Das Foundation Engineering Ch4c
Eccentrically Loaded Foundations
- Introduction to chapter four, focusing on eccentrically loaded foundations and their implications.
- Eccentricity of load (q) affects the foundation's stress distribution.
- Equivalent condition: load applied at center plus additional moment.
Stress Distribution Analysis
- Stress is evenly distributed when load is centered without eccentricity.
- Two loading stages: first stage with q, second stage with moment m.
- Moment m causes clockwise rotation, altering stress distribution.
Impact of Rotation on Stress
- Maximum stress occurs at the toe side; minimum stress at the heel side due to rotation.
- Calculation for maximum stress: q/b cdot l .
- Additional component for second stage: 6m/b^2l .
Limitations of Eccentricity
- Eccentricity should not exceed b/6 ; tension cannot exist between foundation and soil.
- Importance of maintaining compression between foundation bottom and soil surface.
Deriving Stress Calculations
- First loading stage results in evenly distributed stress q/vl .
- Maximum q on toe side; minimum q on heel side after applying moment m.
Triangle Area Calculation
- Area calculation critical in second loading stage; involves triangles formed by stresses.
- Changes in triangle areas lead to trapezoidal shape in second loading stage.
Understanding Moments and Forces
- Moment caused by unevenly distributed loads; requires area calculations for force determination.
Understanding Stress Triangles and Moments
- The triangle represents a stress area; stress times area equals force.
- Q maximum is on the right, while Q minimum is on the left; area calculated as half base times height.
- Moment (M) derived from force times arm; arm depends on triangle's center of gravity.
Calculating Eccentricity and Effective Area Method
- Center of gravity for the triangle is at two-thirds height; distance between centers is b/6.
- Eccentricity defined as moment over force; units are length.
- Effective area method shifts loading point to new center, reducing width to b - 2e.
Handling Two-Way Eccentricity
- For one-way eccentricity, only width reduces to b - 2e.
- Two-way eccentricity involves sequential adjustments in both dimensions: width and length reduced.
- Determine effective dimensions first, then apply near-half's formula for adjusted load.
Understanding Ultimate Bearing Capacity
- Use effective dimensions (b' and l') for ship factor calculations.
- For depth factor, use original dimensions (b and l), even with eccentric loading.
- Calculate k using q' and q_u' times b' and l'.
Calculating Effective Ultimate Bearing Capacity
- Determine new ultimate load capacity using effective ultimate bearing capacity.
- Example: Find ultimate load per unit length of a foundation with given eccentricity.
- Cohesion is zero; only q group and gamma group remain in calculations.
Effective Dimensions in Foundation Calculations
- Original effective stress at the bottom of the foundation is calculated from given values.
- Effective dimension b' is derived from original b minus twice the eccentricity.
- Assume infinite length for continuous foundations, making b/l approach zero.
Shape Factor Considerations
- Use effective dimensions (b' and l') for shape factor calculations.
- Eccentricity present but no inclination affects qi and f_gamma i values.
- Depth factor uses original dimensions; ensure correct values are plugged into calculations.
Final Calculations and Homework Assignment
- The final result for ultimate bearing capacity is 3284.87 kPa.
- Capital Q calculation involves area method; results in force units (kN).
- Homework assigned: complete problem 4.8 from the textbook.