Change in diameter of thin spherical shell Calculator

✖Internal Pressure is a measure of how the internal energy of a system changes when it expands or contracts at a constant temperature.ⓘ Internal Pressure [P_i]			+10% -10%
✖Diameter of Sphere, is a chord that runs through the center point of the circle. It is the longest possible chord of any circle. The center of a circle is the midpoint of its diameter.ⓘ Diameter of Sphere [D]			+10% -10%
✖Thickness Of Thin Spherical Shell is the distance through an object.ⓘ Thickness Of Thin Spherical Shell [t]			+10% -10%
✖Modulus of Elasticity Of Thin 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 Thin Shell [E]			+10% -10%
✖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.ⓘ Poisson's Ratio [𝛎]			+10% -10%

✖The Change in Diameter is the difference between the initial and final diameter.ⓘ Change in diameter of thin spherical shell [∆d]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Strength of Materials Formula PDF PDF Image

Change in diameter of thin spherical shell Solution

STEP 0: Pre-Calculation Summary

Formula Used

Change in Diameter = ((Internal Pressure*(Diameter of Sphere^2))/(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell))*(1-Poisson's Ratio)
∆d = ((P_i*(D^2))/(4*t*E))*(1-𝛎)
This formula uses 6 Variables

Variables Used

Change in Diameter - (Measured in Meter) - The Change in Diameter is the difference between the initial and final diameter.
Internal Pressure - (Measured in Pascal) - Internal Pressure is a measure of how the internal energy of a system changes when it expands or contracts at a constant temperature.
Diameter of Sphere - (Measured in Meter) - Diameter of Sphere, is a chord that runs through the center point of the circle. It is the longest possible chord of any circle. The center of a circle is the midpoint of its diameter.
Thickness Of Thin Spherical Shell - (Measured in Meter) - Thickness Of Thin Spherical Shell is the distance through an object.
Modulus of Elasticity Of Thin Shell - (Measured in Pascal) - Modulus of Elasticity Of Thin Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it.
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.

STEP 1: Convert Input(s) to Base Unit

Internal Pressure: 0.053 Megapascal --> 53000 Pascal (Check conversion here)
Diameter of Sphere: 1500 Millimeter --> 1.5 Meter (Check conversion here)
Thickness Of Thin Spherical Shell: 12 Millimeter --> 0.012 Meter (Check conversion here)
Modulus of Elasticity Of Thin Shell: 10 Megapascal --> 10000000 Pascal (Check conversion here)
Poisson's Ratio: 0.3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∆d = ((P_i*(D^2))/(4*t*E))*(1-𝛎) --> ((53000*(1.5^2))/(4*0.012*10000000))*(1-0.3)

Evaluating ... ...

∆d = 0.17390625

STEP 3: Convert Result to Output's Unit

0.17390625 Meter -->173.90625 Millimeter (Check conversion here)

FINAL ANSWER

173.90625 ≈ 173.9062 Millimeter <-- Change in Diameter

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Strength of Materials » Thin Cylinders And Spheres » Mechanical » Change in Dimension of Thin Spherical Shell due to Internal Pressure » Change in diameter of thin spherical shell

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!

< Change in Dimension of Thin Spherical Shell due to Internal Pressure Calculators

Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio

LaTeX Go Hoop Stress in Thin shell = (Strain in thin shell/(1-Poisson's Ratio))*Modulus of Elasticity Of Thin Shell

Modulus of elasticity of thin spherical shell given strain in any one direction

LaTeX Go Modulus of Elasticity Of Thin Shell = (Hoop Stress in Thin shell/Strain in thin shell)*(1-Poisson's Ratio)

Hoop stress induced in thin spherical shell given strain in any one direction

LaTeX Go Hoop Stress in Thin shell = (Strain in thin shell/(1-Poisson's Ratio))*Modulus of Elasticity Of Thin Shell

Strain in any one direction of thin spherical shell

LaTeX Go Strain in thin shell = (Hoop Stress in Thin shell/Modulus of Elasticity Of Thin Shell)*(1-Poisson's Ratio)

Change in diameter of thin spherical shell Formula

LaTeX Go

Change in Diameter = ((Internal Pressure*(Diameter of Sphere^2))/(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell))*(1-Poisson's Ratio)
∆d = ((P_i*(D^2))/(4*t*E))*(1-𝛎)

How do you reduce stress hoop?

We can suggest that the most efficient method is to apply double cold expansion with high interferences along with axial compression with strain equal to 0.5%. This technique helps to reduce the absolute value of hoop residual stresses by 58%, and decrease radial stresses by 75%.

How to Calculate Change in diameter of thin spherical shell?

Change in diameter of thin spherical shell calculator uses Change in Diameter = ((Internal Pressure*(Diameter of Sphere^2))/(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell))*(1-Poisson's Ratio) to calculate the Change in Diameter, The Change in diameter of thin spherical shell formula is defined as a change that happened in diameter due to the strain in the thin spherical shell. Change in Diameter is denoted by ∆d symbol.

How to calculate Change in diameter of thin spherical shell using this online calculator? To use this online calculator for Change in diameter of thin spherical shell, enter Internal Pressure (P_i), Diameter of Sphere (D), Thickness Of Thin Spherical Shell (t), Modulus of Elasticity Of Thin Shell (E) & Poisson's Ratio (𝛎) and hit the calculate button. Here is how the Change in diameter of thin spherical shell calculation can be explained with given input values -> 173906.2 = ((53000*(1.5^2))/(4*0.012*10000000))*(1-0.3).

FAQ

What is Change in diameter of thin spherical shell?

The Change in diameter of thin spherical shell formula is defined as a change that happened in diameter due to the strain in the thin spherical shell and is represented as ∆d = ((P_i*(D^2))/(4*t*E))*(1-𝛎) or Change in Diameter = ((Internal Pressure*(Diameter of Sphere^2))/(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell))*(1-Poisson's Ratio). Internal Pressure is a measure of how the internal energy of a system changes when it expands or contracts at a constant temperature, Diameter of Sphere, is a chord that runs through the center point of the circle. It is the longest possible chord of any circle. The center of a circle is the midpoint of its diameter, Thickness Of Thin Spherical Shell is the distance through an object, Modulus of Elasticity Of Thin Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it & 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.

How to calculate Change in diameter of thin spherical shell?

The Change in diameter of thin spherical shell formula is defined as a change that happened in diameter due to the strain in the thin spherical shell is calculated using Change in Diameter = ((Internal Pressure*(Diameter of Sphere^2))/(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell))*(1-Poisson's Ratio). To calculate Change in diameter of thin spherical shell, you need Internal Pressure (P_i), Diameter of Sphere (D), Thickness Of Thin Spherical Shell (t), Modulus of Elasticity Of Thin Shell (E) & Poisson's Ratio (𝛎). With our tool, you need to enter the respective value for Internal Pressure, Diameter of Sphere, Thickness Of Thin Spherical Shell, Modulus of Elasticity Of Thin Shell & Poisson's Ratio 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