Maximum circumferential stress in solid disc Solution

STEP 0: Pre-Calculation Summary
Formula Used
Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8
σc = (ρ*(ω^2)*(3+𝛎)*(router^2))/8
This formula uses 5 Variables
Variables Used
Circumferential Stress - (Measured in Pascal) - Circumferential Stress is the force over area exerted circumferentially perpendicular to the axis and the radius.
Density Of Disc - (Measured in Kilogram per Cubic Meter) - Density Of Disc shows the denseness of disc in a specific given area. This is taken as mass per unit volume of a given disc.
Angular Velocity - (Measured in Radian per Second) - The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.
Poisson's Ratio - Poisson's Ratio is defined as the ratio of the lateral and axial strain. For many metals and alloys, values of Poisson’s ratio range between 0.1 and 0.5.
Outer Radius Disc - (Measured in Meter) - Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.
STEP 1: Convert Input(s) to Base Unit
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
Poisson's Ratio: 0.3 --> No Conversion Required
Outer Radius Disc: 900 Millimeter --> 0.9 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
σc = (ρ*(ω^2)*(3+𝛎)*(router^2))/8 --> (2*(11.2^2)*(3+0.3)*(0.9^2))/8
Evaluating ... ...
σc = 83.82528
STEP 3: Convert Result to Output's Unit
83.82528 Pascal -->83.82528 Newton per Square Meter (Check conversion here)
FINAL ANSWER
83.82528 Newton per Square Meter <-- Circumferential Stress
(Calculation completed in 00.020 seconds)

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!

19 Expression for Stresses in Solid Disc Calculators

Circumferential stress in solid disc given Outer radius
Go Circumferential Stress = ((Density Of Disc*(Angular Velocity^2))*(((3+Poisson's Ratio)*Outer Radius Disc^2)-(1+(3*Poisson's Ratio)*Radius of Element^2)))/8
Poisson's ratio given Circumferential stress in solid disc
Go Poisson's Ratio = (((((Constant at boundary condition/2)-Circumferential Stress)*8)/(Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)))-1)/3
Constant at boundary condition given Circumferential stress in solid disc
Go Constant at boundary condition = 2*(Circumferential Stress+((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*((3*Poisson's Ratio)+1))/8))
Circumferential stress in solid disc
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
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
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 and outer radius
Go Poisson's Ratio = ((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*((Outer Radius Disc^2)-(Radius of Element^2))))-3
Radial stress in solid disc given Outer radius
Go Radial Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2)))/8
Poisson's ratio given Radial stress in solid disc
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 constant at boundary condition for circular disc
Go Poisson's Ratio = ((8*Constant at boundary condition)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3
Constant at boundary condition for circular disc
Go Constant at boundary condition = (Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)*(3+Poisson's Ratio))/8
Poisson's ratio given Circumferential stress at center of solid disc
Go Poisson's Ratio = ((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3
Poisson's Ratio given max circumferential stress in solid disc
Go Poisson's Ratio = ((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3
Circumferential stress at center of solid disc
Go Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8
Maximum circumferential stress in solid disc
Go Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8
Poisson's ratio given Radial stress at center of solid disc
Go Poisson's Ratio = ((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3
Poisson's ratio given maximum radial stress in solid disc
Go Poisson's Ratio = ((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3
Maximum Radial Stress in solid disc
Go Radial Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc ^2))/8
Radial stress at center of solid disc
Go Radial Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8

Maximum circumferential stress in solid disc Formula

Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8
σc = (ρ*(ω^2)*(3+𝛎)*(router^2))/8

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 Maximum circumferential stress in solid disc?

Maximum circumferential stress in solid disc calculator uses Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8 to calculate the Circumferential Stress, The Maximum circumferential stress in solid disc formula is defined as hoop stress, a normal stress in the tangential (azimuth) direction. Circumferential Stress is denoted by σc symbol.

How to calculate Maximum circumferential stress in solid disc using this online calculator? To use this online calculator for Maximum circumferential stress in solid disc, enter Density Of Disc (ρ), Angular Velocity (ω), Poisson's Ratio (𝛎) & Outer Radius Disc (router) and hit the calculate button. Here is how the Maximum circumferential stress in solid disc calculation can be explained with given input values -> 83.82528 = (2*(11.2^2)*(3+0.3)*(0.9^2))/8.

FAQ

What is Maximum circumferential stress in solid disc?
The Maximum circumferential stress in solid disc formula is defined as hoop stress, a normal stress in the tangential (azimuth) direction and is represented as σc = (ρ*(ω^2)*(3+𝛎)*(router^2))/8 or Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8. Density Of Disc shows the denseness of disc in a specific given area. This is taken as mass per unit volume of a given disc, The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time, Poisson's Ratio is defined as the ratio of the lateral and axial strain. For many metals and alloys, values of Poisson’s ratio range between 0.1 and 0.5 & Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.
How to calculate Maximum circumferential stress in solid disc?
The Maximum circumferential stress in solid disc formula is defined as hoop stress, a normal stress in the tangential (azimuth) direction is calculated using Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8. To calculate Maximum circumferential stress in solid disc, you need Density Of Disc (ρ), Angular Velocity (ω), Poisson's Ratio (𝛎) & Outer Radius Disc (router). With our tool, you need to enter the respective value for Density Of Disc, Angular Velocity, Poisson's Ratio & Outer Radius Disc 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 Circumferential Stress?
In this formula, Circumferential Stress uses Density Of Disc, Angular Velocity, Poisson's Ratio & Outer Radius Disc. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Circumferential Stress = (Constant at boundary condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*((3*Poisson's Ratio)+1))/8)
  • Circumferential Stress = ((Density Of Disc*(Angular Velocity^2))*(((3+Poisson's Ratio)*Outer Radius Disc^2)-(1+(3*Poisson's Ratio)*Radius of Element^2)))/8
  • Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!