Ultimate Bearing Capacity given Angle of Shearing Resistance Calculator

✖Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.ⓘ Unit Weight of Soil [γ]			+10% -10%
✖Depth of Footing is the longer dimension of the footing.ⓘ Depth of Footing [D]			+10% -10%
✖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.ⓘ Angle of Shearing Resistance [φ]			+10% -10%

✖The Ultimate Bearing Capacity in soil mechanics is defined as the minimum gross pressure intensity at the base of the foundation at which the soil fails in shear.ⓘ Ultimate Bearing Capacity given Angle of Shearing Resistance [q_f]

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Ultimate Bearing Capacity given Angle of Shearing Resistance

Formula

`"q"_{"f"} = ("γ"*"D")*((1+sin(("φ"*pi)/180))/(1-sin(("φ"*pi)/180)))^2`

Example

`"0.289021kPa"=("18kN/m³"*"15.2m")*((1+sin(("45°"*pi)/180))/(1-sin(("45°"*pi)/180)))^2`

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Ultimate Bearing Capacity given Angle of Shearing Resistance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Ultimate Bearing Capacity in Soil = (Unit Weight of Soil*Depth of Footing)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2
q_f = (γ*D)*((1+sin((φ*pi)/180))/(1-sin((φ*pi)/180)))^2
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Ultimate Bearing Capacity in Soil - (Measured in Pascal) - The Ultimate Bearing Capacity in soil mechanics is defined as the minimum gross pressure intensity at the base of the foundation at which the soil fails in shear.
Unit Weight of Soil - (Measured in Kilonewton per Cubic Meter) - Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.
Depth of Footing - (Measured in Meter) - Depth of Footing is the longer dimension of the footing.
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

Unit Weight of Soil: 18 Kilonewton per Cubic Meter --> 18 Kilonewton per Cubic Meter No Conversion Required
Depth of Footing: 15.2 Meter --> 15.2 Meter No Conversion Required
Angle of Shearing Resistance: 45 Degree --> 0.785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

q_f = (γ*D)*((1+sin((φ*pi)/180))/(1-sin((φ*pi)/180)))^2 --> (18*15.2)*((1+sin((0.785398163397301*pi)/180))/(1-sin((0.785398163397301*pi)/180)))^2

Evaluating ... ...

q_f = 289.021199053804

STEP 3: Convert Result to Output's Unit

289.021199053804 Pascal -->0.289021199053804 Kilopascal (Check conversion here)

FINAL ANSWER

0.289021199053804 ≈ 0.289021 Kilopascal <-- Ultimate Bearing Capacity in Soil

(Calculation completed in 00.004 seconds)

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Birsa Institute of Technology (BIT), Sindri

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< 15 Minimum Depth of Foundation by Rankine's Analysis Calculators

Major Stress during Shear Failure by Rankine Analysis

Go Major Principal Stress in Soil = Minor Principal Stress in Soil*(tan((Angle of Inclination to Horizontal in Soil*180)/pi))^2+(2*Cohesion of Soil*tan((Angle of Inclination to Horizontal in Soil*180)/pi))

Minimum Depth of Foundation given Intensity of Loading

Go Minimum Depth of Foundation = Intensity of Loading in Kilopascal/((Unit Weight of Soil)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2)

Unit Weight of Soil given Intensity of Loading

Go Unit Weight of Soil = Intensity of Loading in Kilopascal/((Minimum Depth of Foundation)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2)

Intensity of Loading given Minimum Depth of Foundation

Go Intensity of Loading in Kilopascal = (Unit Weight of Soil*Minimum Depth of Foundation)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2

Ultimate Bearing Capacity given Angle of Shearing Resistance

Go Ultimate Bearing Capacity in Soil = (Unit Weight of Soil*Depth of Footing)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2

Unit Weight of Soil given Angle of Shearing Resistance

Go Unit Weight of Soil = Ultimate Bearing Capacity in Soil/(Depth of Footing)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2

Minor Normal Stress during Shear Failure by Rankine Analysis

Go Minor Principal Stress in Soil = (Major Principal Stress in Soil-(2*Cohesion of Soil*tan((Angle of Inclination to Horizontal in Soil))))/(tan((Angle of Inclination to Horizontal in Soil)))^2

