Foundation Design for Shallow Foundations - Example / Tutorial 4
A concentric vertical load of 15 kips/ft and a moment load of 10 kips/ft are applied to a 5.5 ft wide continuous footing. The groundwater table is at a depth of 50 ft. Calculate the maximum and minimum bearing pressures.
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This is example number four for foundation design for shallow foundations. The problem statement that we have is we have a concentric vertical load of 15 kips per foot and a moment load of 10 kips-ft per foot applied to a five and a half feet wide continuous footing foundation. The groundwater tables is at a depth of 50 feet. We’re asked to calculate the maximum and minimum bearing pressure.
Here is our figure with our moment load of 10 kips-feet per foot and a vertical load of 15 kips per feet. The width is five and a half feet. The distance from the ground surface to the bottom of the foundation is 1.75 feet.
The first thing we need to do is calculate the weight of the foundation. Since this is a continuous footing we're going to express apply loads as a force per unit length. The weight of the foundation is going to be equal to the width multiplied by the thickness or the height you can say and then multiply that by the unit weight of the concrete which is about 150 pounds per feet cubed. The weight per unit length is 1443.75 pounds per feet
Next, we need to calculate the eccentricity. Because we have this overturning moment, we have to calculate the eccentricity of the bearing pressure. We're going to have a non-uniform bearing pressure. It will not be a uniform distribution. Eccentricity is equal to the moment divided by the sum of the vertical load and the weight of the foundation. Eccentricity is equal to 0.608 ft. If we were to replace our entire bearing stress distribution by a resultant force, the eccentricity would be .608 feet.
We don't need to calculate the pore water pressure because in the problem statement the groundwater table is at a depth of 50 feet. The distance from the ground surface to the bottom of the foundations is 1.75 feet which is smaller than the distance from the ground surface to the groundwater table of 50 feet. This tells us that our poor water pressure at the bottom the foundation is 0.
After that, we calculate a value of which is the width divided by six. This value will tell us what type of distribution we have. Do we have a trapezoidal distribution or do we have a triangular distribution? We compare this width over 6 value to the eccentricity. The eccentricity is less than width over 6. This tells us that we have a pressure bearing pressure distribution which is trapezoidal. If we were to draw the pressure distribution it will look like a trapezoidal distribution.
Also, this criteria of eccentricity less than width over 6 maintains compressive stress along the entire base area. If eccentricity is greater than width over 6, then we'll have one part of the foundation that lifts up and the other part will be settling. We try to avoid this and that's why we tried to keep the eccentricity less than b/6.
Now we can calculate the minimum and maximum bearing pressure
The minimum bearing pressure is the vertical load plus the weight of the foundation divided by the width minus the pore water pressure multiplied by 1 - 6 times the eccentricity divided by the width. The minimum bearing pressure is 1006.3 pounds per foot squared
We can also calculate the maximum bearing pressure. It's exactly the same as the previous formula with the exception that instead of 1 minus 6 times the eccentricity divided by width, its’s 1 plus 6 times the eccentricity divided by the width. The maximum bearing pressure is equal to 4973.224 pounds per foot squared.
This is the end of this example. I also made a spreadsheet for this example. Everything in yellow is input and everything else is output. I'll post this on the website at engineering examples. Please subscribe to the channel and also like our Facebook page at facebook.com/engineering examples.