Poisson's ratio given Radial stress in solid disc Calculator

✖Constant at boundary condition refers to a type of boundary condition in mathematical and physical problems where a specific variable is held constant along the boundary of the domain.ⓘ Constant at Boundary [C]			+10% -10%
✖Radial stress refers to the stress that acts perpendicular to the longitudinal axis of a component, directed either towards or away from the central axis.ⓘ Radial Stress [σ_r]			+10% -10%
✖Density of disc typically refers to the mass per unit volume of the disc material. It is a measure of how much mass is contained in a given volume of the disc.ⓘ Density Of Disc [ρ]			+10% -10%
✖Angular velocity is a measure of how quickly an object rotates or revolves around a central point or axis, describes the rate of change of the angular position of the object with respect to time.ⓘ Angular Velocity [ω]			+10% -10%
✖Disc radius is the distance from the center of the disc to any point on its circumference.ⓘ Disc Radius [r_disc]			+10% -10%

✖Poisson's ratio is a measure of the deformation of a material in directions perpendicular to the direction of loading. It is defined as the negative ratio of transverse strain to axial strain.ⓘ Poisson's ratio given Radial stress in solid disc [𝛎]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Strength of Materials Formula PDF PDF Image

Poisson's ratio given Radial stress in solid disc Solution

STEP 0: Pre-Calculation Summary

Formula Used

Poisson's Ratio = ((((Constant at Boundary/2)-Radial Stress)*8)/(Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)))-3
𝛎 = ((((C/2)-σ_r)*8)/(ρ*(ω^2)*(r_disc^2)))-3
This formula uses 6 Variables

Variables Used

Poisson's Ratio - Poisson's ratio is a measure of the deformation of a material in directions perpendicular to the direction of loading. It is defined as the negative ratio of transverse strain to axial strain.
Constant at Boundary - Constant at boundary condition refers to a type of boundary condition in mathematical and physical problems where a specific variable is held constant along the boundary of the domain.
Radial Stress - (Measured in Pascal) - Radial stress refers to the stress that acts perpendicular to the longitudinal axis of a component, directed either towards or away from the central axis.
Density Of Disc - (Measured in Kilogram per Cubic Meter) - Density of disc typically refers to the mass per unit volume of the disc material. It is a measure of how much mass is contained in a given volume of the disc.
Angular Velocity - (Measured in Radian per Second) - Angular velocity is a measure of how quickly an object rotates or revolves around a central point or axis, describes the rate of change of the angular position of the object with respect to time.
Disc Radius - (Measured in Meter) - Disc radius is the distance from the center of the disc to any point on its circumference.

STEP 1: Convert Input(s) to Base Unit

Constant at Boundary: 400 --> No Conversion Required
Radial Stress: 100 Newton per Square Meter --> 100 Pascal (Check conversion here)
Density Of Disc: 2 Kilogram per Cubic Meter --> 2 Kilogram per Cubic Meter No Conversion Required
Angular Velocity: 11.2 Radian per Second --> 11.2 Radian per Second No Conversion Required
Disc Radius: 1000 Millimeter --> 1 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝛎 = ((((C/2)-σ_r)*8)/(ρ*(ω^2)*(r_disc^2)))-3 --> ((((400/2)-100)*8)/(2*(11.2^2)*(1^2)))-3

Evaluating ... ...

𝛎 = 0.188775510204082

STEP 3: Convert Result to Output's Unit

0.188775510204082 --> No Conversion Required

FINAL ANSWER

0.188775510204082 ≈ 0.188776 <-- Poisson's Ratio

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Strength of Materials » Rotating Disc And Cylinder » Expression for Stresses in Solid Disc » Mechanical » Stresses in Disc » Poisson's ratio given Radial stress in solid disc

Credits

Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Calculator and 2000+ more calculators!

Verified by Payal Priya

Birsa Institute of Technology (BIT), Sindri

Payal Priya has verified this Calculator and 1900+ more calculators!

