Angle of Inclination given Vertical Stress on Surface of Prism Calculator

✖Vertical Stress at a Point in Pascal is the stress acting perpendicular to the surface.ⓘ Vertical Stress at a Point in Pascal [σ_vertical]			+10% -10%
✖Depth of Prism is the length of prism along z direction.ⓘ Depth of Prism [z]			+10% -10%
✖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%

✖Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object.ⓘ Angle of Inclination given Vertical Stress on Surface of Prism [I]

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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(σ_vertical/(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(σ_vertical/(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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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Calculator and 2100+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< Stability Analysis of Infinite Slopes in Prism Calculators

Inclined Length along Slope given Weight of Soil Prism

LaTeX 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

LaTeX Go Unit Weight of Soil = Weight of Prism/(Depth of Prism*Inclined Length*cos((Angle of Inclination)))

Weight of Soil Prism in Stability Analysis

LaTeX 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

LaTeX Go Depth of Prism = Weight of Prism/(Unit Weight of Soil*Inclined Length*cos((Angle of Inclination)))

Angle of Inclination given Vertical Stress on Surface of Prism Formula

LaTeX Go

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