### Bearing Capacity Calculation Using Terzaghi's Equation**Problem Statement:**2. Assuming general shear failure and using the Terzaghi equation with a Factor of Safety (FOS) of 4, find the allowable gross bearing load the following footing can sustain. The footing is characterized as follows:- **Type:** 1.5m continuous footing- **Depth:** Set 1.2m below grade- **Soil Properties:** - Friction angle (φ): 35 degrees - Cohesion (c’): 0 - Unit weight (γ): 17.8 kN/m²**Objective:**Calculate the allowable gross bearing load using the given parameters.---### Explanation:- **General Shear Failure:** This refers to a scenario where the soil mass beneath the footing fails along a distinct surface, leading to a pronounced soil heaving on both sides.- **Terzaghi Equation:** This classical soil mechanics equation is used to estimate the ultimate bearing capacity of shallow foundations. The ultimate bearing capacity can be adjusted using the Factor of Safety to provide an allowable bearing capacity. ---### Key Parameters:- **Footing Width (B):** 1.5m- **Depth of Footing (D):** 1.2m- **Soil Friction Angle (φ):** 35 degrees- **Cohesion (c’):** 0- **Unit Weight (γ):** 17.8 kN/m²- **Factor of Safety (FOS):** 4---### Solution Steps:1. **Terzaghi's Bearing Capacity Equation** for strip footings: \( q_{ult} = c'N_c + \gamma D N_q + 0.5 \gamma B N_γ \) Where: - \( N_c, N_q, N_γ \) are bearing capacity factors dependent on the soil friction angle (\(φ\)). - Given \( φ = 35° \), consult standard bearing capacity factor tables or charts to find \( N_c, N_q, N_γ \). 2. **Evaluate Bearing Capacity Factors** (for \( φ = 35° \)): - \( N_c ≈ 46.12 \) - \( N_q ≈ 33.3 \) - \( N_γ ≈ 42.4 \

Given:- To find:- allowable gross bearing load

2. Assuming general shear failure and using the Terzaghi equation with a FOS of 4 find the allowable gross bearing load the following footing can sustain: 1.5m continuous footing set 1.2mbelow grade in a 35deg phi soil with a c' of 0 and a unit wt of 17.8kN/m^2

2. Assuming general shear failure and using the Terzaghi equation with a FOS of 4 find the allowable gross bearing load the following footing can sustain: 1.5m continuous footing set 1.2mbelow grade in a 35deg phi soil with a c' of 0 and a unit wt of 17.8kN/m^2

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

### Bearing Capacity Calculation Using Terzaghi's Equation

**Problem Statement:**

2. Assuming general shear failure and using the Terzaghi equation with a Factor of Safety (FOS) of 4, find the allowable gross bearing load the following footing can sustain. The footing is characterized as follows:
- **Type:** 1.5m continuous footing
- **Depth:** Set 1.2m below grade
- **Soil Properties:**
- Friction angle (φ): 35 degrees
- Cohesion (c’): 0
- Unit weight (γ): 17.8 kN/m²

**Objective:**

Calculate the allowable gross bearing load using the given parameters.

---

### Explanation:

- **General Shear Failure:** This refers to a scenario where the soil mass beneath the footing fails along a distinct surface, leading to a pronounced soil heaving on both sides.
- **Terzaghi Equation:** This classical soil mechanics equation is used to estimate the ultimate bearing capacity of shallow foundations. The ultimate bearing capacity can be adjusted using the Factor of Safety to provide an allowable bearing capacity.

---

### Key Parameters:

- **Footing Width (B):** 1.5m
- **Depth of Footing (D):** 1.2m
- **Soil Friction Angle (φ):** 35 degrees
- **Cohesion (c’):** 0
- **Unit Weight (γ):** 17.8 kN/m²
- **Factor of Safety (FOS):** 4

---

### Solution Steps:

1. **Terzaghi's Bearing Capacity Equation** for strip footings:

\( q_{ult} = c'N_c + \gamma D N_q + 0.5 \gamma B N_γ \)

Where:
- \( N_c, N_q, N_γ \) are bearing capacity factors dependent on the soil friction angle (\(φ\)).
- Given \( φ = 35° \), consult standard bearing capacity factor tables or charts to find \( N_c, N_q, N_γ \).

2. **Evaluate Bearing Capacity Factors** (for \( φ = 35° \)):
- \( N_c ≈ 46.12 \)
- \( N_q ≈ 33.3 \)
- \( N_γ ≈ 42.4 \

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