Constant 'a' for inner cylinder given original difference of radii at junction Calculator

✖Constant 'a' for outer cylinder is defined as the constant used in lame's equation.ⓘ Constant 'a' for outer cylinder [a₁]			+10% -10%
✖Original difference of radii is the original difference happened in the inner and outer radius of compound cylinder.ⓘ Original difference of radii [Δr_original]			+10% -10%
✖Modulus of Elasticity Of Thick Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it.ⓘ Modulus of Elasticity Of Thick Shell [E]			+10% -10%
✖The Radius at Junction is the radius value at the junction of compound cylinders.ⓘ Radius at Junction [r_*]			+10% -10%

✖Constant 'a' for inner cylinder is defined as the constant used in lame's equation.ⓘ Constant 'a' for inner cylinder given original difference of radii at junction [a₂]

⎘ Copy

👎

Formula

✖

Constant 'a' for inner cylinder given original difference of radii at junction

Formula

a 2 = a 1 - (Δr original \cdot \frac{E}{2 \cdot r *})

Example

-2.5 = 4 - (0.02 mm \cdot \frac{2.6 MPa}{2 \cdot 4000 mm})

Calculator

LaTeX

Reset

👍

Download Strength of Materials Formula PDF PDF Image

Constant 'a' for inner cylinder given original difference of radii at junction Solution

STEP 0: Pre-Calculation Summary

Formula Used

Constant 'a' for inner cylinder = Constant 'a' for outer cylinder-(Original difference of radii*Modulus of Elasticity Of Thick Shell/(2*Radius at Junction))
a₂ = a₁-(Δr_original*E/(2*r_*))
This formula uses 5 Variables

Variables Used

Constant 'a' for inner cylinder - Constant 'a' for inner cylinder is defined as the constant used in lame's equation.
Constant 'a' for outer cylinder - Constant 'a' for outer cylinder is defined as the constant used in lame's equation.
Original difference of radii - (Measured in Meter) - Original difference of radii is the original difference happened in the inner and outer radius of compound cylinder.
Modulus of Elasticity Of Thick Shell - (Measured in Pascal) - Modulus of Elasticity Of Thick Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it.
Radius at Junction - (Measured in Meter) - The Radius at Junction is the radius value at the junction of compound cylinders.

STEP 1: Convert Input(s) to Base Unit

Constant 'a' for outer cylinder: 4 --> No Conversion Required
Original difference of radii: 0.02 Millimeter --> 2E-05 Meter (Check conversion here)
Modulus of Elasticity Of Thick Shell: 2.6 Megapascal --> 2600000 Pascal (Check conversion here)
Radius at Junction: 4000 Millimeter --> 4 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a₂ = a₁-(Δr_original*E/(2*r_*)) --> 4-(2E-05*2600000/(2*4))

Evaluating ... ...

a₂ = -2.5

STEP 3: Convert Result to Output's Unit

-2.5 --> No Conversion Required

FINAL ANSWER

-2.5 <-- Constant 'a' for inner cylinder

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Strength of Materials » Thick Cylinders And Spheres » Mechanical » Compound Cylinder Shrinkage Radii Change » Constant 'a' for inner cylinder given original difference of radii at junction

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!

< Compound Cylinder Shrinkage Radii Change Calculators

Radius at junction of compound cylinder given increase in inner radius of outer cylinder

Go Radius at Junction = (Increase in radius*Modulus of Elasticity Of Thick Shell)/(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))

Increase in inner radius of outer cylinder at junction of compound cylinder

Go Increase in radius = (Radius at Junction/Modulus of Elasticity Of Thick Shell)*(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))

Radial pressure given increase in inner radius of outer cylinder

Go Radial Pressure = ((Increase in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-Hoop Stress on thick shell)*Mass Of Shell

Hoop stress given increase in inner radius of outer cylinder

Go Hoop Stress on thick shell = (Increase in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-(Radial Pressure/Mass Of Shell)

Constant 'a' for inner cylinder given original difference of radii at junction Formula

Constant 'a' for inner cylinder = Constant 'a' for outer cylinder-(Original difference of radii*Modulus of Elasticity Of Thick Shell/(2*Radius at Junction))
a₂ = a₁-(Δr_original*E/(2*r_*))

What is meant by hoop stress?

The hoop stress is the force over the area exerted circumferentially (perpendicular to the axis and the radius of the object) in both directions on every particle in the cylinder wall.

How to Calculate Constant 'a' for inner cylinder given original difference of radii at junction?

Constant 'a' for inner cylinder given original difference of radii at junction calculator uses Constant 'a' for inner cylinder = Constant 'a' for outer cylinder-(Original difference of radii*Modulus of Elasticity Of Thick Shell/(2*Radius at Junction)) to calculate the Constant 'a' for inner cylinder, The Constant 'a' for inner cylinder given original difference of radii at junction formula is defined as the constant used in lame's equation for the compound cylinder. Constant 'a' for inner cylinder is denoted by a₂ symbol.

How to calculate Constant 'a' for inner cylinder given original difference of radii at junction using this online calculator? To use this online calculator for Constant 'a' for inner cylinder given original difference of radii at junction, enter Constant 'a' for outer cylinder (a₁), Original difference of radii (Δr_original), Modulus of Elasticity Of Thick Shell (E) & Radius at Junction (r_*) and hit the calculate button. Here is how the Constant 'a' for inner cylinder given original difference of radii at junction calculation can be explained with given input values -> -2.5 = 4-(2E-05*2600000/(2*4)).

FAQ

What is Constant 'a' for inner cylinder given original difference of radii at junction?

The Constant 'a' for inner cylinder given original difference of radii at junction formula is defined as the constant used in lame's equation for the compound cylinder and is represented as a₂ = a₁-(Δr_original*E/(2*r_*)) or Constant 'a' for inner cylinder = Constant 'a' for outer cylinder-(Original difference of radii*Modulus of Elasticity Of Thick Shell/(2*Radius at Junction)). Constant 'a' for outer cylinder is defined as the constant used in lame's equation, Original difference of radii is the original difference happened in the inner and outer radius of compound cylinder, Modulus of Elasticity Of Thick Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it & The Radius at Junction is the radius value at the junction of compound cylinders.

How to calculate Constant 'a' for inner cylinder given original difference of radii at junction?

The Constant 'a' for inner cylinder given original difference of radii at junction formula is defined as the constant used in lame's equation for the compound cylinder is calculated using Constant 'a' for inner cylinder = Constant 'a' for outer cylinder-(Original difference of radii*Modulus of Elasticity Of Thick Shell/(2*Radius at Junction)). To calculate Constant 'a' for inner cylinder given original difference of radii at junction, you need Constant 'a' for outer cylinder (a₁), Original difference of radii (Δr_original), Modulus of Elasticity Of Thick Shell (E) & Radius at Junction (r_*). With our tool, you need to enter the respective value for Constant 'a' for outer cylinder, Original difference of radii, Modulus of Elasticity Of Thick Shell & Radius at Junction and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search