Angle of Inclination given Vertical Stress on Surface of Prism Solution

STEP 0: Pre-Calculation Summary
Formula Used
Angle of Inclination = acos(Vertical Stress at a Point in Pascal/(Depth of Prism*Unit Weight of Soil))
I = acos(σvertical/(z*γ))
This formula uses 2 Functions, 4 Variables
Functions Used
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)
Variables Used
Angle of Inclination - (Measured in Radian) - Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object.
Vertical Stress at a Point in Pascal - (Measured in Pascal) - Vertical Stress at a Point in Pascal is the stress acting perpendicular to the surface.
Depth of Prism - (Measured in Meter) - Depth of Prism is the length of prism along z 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.
STEP 1: Convert Input(s) to Base Unit
Vertical Stress at a Point in Pascal: 10 Pascal --> 10 Pascal No Conversion Required
Depth of Prism: 3 Meter --> 3 Meter No Conversion Required
Unit Weight of Soil: 18 Kilonewton per Cubic Meter --> 18000 Newton per Cubic Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
I = acos(σvertical/(z*γ)) --> acos(10/(3*18000))
Evaluating ... ...
I = 1.57061114160865
STEP 3: Convert Result to Output's Unit
1.57061114160865 Radian -->89.9893896704168 Degree (Check conversion here)
FINAL ANSWER
89.9893896704168 89.98939 Degree <-- Angle of Inclination
(Calculation completed in 00.004 seconds)

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Birsa Institute of Technology (BIT), Sindri
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23 Stability Analysis of Infinite Slopes in Prism Calculators

Unit Weight of Soil given Factor of Safety for Cohesive Soil
Go Unit Weight of Soil = Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction*pi)/180)/tan((Angle of Inclination*pi)/180)))*Depth of Prism*cos((Angle of Inclination*pi)/180)*sin((Angle of Inclination*pi)/180))
Cohesion given Factor of Safety for Cohesive Soil
Go Cohesion of Soil = (Factor of Safety-(tan((Angle of Internal Friction*pi)/180)/tan((Angle of Inclination*pi)/180)))*(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination*pi)/180)*sin((Angle of Inclination*pi)/180))
Depth of Prism given Factor of Safety for Cohesive Soil
Go Depth of Prism = Unit Cohesion/((Factor of Safety-(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination))))*Unit Weight of Soil*cos((Angle of Inclination))*sin((Angle of Inclination)))
Factor of Safety for Cohesive Soil given Cohesion
Go Factor of Safety = (Unit Cohesion/(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination))*sin((Angle of Inclination))))+(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination)))
Inclined Length along Slope given Weight of Soil Prism
Go Inclined Length = Weight of Prism/(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination)))
Unit Weight of Soil given Weight of Soil Prism
Go Unit Weight of Soil = Weight of Prism/(Depth of Prism*Inclined Length*cos((Angle of Inclination)))
Weight of Soil Prism in Stability Analysis
Go Weight of Prism = (Unit Weight of Soil*Depth of Prism*Inclined Length*cos((Angle of Inclination)))
Depth of Prism given Weight of Soil Prism
Go Depth of Prism = Weight of Prism/(Unit Weight of Soil*Inclined Length*cos((Angle of Inclination)))
Angle of Inclination given Weight of Soil Prism
Go Angle of Inclination = acos(Weight of Prism/(Unit Weight of Soil*Depth of Prism*Inclined Length))
Unit Weight of Soil given Vertical Stress on Surface of Prism
Go Unit Weight of Soil = Vertical Stress at a Point in Pascal/(Depth of Prism*cos((Angle of Inclination)))
Depth of Prism given Vertical Stress on Surface of Prism
Go Depth of Prism = Vertical Stress at a Point in Pascal/(Unit Weight of Soil*cos((Angle of Inclination)))
Angle of Inclination given Vertical Stress on Surface of Prism
Go Angle of Inclination = acos(Vertical Stress at a Point in Pascal/(Depth of Prism*Unit Weight of Soil))
Inclined Length along Slope given Volume Per Unit Length of Prism
Go Inclined Length = Volume per unit length of prism/(Depth of Prism*cos((Angle of Inclination)))
Depth of Prism given Volume per Unit Length of Prism
Go Depth of Prism = Volume per unit length of prism/(Inclined Length*cos((Angle of Inclination)))
Volume Per Unit Length of Prism
Go Volume per unit length of prism = (Depth of Prism*Inclined Length*cos((Angle of Inclination)))
Vertical Stress on Surface of Prism given Unit Weight of Soil
Go Vertical Stress at a Point = (Depth of Prism*Unit Weight of Soil*cos((Angle of Inclination)))
Angle of Inclination given Volume per Unit Length of Prism
Go Angle of Inclination = acos(Volume per unit length of prism/(Depth of Prism*Inclined Length))
Inclined Length along Slope given Horizontal Length of Prism
Go Inclined Length = Horizontal Length of Prism/cos((Angle of Inclination))
Horizontal Length of Prism
Go Horizontal Length of Prism = Inclined Length*cos((Angle of Inclination))
Angle of Inclination given Horizontal Length of Prism
Go Angle of Inclination = acos(Horizontal Length of Prism/Inclined Length)
Weight of Soil Prism given Vertical Stress on Surface of Prism
Go Weight of Prism = Vertical Stress at a Point in Pascal*Inclined Length
Inclined Length along Slope given Vertical Stress on Surface of Prism
Go Inclined Length = Weight of Prism/Vertical Stress at a Point*5
Vertical Stress on Surface of Prism
Go Vertical Stress at a Point = Weight of Prism/Inclined Length

