Exercice N°2 et N°3 sur la capacité portant, avec des calculs à valider.

Steps to Solve

1. Understanding the given equations

The equation for the total load $Q_e$ is given as:
$$ Q_e = s_c \cdot C_u \cdot N_c(0) + s_g \cdot \gamma_d \cdot D $$

Where:

• $s_c$, $C_u$, $N_c(0)$, $s_g$, and $\gamma_d$ are coefficients and parameters that need to be evaluated.

2. Substituting known values for Exercise 2

From Exercise 2, we are given:

• $N_c = 5.14$ (calculated using $\pi$)
• $s_c = 1.2$
• $s_g = 1$

Also given is:
$$ C_u = \frac{q_u}{2} = 1.36 , \text{t/m}^2 $$

Substituting these values into the equation:
$$ Q_e = 1.2 \cdot 1.36 \cdot 5.14 + 1 \cdot \gamma_d \cdot D $$

3. Compute $Q_e$ for Exercise 2

Completing the calculation for $Q_e$:

• Calculate the first part:
  $$ Q_e = 1.2 \cdot 1.36 \cdot 5.14 $$
  This gives approximately $10.80 , \text{t/m}^2$.

4. Equating with the measured value

The exercise also states that the measured value $Q_e$ is $11.6 , \text{t/m}^2$. Confirming the calculated result against this empirical measurement provides consistency.

5. Assessing Exercise 3 conditions

For Exercise 3, use:
$$ M_x = \frac{200}{400} = 0.5 , \text{ft} $$
$$ M_y = \frac{120}{400} = 0.3 , \text{ft} $$

6. Finding necessary coefficients

Substituting these values into $B' = B - 2 \cdot 0.5$ and $L' = L - 2 \cdot 0.3$:

• First find $B'$ and $L'$ to compute $N_q$, $N_c$, and $N_s$.

Continue using the values for load calculations as shown in Exercise 3 to obtain $Q_a = 22.8 , \text{ksf} \times 11.4 , \text{bars}$.

7. Final calculations for pressure application

For the pressure applied, use:
$$ Q_{app} = \frac{400}{5 \cdot 5.4} $$
This gives the final confirmation of applied pressure conditions.