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

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Question: 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?

Options:

  1. 1.5
  2. 2.5
  3. 3.5
  4. 4.5

Correct Answer: 3.5

Solution:

For a friction angle of 30 degrees, the bearing capacity factor N_q can be approximated using the formula N_q = e^(Ο€ * tan(Ο†)) * tan(45 + Ο†/2). For Ο† = 30 degrees, N_q is approximately 3.5.

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

Practice Questions

Q1
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?
  1. 1.5
  2. 2.5
  3. 3.5
  4. 4.5

Questions & Step-by-Step Solutions

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 (Ο†) of the soil, which is given as 30 degrees.
  • Step 2: Recall the formula for the bearing capacity factor N_q: N_q = e^(Ο€ * tan(Ο†)) * tan(45 + Ο†/2).
  • Step 3: Calculate tan(Ο†) for Ο† = 30 degrees. The value of tan(30 degrees) is approximately 0.577.
  • Step 4: Calculate 45 + Ο†/2. For Ο† = 30 degrees, Ο†/2 = 15 degrees, so 45 + 15 = 60 degrees.
  • Step 5: Calculate tan(60 degrees), which is approximately 1.732.
  • Step 6: Calculate e^(Ο€ * tan(30 degrees)). First, find Ο€ * tan(30 degrees) = Ο€ * 0.577. Then, calculate e^(Ο€ * 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 (Ο†) 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.
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