< Stresses in Disc Calculators

Circumferential stress in solid disc

LaTeX Go Circumferential Stress = (Constant at Boundary Condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*((3*Poisson's Ratio)+1))/8)

Constant at boundary condition given Radial stress in solid disc

LaTeX Go Constant at Boundary Condition = 2*(Radial Stress+((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*(3+Poisson's Ratio))/8))

Radial stress in solid disc

LaTeX Go Radial Stress = (Constant at Boundary Condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*(3+Poisson's Ratio))/8)

Poisson's ratio given Radial stress in solid disc

LaTeX Go Poisson's Ratio = ((((Constant at Boundary/2)-Radial Stress)*8)/(Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)))-3

Poisson's ratio given Radial stress in solid disc Formula

LaTeX Go

Poisson's Ratio = ((((Constant at Boundary/2)-Radial Stress)*8)/(Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)))-3
𝛎 = ((((C/2)-σ_r)*8)/(ρ*(ω^2)*(r_disc^2)))-3

What is radial and tangential stress?

The “Hoop Stress” or “Tangential Stress” acts on a line perpendicular to the “longitudinal “and the “radial stress;” this stress attempts to separate the pipe wall in the circumferential direction. This stress is caused by internal pressure.

How to Calculate Poisson's ratio given Radial stress in solid disc?

Poisson's ratio given Radial stress in solid disc calculator uses Poisson's Ratio = ((((Constant at Boundary/2)-Radial Stress)*8)/(Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)))-3 to calculate the Poisson's Ratio, The Poisson's ratio given Radial stress in solid disc formula is defined as a measure of the Poisson effect, the phenomenon in which a material tends to expand in directions perpendicular to the direction of compression. Poisson's Ratio is denoted by 𝛎 symbol.

How to calculate Poisson's ratio given Radial stress in solid disc using this online calculator? To use this online calculator for Poisson's ratio given Radial stress in solid disc, enter Constant at Boundary (C), Radial Stress (σ_r), Density Of Disc (ρ), Angular Velocity (ω) & Disc Radius (r_disc) and hit the calculate button. Here is how the Poisson's ratio given Radial stress in solid disc calculation can be explained with given input values -> 0.188776 = ((((400/2)-100)*8)/(2*(11.2^2)*(1^2)))-3.

FAQ

What is Poisson's ratio given Radial stress in solid disc?

The Poisson's ratio given Radial stress in solid disc formula is defined as a measure of the Poisson effect, the phenomenon in which a material tends to expand in directions perpendicular to the direction of compression and is represented as 𝛎 = ((((C/2)-σ_r)*8)/(ρ*(ω^2)*(r_disc^2)))-3 or Poisson's Ratio = ((((Constant at Boundary/2)-Radial Stress)*8)/(Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)))-3. Constant at boundary condition refers to a type of boundary condition in mathematical and physical problems where a specific variable is held constant along the boundary of the domain, Radial stress refers to the stress that acts perpendicular to the longitudinal axis of a component, directed either towards or away from the central axis, Density of disc typically refers to the mass per unit volume of the disc material. It is a measure of how much mass is contained in a given volume of the disc, Angular velocity is a measure of how quickly an object rotates or revolves around a central point or axis, describes the rate of change of the angular position of the object with respect to time & Disc radius is the distance from the center of the disc to any point on its circumference.

How to calculate Poisson's ratio given Radial stress in solid disc?

The Poisson's ratio given Radial stress in solid disc formula is defined as a measure of the Poisson effect, the phenomenon in which a material tends to expand in directions perpendicular to the direction of compression is calculated using Poisson's Ratio = ((((Constant at Boundary/2)-Radial Stress)*8)/(Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)))-3. To calculate Poisson's ratio given Radial stress in solid disc, you need Constant at Boundary (C), Radial Stress (σ_r), Density Of Disc (ρ), Angular Velocity (ω) & Disc Radius (r_disc). With our tool, you need to enter the respective value for Constant at Boundary, Radial Stress, Density Of Disc, Angular Velocity & Disc Radius 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 Poisson's Ratio?

In this formula, Poisson's Ratio uses Constant at Boundary, Radial Stress, Density Of Disc, Angular Velocity & Disc Radius. We can use 3 other way(s) to calculate the same, which is/are as follows -

Poisson's Ratio = (((((Constant at Boundary Condition/2)-Circumferential Stress)*8)/(Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)))-1)/3
Poisson's Ratio = ((8*Constant at Boundary Condition)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3
Poisson's Ratio = ((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*((Outer Radius Disc^2)-(Radius of Element^2))))-3

Home

FREE PDFs

🔍 Search