Depth of Footing given Angle of Inclination from Horizontal

Go Depth of Footing = Ultimate Bearing Capacity in Soil/(Unit Weight of Soil*(tan((Angle of Inclination to Horizontal in Soil*pi)/180))^4)

Depth of Footing given Major Normal Stress

Go Depth of Footing = Major Principal Stress in Soil/(Unit Weight of Soil*(tan(Angle of Inclination to Horizontal in Soil))^2)

Unit Weight of Soil given Angle of Inclination from Horizontal

Go Unit Weight of Soil = Net Ultimate Bearing Capacity/(Depth of Footing*(tan(Angle of Inclination to Horizontal in Soil))^4)

Ultimate Bearing Capacity provided Angle of Inclination from Horizontal

Go Net Ultimate Bearing Capacity = Unit Weight of Soil*Depth of Footing*(tan(Angle of Inclination to Horizontal in Soil))^4

Depth of Footing given Net Pressure Intensity

Go Depth of Footing = (Gross Pressure-Net Pressure)/Unit Weight of Soil

Minor Normal Stress given Unit Weight of Soil

Go Minor Principal Stress in Soil = Unit Weight of Soil*Depth of Footing

Unit Weight of Soil given Minor Normal Stress

Go Unit Weight of Soil = Minor Principal Stress in Soil/Depth of Footing

Depth of Footing given Minor Normal Stress

Go Depth of Footing = Minor Principal Stress in Soil/Unit Weight of Soil

Ultimate Bearing Capacity given Angle of Shearing Resistance Formula

What is Ultimate Bearing Capacity?

The ultimate bearing capacity of a foundation denotes the maximum load that foundation soils can withstand, and its reasonable determination is one of the pivotal parts in foundation designs. Numerous studies about the ultimate bearing capacity of strip foundations are focused on saturated soils.

How to Calculate Ultimate Bearing Capacity given Angle of Shearing Resistance?

Ultimate Bearing Capacity given Angle of Shearing Resistance calculator uses Ultimate Bearing Capacity in Soil = (Unit Weight of Soil*Depth of Footing)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2 to calculate the Ultimate Bearing Capacity in Soil, The Ultimate Bearing Capacity given Angle of Shearing Resistance is defined as the value of ultimate bearing capacity when we have prior information of other parameters used. Ultimate Bearing Capacity in Soil is denoted by q_f symbol.

How to calculate Ultimate Bearing Capacity given Angle of Shearing Resistance using this online calculator? To use this online calculator for Ultimate Bearing Capacity given Angle of Shearing Resistance, enter Unit Weight of Soil (γ), Depth of Footing (D) & Angle of Shearing Resistance (φ) and hit the calculate button. Here is how the Ultimate Bearing Capacity given Angle of Shearing Resistance calculation can be explained with given input values -> 0.289021 = (18000*15.2)*((1+sin((0.785398163397301*pi)/180))/(1-sin((0.785398163397301*pi)/180)))^2.

FAQ

What is Ultimate Bearing Capacity given Angle of Shearing Resistance?

The Ultimate Bearing Capacity given Angle of Shearing Resistance is defined as the value of ultimate bearing capacity when we have prior information of other parameters used and is represented as q_f = (γ*D)*((1+sin((φ*pi)/180))/(1-sin((φ*pi)/180)))^2 or Ultimate Bearing Capacity in Soil = (Unit Weight of Soil*Depth of Footing)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2. Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil, Depth of Footing is the longer dimension of the footing & 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 Ultimate Bearing Capacity given Angle of Shearing Resistance?

The Ultimate Bearing Capacity given Angle of Shearing Resistance is defined as the value of ultimate bearing capacity when we have prior information of other parameters used is calculated using Ultimate Bearing Capacity in Soil = (Unit Weight of Soil*Depth of Footing)*((1+sin((Angle of Shearing Resistance*pi)/180))/(1-sin((Angle of Shearing Resistance*pi)/180)))^2. To calculate Ultimate Bearing Capacity given Angle of Shearing Resistance, you need Unit Weight of Soil (γ), Depth of Footing (D) & Angle of Shearing Resistance (φ). With our tool, you need to enter the respective value for Unit Weight of Soil, Depth of Footing & 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.

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