Width of Footing given Load Intensity Solution

STEP 0: Pre-Calculation Summary
Formula Used
Width of Footing = (-Load Intensity+sqrt((Load Intensity)^2+Total Downward Force in Soil*Unit Weight of Soil*tan(Angle of Shearing Resistance)))/((Unit Weight of Soil*tan(Angle of Shearing Resistance))/2)
B = (-q+sqrt((q)^2+Rv*γ*tan(φ)))/((γ*tan(φ))/2)
This formula uses 2 Functions, 5 Variables
Functions Used
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Width of Footing - (Measured in Meter) - Width of Footing is the shorter dimension of the footing.
Load Intensity - (Measured in Pascal) - Load Intensity is defined as load applied per unit area.
Total Downward Force in Soil - (Measured in Newton) - Total Downward Force in Soil is the net force on soil in the vertical direction.
Unit Weight of Soil - (Measured in Newton per Cubic Meter) - Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.
Angle of Shearing Resistance - (Measured in Radian) - Angle of Shearing Resistance is known as a component of the shear strength of the soils which is basically frictional material and composed of individual particles.
STEP 1: Convert Input(s) to Base Unit
Load Intensity: 26.85 Kilopascal --> 26850 Pascal (Check conversion here)
Total Downward Force in Soil: 50 Kilonewton --> 50000 Newton (Check conversion here)
Unit Weight of Soil: 18 Kilonewton per Cubic Meter --> 18000 Newton per Cubic Meter (Check conversion here)
Angle of Shearing Resistance: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
B = (-q+sqrt((q)^2+Rv*γ*tan(φ)))/((γ*tan(φ))/2) --> (-26850+sqrt((26850)^2+50000*18000*tan(0.785398163397301)))/((18000*tan(0.785398163397301))/2)
Evaluating ... ...
B = 1.49007575693435
STEP 3: Convert Result to Output's Unit
1.49007575693435 Meter --> No Conversion Required
FINAL ANSWER
1.49007575693435 1.490076 Meter <-- Width of Footing
(Calculation completed in 00.004 seconds)

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Birsa Institute of Technology (BIT), Sindri
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8 Bearing Capacity of Soil: Terzaghi's Analysis Calculators

Cohesion of Soil given Loading Intensity by Terzaghi's Analysis
Go Cohesion in Soil as Kilopascal = (Load Intensity-(((2*Passive Earth Pressure in kilopascal)/Width of Footing)-((Unit Weight of Soil*Width of Footing*tan((Angle of Shearing Resistance*pi)/180))/4)))/tan((Angle of Shearing Resistance*pi)/180)
Width of Footing given Load Intensity
Go Width of Footing = (-Load Intensity+sqrt((Load Intensity)^2+Total Downward Force in Soil*Unit Weight of Soil*tan(Angle of Shearing Resistance)))/((Unit Weight of Soil*tan(Angle of Shearing Resistance))/2)
Loading Intensity using Bearing Capacity Factors
Go Load Intensity = (Cohesion in Soil as Kilopascal*Bearing Capacity Factor dependent on Cohesion)+(Effective Surcharge in KiloPascal*Bearing Capacity Factor dependent on Surcharge)+(0.5*Unit Weight of Soil*Width of Footing*Bearing Capacity Factor dependent on Unit Weight)
Downward Force on Wedge of Soil given Load Intensity
Go Total Downward Force in Soil = Load Intensity*Width of Footing+((Unit Weight of Soil*Width of Footing^2*tan(Angle of Shearing Resistance)*(pi/180))/4)
Width of Footing given Weight of Wedge
Go Width of Footing = sqrt((Weight of Wedge*4)/(tan((Angle of Shearing Resistance*pi)/180)*Unit Weight of Soil))
Unit Weight of Soil given Weight of Wedge and Width of Footing
Go Unit Weight of Soil = (Weight of Wedge in Kilonewton*4)/(tan((Angle of Shearing Resistance))*(Width of Footing)^2)
Angle of Shearing Resistance given Weight of Wedge
Go Angle of Shearing Resistance = atan((Weight of Wedge in Kilonewton*4)/(Unit Weight of Soil*(Width of Footing)^2))
Weight of Wedge given Width of Footing
Go Weight of Wedge in Kilonewton = (tan(Angle of Shearing Resistance)*Unit Weight of Soil*(Width of Footing)^2)/4

