A strip footing is placed on a sandy soil with a friction angle of 30 degrees. W

A strip footing is placed on a sandy soil with a friction angle of 30 degrees. What is the approximate value of the bearing capacity factor N_q?

A strip footing is placed on a sandy soil with a friction angle of 30 degrees. What is the approximate value of the bearing capacity factor N_q?

Step 1: Identify the friction angle (φ) of the soil, which is given as 30 degrees.
Step 2: Recall the formula for the bearing capacity factor N_q: N_q = e^(π * tan(φ)) * tan(45 + φ/2).
Step 3: Calculate tan(φ) for φ = 30 degrees. The value of tan(30 degrees) is approximately 0.577.
Step 4: Calculate 45 + φ/2. For φ = 30 degrees, φ/2 = 15 degrees, so 45 + 15 = 60 degrees.
Step 5: Calculate tan(60 degrees), which is approximately 1.732.
Step 6: Calculate e^(π * tan(30 degrees)). First, find π * tan(30 degrees) = π * 0.577. Then, calculate e^(π * 0.577).
Step 7: Multiply the results from Step 6 and Step 5 to find N_q.
Step 8: The approximate value of N_q is found to be around 3.5.

Bearing Capacity Factors – Understanding how to calculate bearing capacity factors (N_q) based on soil friction angle (φ) is crucial for foundation design.
Soil Mechanics – Knowledge of soil properties, particularly the friction angle, and their impact on bearing capacity is essential in geotechnical engineering.
Mathematical Application – Applying the correct formula for calculating N_q and understanding the significance of the parameters involved.