Radius of disc given stresses on disc Calculator

✖Increase in radius refers to the change or growth in the radius of a circular object (such as a disc, cylinder, or sphere) due to external or internal factors.ⓘ Increase in Radius [ΔR]			+10% -10%
✖Circumferential stress is the stress that acts along the circumference of a cylindrical or spherical object, the stress that develops when the object is subjected to internal or external pressure.ⓘ Circumferential Stress [σ_c]			+10% -10%
✖Poisson's ratio is a material property that describes the relationship between the lateral strain and the longitudinal strain.ⓘ Poisson's Ratio [𝛎]			+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%
✖Modulus of elasticity of disc refers to a material property that measures its ability to resist deformation under stress, specifically in response to stretching or compressing forces.ⓘ Modulus of Elasticity of Disc [E]			+10% -10%

✖Radius of disc is the distance from the center of the disc to any point on its edge (circumference).ⓘ Radius of disc given stresses on disc [r_disc]

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Radius of disc given stresses on disc Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Disc = Increase in Radius/((Circumferential Stress-(Poisson's Ratio*Radial Stress))/Modulus of Elasticity of Disc)
r_disc = ΔR/((σ_c-(𝛎*σ_r))/E)
This formula uses 6 Variables

Variables Used

Radius of Disc - (Measured in Meter) - Radius of disc is the distance from the center of the disc to any point on its edge (circumference).
Increase in Radius - (Measured in Meter) - Increase in radius refers to the change or growth in the radius of a circular object (such as a disc, cylinder, or sphere) due to external or internal factors.
Circumferential Stress - (Measured in Pascal) - Circumferential stress is the stress that acts along the circumference of a cylindrical or spherical object, the stress that develops when the object is subjected to internal or external pressure.
Poisson's Ratio - Poisson's ratio is a material property that describes the relationship between the lateral strain and the longitudinal strain.
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.
Modulus of Elasticity of Disc - (Measured in Pascal) - Modulus of elasticity of disc refers to a material property that measures its ability to resist deformation under stress, specifically in response to stretching or compressing forces.

STEP 1: Convert Input(s) to Base Unit

Increase in Radius: 6.5 Millimeter --> 0.0065 Meter (Check conversion here)
Circumferential Stress: 80 Newton per Square Meter --> 80 Pascal (Check conversion here)
Poisson's Ratio: 0.3 --> No Conversion Required
Radial Stress: 100 Newton per Square Meter --> 100 Pascal (Check conversion here)
Modulus of Elasticity of Disc: 8 Newton per Square Meter --> 8 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_disc = ΔR/((σ_c-(𝛎*σ_r))/E) --> 0.0065/((80-(0.3*100))/8)

Evaluating ... ...

r_disc = 0.00104

STEP 3: Convert Result to Output's Unit

0.00104 Meter -->1.04 Millimeter (Check conversion here)

FINAL ANSWER

1.04 Millimeter <-- Radius of Disc

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Rotating Disc And Cylinder » Expression for Stresses in Rotating Thin Disc » Mechanical » Relation of Parameters » Radius of disc given stresses on disc

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< Relation of Parameters Calculators

Angular speed of rotation for thin cylinder given hoop stress in thin cylinder

LaTeX Go Angular Velocity = Hoop Stress in Disc/(Density of Disc*Radius of Disc)

Density of cylinder material given hoop stress (for thin cylinder)

LaTeX Go Density of Disc = Hoop Stress in Disc/(Angular Velocity*Radius of Disc)

Mean radius of cylinder given hoop stress in thin cylinder

LaTeX Go Radius of Disc = Hoop Stress in Disc/(Density of Disc*Angular Velocity)

Hoop stress in thin cylinder

LaTeX Go Hoop Stress in Disc = Density of Disc*Angular Velocity*Radius of Disc

Radius of disc given stresses on disc Formula

LaTeX Go

Radius of Disc = Increase in Radius/((Circumferential Stress-(Poisson's Ratio*Radial Stress))/Modulus of Elasticity of Disc)
r_disc = ΔR/((σ_c-(𝛎*σ_r))/E)

What is the Allowable Stress?

Allowable stress, also known as allowable strength, is the maximum stress that a material or structure can safely withstand without experiencing failure or permanent deformation. Allowable stress is the stress at which a member is not expected to fail under the given loading conditions.

What is Compression Stress Force?

Compression stress force is the stress that squeezes something. It is the stress component perpendicular to a given surface, such as a fault plane, that results from forces applied perpendicular to the surface or from remote forces transmitted through the surrounding rock.

How to Calculate Radius of disc given stresses on disc?

Radius of disc given stresses on disc calculator uses Radius of Disc = Increase in Radius/((Circumferential Stress-(Poisson's Ratio*Radial Stress))/Modulus of Elasticity of Disc) to calculate the Radius of Disc, Radius of disc given stresses on disc formula is defined as a relationship that describes how the radius of a rotating disc is influenced by the stresses acting on it, accounting for material properties and deformation under load. Radius of Disc is denoted by r_disc symbol.

How to calculate Radius of disc given stresses on disc using this online calculator? To use this online calculator for Radius of disc given stresses on disc, enter Increase in Radius (ΔR), Circumferential Stress (σ_c), Poisson's Ratio (𝛎), Radial Stress (σ_r) & Modulus of Elasticity of Disc (E) and hit the calculate button. Here is how the Radius of disc given stresses on disc calculation can be explained with given input values -> 1040 = 0.0065/((80-(0.3*100))/8).

FAQ

What is Radius of disc given stresses on disc?

Radius of disc given stresses on disc formula is defined as a relationship that describes how the radius of a rotating disc is influenced by the stresses acting on it, accounting for material properties and deformation under load and is represented as r_disc = ΔR/((σ_c-(𝛎*σ_r))/E) or Radius of Disc = Increase in Radius/((Circumferential Stress-(Poisson's Ratio*Radial Stress))/Modulus of Elasticity of Disc). Increase in radius refers to the change or growth in the radius of a circular object (such as a disc, cylinder, or sphere) due to external or internal factors, Circumferential stress is the stress that acts along the circumference of a cylindrical or spherical object, the stress that develops when the object is subjected to internal or external pressure, Poisson's ratio is a material property that describes the relationship between the lateral strain and the longitudinal strain, 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 & Modulus of elasticity of disc refers to a material property that measures its ability to resist deformation under stress, specifically in response to stretching or compressing forces.

How to calculate Radius of disc given stresses on disc?

Radius of disc given stresses on disc formula is defined as a relationship that describes how the radius of a rotating disc is influenced by the stresses acting on it, accounting for material properties and deformation under load is calculated using Radius of Disc = Increase in Radius/((Circumferential Stress-(Poisson's Ratio*Radial Stress))/Modulus of Elasticity of Disc). To calculate Radius of disc given stresses on disc, you need Increase in Radius (ΔR), Circumferential Stress (σ_c), Poisson's Ratio (𝛎), Radial Stress (σ_r) & Modulus of Elasticity of Disc (E). With our tool, you need to enter the respective value for Increase in Radius, Circumferential Stress, Poisson's Ratio, Radial Stress & Modulus of Elasticity of 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 Radius of Disc?

In this formula, Radius of Disc uses Increase in Radius, Circumferential Stress, Poisson's Ratio, Radial Stress & Modulus of Elasticity of Disc. We can use 2 other way(s) to calculate the same, which is/are as follows -

Radius of Disc = Hoop Stress in Disc/(Density of Disc*Angular Velocity)
Radius of Disc = Increase in Radius/Circumferential Strain

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