Width of Footing given Load Intensity Formula

Width of Footing = (-Load Intensity+sqrt((Load Intensity)^2+Total Downward Force in Soil*Unit Weight of Soil*tan(Angle of Shearing Resistance)))/((Unit Weight of Soil*tan(Angle of Shearing Resistance))/2)
B = (-q+sqrt((q)^2+Rv*γ*tan(φ)))/((γ*tan(φ))/2)

What is Footing?

Footings are an important part of foundation construction. They are typically made of concrete with rebar reinforcement that has been poured into an excavated trench. The purpose of footings is to support the foundation and prevent settling. Footings are especially important in areas with troublesome soils.

How to Calculate Width of Footing given Load Intensity?

Width of Footing given Load Intensity calculator uses Width of Footing = (-Load Intensity+sqrt((Load Intensity)^2+Total Downward Force in Soil*Unit Weight of Soil*tan(Angle of Shearing Resistance)))/((Unit Weight of Soil*tan(Angle of Shearing Resistance))/2) to calculate the Width of Footing, The Width of Footing given Load Intensity is defined as the value of width of footing when we have prior information of other parameters used. Width of Footing is denoted by B symbol.

How to calculate Width of Footing given Load Intensity using this online calculator? To use this online calculator for Width of Footing given Load Intensity, enter Load Intensity (q), Total Downward Force in Soil (Rv), Unit Weight of Soil (γ) & Angle of Shearing Resistance (φ) and hit the calculate button. Here is how the Width of Footing given Load Intensity calculation can be explained with given input values -> 1.490076 = (-26850+sqrt((26850)^2+50000*18000*tan(0.785398163397301)))/((18000*tan(0.785398163397301))/2).

FAQ

What is Width of Footing given Load Intensity?
The Width of Footing given Load Intensity is defined as the value of width of footing when we have prior information of other parameters used and is represented as B = (-q+sqrt((q)^2+Rv*γ*tan(φ)))/((γ*tan(φ))/2) or Width of Footing = (-Load Intensity+sqrt((Load Intensity)^2+Total Downward Force in Soil*Unit Weight of Soil*tan(Angle of Shearing Resistance)))/((Unit Weight of Soil*tan(Angle of Shearing Resistance))/2). Load Intensity is defined as load applied per unit area, Total Downward Force in Soil is the net force on soil in the vertical direction, Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil & Angle of Shearing Resistance is known as a component of the shear strength of the soils which is basically frictional material and composed of individual particles.
How to calculate Width of Footing given Load Intensity?
The Width of Footing given Load Intensity is defined as the value of width of footing when we have prior information of other parameters used is calculated using Width of Footing = (-Load Intensity+sqrt((Load Intensity)^2+Total Downward Force in Soil*Unit Weight of Soil*tan(Angle of Shearing Resistance)))/((Unit Weight of Soil*tan(Angle of Shearing Resistance))/2). To calculate Width of Footing given Load Intensity, you need Load Intensity (q), Total Downward Force in Soil (Rv), Unit Weight of Soil (γ) & Angle of Shearing Resistance (φ). With our tool, you need to enter the respective value for Load Intensity, Total Downward Force in Soil, Unit Weight of Soil & Angle of Shearing Resistance and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Width of Footing?
In this formula, Width of Footing uses Load Intensity, Total Downward Force in Soil, Unit Weight of Soil & Angle of Shearing Resistance. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Width of Footing = sqrt((Weight of Wedge*4)/(tan((Angle of Shearing Resistance*pi)/180)*Unit Weight of Soil))
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