$
where $B$ width (m); $e_B$ eccentricity along the width (m); $L$ length (m); $e_L$ eccentricity along the length (m)
Load inclination
$\beta = \arctan(|H| / V)$
where $H$ horizontal load (kN); $V$ vertical load (kN)

Overburden at the base
$q = \sigma'_v(D_f)$
Effective unit weight under the base
$\gamma' \text{ (average from } D_f \text{ to } D_f + B \text{, } B \text{ the shorter side)}$
Ultimate bearing capacity
$q_u = c N_c F_{cs} F_{cd} F_{ci} + q N_q F_{qs} F_{qd} F_{qi} + \tfrac{1}{2} \gamma' B' N_\gamma F_{\gamma s} F_{\gamma d} F_{\gamma i}$
where $q$ overburden at the base (kPa); $\gamma'$ effective unit weight under the base (kN/m³); $B'$ effective width (m); $N_c$ bearing capacity factor; $N_q$ bearing capacity factor; $N_\gamma$ bearing capacity factor; $F_{cs}$ fcs; $F_{qs}$ fqs; $F_{\gamma s}$ fgs; $F_{cd}$ fcd; $F_{qd}$ fqd; $F_{\gamma d}$ fgd; $F_{ci}$ fci; $F_{qi}$ fqi; $F_{\gamma i}$ fgi
Maximum contact pressure
$q_{max} = \frac{V}{A} \left(1 + \frac{6 e_B}{B} + \frac{6 e_L}{L}\right)$
where $V$ vertical load (kN); $B$ width (m); $e_B$ eccentricity along the width (m); $L$ length (m); $e_L$ eccentricity along the length (m)
Minimum contact pressure
$q_{min} = \frac{V}{A} \left(1 - \frac{6 e_B}{B} - \frac{6 e_L}{L}\right)$
where $V$ vertical load (kN); $B$ width (m); $e_B$ eccentricity along the width (m); $L$ length (m); $e_L$ eccentricity along the length (m)
Bearing capacity
$FS = \frac{q_u}{q_{max}} \; \ge 3.0$

Depth of influence
$H = \min(D_f + 5B, \text{profile})$
Average elastic modulus
$E_s = \Sigma E_i h_i / \Sigma h_i$
Average Poisson's ratio
$\mu_s = \Sigma \mu_i h_i / \Sigma h_i$
Elastic settlement
$S_e = q_0 (\alpha B') \frac{1 - \mu_s^2}{E_s} I_s I_f$
where $E_s$ average elastic modulus (kPa); $\mu_s$ average Poisson's ratio; $I_s$ shape factor; $I_f$ depth factor
Settlement
$S_e \le 25 \text{ mm}$