Angle of Inclination given Vertical Stress on Surface of Prism Formula

Angle of Inclination = acos(Vertical Stress at a Point in Pascal/(Depth of Prism*Unit Weight of Soil))
I = acos(σvertical/(z*γ))

What is Angle of Inclination?

The angle inclination of a line is the angle formed by the intersection of the line and the x-axis. Using a horizontal "run" of 1 and m for slope, the angle of inclination, theta=tan-1(m), or m=tan(theta).

How to Calculate Angle of Inclination given Vertical Stress on Surface of Prism?

Angle of Inclination given Vertical Stress on Surface of Prism calculator uses Angle of Inclination = acos(Vertical Stress at a Point in Pascal/(Depth of Prism*Unit Weight of Soil)) to calculate the Angle of Inclination, The Angle of Inclination given Vertical Stress on Surface of Prism is defined as the slope at which a prism's surface yields under vertical stress, determining its stability. Angle of Inclination is denoted by I symbol.

How to calculate Angle of Inclination given Vertical Stress on Surface of Prism using this online calculator? To use this online calculator for Angle of Inclination given Vertical Stress on Surface of Prism, enter Vertical Stress at a Point in Pascal vertical), Depth of Prism (z) & Unit Weight of Soil (γ) and hit the calculate button. Here is how the Angle of Inclination given Vertical Stress on Surface of Prism calculation can be explained with given input values -> 5156.547 = acos(10/(3*18000)).

FAQ

What is Angle of Inclination given Vertical Stress on Surface of Prism?
The Angle of Inclination given Vertical Stress on Surface of Prism is defined as the slope at which a prism's surface yields under vertical stress, determining its stability and is represented as I = acos(σvertical/(z*γ)) or Angle of Inclination = acos(Vertical Stress at a Point in Pascal/(Depth of Prism*Unit Weight of Soil)). Vertical Stress at a Point in Pascal is the stress acting perpendicular to the surface, Depth of Prism is the length of prism along z direction & Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.
How to calculate Angle of Inclination given Vertical Stress on Surface of Prism?
The Angle of Inclination given Vertical Stress on Surface of Prism is defined as the slope at which a prism's surface yields under vertical stress, determining its stability is calculated using Angle of Inclination = acos(Vertical Stress at a Point in Pascal/(Depth of Prism*Unit Weight of Soil)). To calculate Angle of Inclination given Vertical Stress on Surface of Prism, you need Vertical Stress at a Point in Pascal vertical), Depth of Prism (z) & Unit Weight of Soil (γ). With our tool, you need to enter the respective value for Vertical Stress at a Point in Pascal, Depth of Prism & Unit Weight of Soil 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 Angle of Inclination?
In this formula, Angle of Inclination uses Vertical Stress at a Point in Pascal, Depth of Prism & Unit Weight of Soil. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Angle of Inclination = acos(Weight of Prism/(Unit Weight of Soil*Depth of Prism*Inclined Length))
  • Angle of Inclination = acos(Horizontal Length of Prism/Inclined Length)
  • Angle of Inclination = acos(Volume per unit length of prism/(Depth of Prism*Inclined Length))
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