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A foundation is constructed in a soil with the following parameters: c' = 5.0kN/m? y = 18.5 kN/m³ Ø' = 32° The footing dimensions are: L= 3m B= 2m %3D D; = 2m MB = 300kN m Q = 3000KN Find the factor of safety using the Meyerhof effective area method.

A foundation is constructed in a soil with the following parameters: c' = 5.0kN/m? y = 18.5 kN/m³ Ø' = 32° The footing dimensions are: L= 3m B= 2m %3D D; = 2m MB = 300kN m Q = 3000KN Find the factor of safety using the Meyerhof effective area method.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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### Foundation Stability and Safety Analysis This educational text assists in understanding the parameters and methods necessary for calculating the factor of safety for a foundation constructed in a specified soil type, utilizing the Meyerhof effective area method. #### Soil Parameters - **Cohesion (c')**: 5.0 kN/m² - **Unit Weight (γ)**: 18.5 kN/m³ - **Angle of Internal Friction (Ø')**: 32° #### Footing Dimensions - **Length (L)**: 3 meters - **Breadth (B)**: 2 meters - **Depth of Footing (D<sub>f</sub>)**: 2 meters #### Applied Moments and Forces - **Moment about Base (M<sub>B</sub>)**: 300 kN∙m - **Vertical Load (Q)**: 3000 kN #### Objective We aim to calculate the **factor of safety** (FoS) for the given footing conditions using the **Meyerhof Effective Area Method**. ### Explanation of the Meyerhof Effective Area Method The Meyerhof effective area method involves reducing the size of the loaded area on the footing to account for the effect of eccentric loading and moments, focusing the analysis on the effective base area. This helps ensure the stability and uniformity of the stress distribution beneath the foundation. #### Calculation Steps: 1. **Determine the Eccentricity (e)**: - \( e = \frac{M_{B}}{Q} \) 2. **Calculate the Effective Dimensions**: - Effective Length \( L_e = L - 2e \) - Effective Width \( B_e = B \) 3. **Effective Area (A_e)**: - \( A_e = L_e \times B_e \) 4. **Average Bearing Pressure (q_avg)**: - \( q_{avg} = \frac{Q}{A_e} \) 5. **Bearing Capacity**: - Use the appropriate bearing capacity formula including cohesion, unit weight, and angle of friction parameters. 6. **Factor of Safety (FoS)**: - \( FoS = \frac{q_{ultimate}}{q_{avg}} \) The factor of safety is then determined by comparing the ultimate bearing capacity to the actual average bearing pressure on the effective area. This methodology ensures that the foundation’s design is robust
Transcribed Image Text:### Foundation Stability and Safety Analysis This educational text assists in understanding the parameters and methods necessary for calculating the factor of safety for a foundation constructed in a specified soil type, utilizing the Meyerhof effective area method. #### Soil Parameters - **Cohesion (c')**: 5.0 kN/m² - **Unit Weight (γ)**: 18.5 kN/m³ - **Angle of Internal Friction (Ø')**: 32° #### Footing Dimensions - **Length (L)**: 3 meters - **Breadth (B)**: 2 meters - **Depth of Footing (D<sub>f</sub>)**: 2 meters #### Applied Moments and Forces - **Moment about Base (M<sub>B</sub>)**: 300 kN∙m - **Vertical Load (Q)**: 3000 kN #### Objective We aim to calculate the **factor of safety** (FoS) for the given footing conditions using the **Meyerhof Effective Area Method**. ### Explanation of the Meyerhof Effective Area Method The Meyerhof effective area method involves reducing the size of the loaded area on the footing to account for the effect of eccentric loading and moments, focusing the analysis on the effective base area. This helps ensure the stability and uniformity of the stress distribution beneath the foundation. #### Calculation Steps: 1. **Determine the Eccentricity (e)**: - \( e = \frac{M_{B}}{Q} \) 2. **Calculate the Effective Dimensions**: - Effective Length \( L_e = L - 2e \) - Effective Width \( B_e = B \) 3. **Effective Area (A_e)**: - \( A_e = L_e \times B_e \) 4. **Average Bearing Pressure (q_avg)**: - \( q_{avg} = \frac{Q}{A_e} \) 5. **Bearing Capacity**: - Use the appropriate bearing capacity formula including cohesion, unit weight, and angle of friction parameters. 6. **Factor of Safety (FoS)**: - \( FoS = \frac{q_{ultimate}}{q_{avg}} \) The factor of safety is then determined by comparing the ultimate bearing capacity to the actual average bearing pressure on the effective area. This methodology ensures that the foundation’s design is robust
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