T-shaped foundation, stress at P

Method

Divide the T-shaped loaded area into rectangles that have P as a common corner, and use the corner stress $\Delta\sigma_z = q\,I_N$ for each. Depth $z = 5$ m, $q = 120$ kPa.

 +--------+---------------------+
 |  (1)   |        (2)          |  3 m
 |  3x3   |        6x3          |
 +--------P-----+---------------+
          | (3)  |
          | 3x1.5|              1.5 m
          +------+

P lies at the left corner where the stem meets the flange (on the lower edge of the flange).

• Rectangle (1): left flange, 3 m × 3 m: $m = 0.6$, $n = 0.6$, $I_N = 0.1069$
• Rectangle (2): right flange, 6 m × 3 m: $m = 0.6$, $n = 6/5 = 1.2$, $I_N = 0.1431$ (the question prints $n = 1.0$, but 0.1431 is the correct factor for $n = 1.2$)
• Rectangle (3): stem, 3 m × 1.5 m: $m = 0.6$, $n = 0.3$, $I_N = 0.0629$

(The given values match the exact influence factors for these shapes.)

Stress at P

$$\Delta\sigma_z = q\,(I_1 + I_2 + I_3) = 120\,(0.1069 + 0.1431 + 0.0629) = 120\times0.3129$$ $$\Delta\sigma_z = 37.5\ \text{kPa}$$

Answer: The vertical stress at P at 5 m depth $\approx 37.5$ kPa.