Distance from Middle Surface given Normal Stress in Thin Shells Calculator

✖Shell thickness is the the distance through the shell.ⓘ Shell Thickness [t]			+10% -10%
✖Unit Bending Moment is the external force or moment acting on a member which allows the member to bend whose magnitude is unity.ⓘ Unit Bending Moment [M_x]			+10% -10%
✖Normal Stress on Thin Shells is the stress caused on the thin shell due to the normal force (axial load) on the surface.ⓘ Normal Stress on Thin Shells [f_x]			+10% -10%
✖Unit Normal Force is the force acting perpendicular to the surface in contact with each other whose magnitude is unity.ⓘ Unit Normal Force [N_x]			+10% -10%

✖Distance from Middle Surface is the half distance from middle surface to extreme surface, say half the thickness.ⓘ Distance from Middle Surface given Normal Stress in Thin Shells [z]

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Distance from Middle Surface given Normal Stress in Thin Shells Solution

STEP 0: Pre-Calculation Summary

Formula Used

Distance from Middle Surface = (Shell Thickness^(2)/(12*Unit Bending Moment))*((Normal Stress on Thin Shells*Shell Thickness)-(Unit Normal Force))
z = (t^(2)/(12*M_x))*((f_x*t)-(N_x))
This formula uses 5 Variables

Variables Used

Distance from Middle Surface - (Measured in Meter) - Distance from Middle Surface is the half distance from middle surface to extreme surface, say half the thickness.
Shell Thickness - (Measured in Meter) - Shell thickness is the the distance through the shell.
Unit Bending Moment - (Measured in Newton Meter) - Unit Bending Moment is the external force or moment acting on a member which allows the member to bend whose magnitude is unity.
Normal Stress on Thin Shells - (Measured in Pascal) - Normal Stress on Thin Shells is the stress caused on the thin shell due to the normal force (axial load) on the surface.
Unit Normal Force - (Measured in Newton) - Unit Normal Force is the force acting perpendicular to the surface in contact with each other whose magnitude is unity.

STEP 1: Convert Input(s) to Base Unit

Shell Thickness: 200 Millimeter --> 0.2 Meter (Check conversion here)
Unit Bending Moment: 90 Kilonewton Meter --> 90000 Newton Meter (Check conversion here)
Normal Stress on Thin Shells: 2.7 Megapascal --> 2700000 Pascal (Check conversion here)
Unit Normal Force: 15 Newton --> 15 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z = (t^(2)/(12*M_x))*((f_x*t)-(N_x)) --> (0.2^(2)/(12*90000))*((2700000*0.2)-(15))

Evaluating ... ...

z = 0.0199994444444444

STEP 3: Convert Result to Output's Unit

0.0199994444444444 Meter --> No Conversion Required

FINAL ANSWER

0.0199994444444444 ≈ 0.019999 Meter <-- Distance from Middle Surface

(Calculation completed in 00.004 seconds)

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NSS College of Engineering (NSSCE), Palakkad

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< Stresses in Thin Shells Calculators

Distance from Middle Surface given Normal Stress in Thin Shells

LaTeX Go Distance from Middle Surface = (Shell Thickness^(2)/(12*Unit Bending Moment))*((Normal Stress on Thin Shells*Shell Thickness)-(Unit Normal Force))

Normal Stress in Thin Shells

LaTeX Go Normal Stress on Thin Shells = (Unit Normal Force/Shell Thickness)+((Unit Bending Moment*Distance from Middle Surface)/(Shell Thickness^(3)/12))

Shearing Stresses on Shells

LaTeX Go Shearing Stress on Shells = ((Central Shear/Shell Thickness)+((Twisting Moments on Shells*Distance from Middle Surface*12)/Shell Thickness^3))

Central Shear given Shearing Stress

LaTeX Go Central Shear = (Shearing Stress on Shells-((Twisting Moments on Shells*Distance from Middle Surface*12)/Shell Thickness^3))*Shell Thickness

Distance from Middle Surface given Normal Stress in Thin Shells Formula

LaTeX Go

Distance from Middle Surface = (Shell Thickness^(2)/(12*Unit Bending Moment))*((Normal Stress on Thin Shells*Shell Thickness)-(Unit Normal Force))
z = (t^(2)/(12*M_x))*((f_x*t)-(N_x))

What is Shell Theory?

The shell theories are based on the assumption that the strains in the shell are small enough to be discarded in comparison with unity. It is also assumed that the shell is thin enough that quantities, such as the thickness/radius ratio may be discarded in comparison with unity. The theorem says that a spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its center.

What is Normal Stress?

The Normal Stress is a result of load applied perpendicular to a member. Shear stress however results when a load is applied parallel to an area. If in case the shear force acting is normal to the surface, normal stress occurs.

How to Calculate Distance from Middle Surface given Normal Stress in Thin Shells?

Distance from Middle Surface given Normal Stress in Thin Shells calculator uses Distance from Middle Surface = (Shell Thickness^(2)/(12*Unit Bending Moment))*((Normal Stress on Thin Shells*Shell Thickness)-(Unit Normal Force)) to calculate the Distance from Middle Surface, The Distance from Middle Surface given Normal Stress in Thin Shells formula is defined as the relation between the unit normal force and stress and the bending moment on the shell surface. Distance from Middle Surface is denoted by z symbol.

How to calculate Distance from Middle Surface given Normal Stress in Thin Shells using this online calculator? To use this online calculator for Distance from Middle Surface given Normal Stress in Thin Shells, enter Shell Thickness (t), Unit Bending Moment (M_x), Normal Stress on Thin Shells (f_x) & Unit Normal Force (N_x) and hit the calculate button. Here is how the Distance from Middle Surface given Normal Stress in Thin Shells calculation can be explained with given input values -> 0.019999 = (0.2^(2)/(12*90000))*((2700000*0.2)-(15)).

FAQ

What is Distance from Middle Surface given Normal Stress in Thin Shells?

The Distance from Middle Surface given Normal Stress in Thin Shells formula is defined as the relation between the unit normal force and stress and the bending moment on the shell surface and is represented as z = (t^(2)/(12*M_x))*((f_x*t)-(N_x)) or Distance from Middle Surface = (Shell Thickness^(2)/(12*Unit Bending Moment))*((Normal Stress on Thin Shells*Shell Thickness)-(Unit Normal Force)). Shell thickness is the the distance through the shell, Unit Bending Moment is the external force or moment acting on a member which allows the member to bend whose magnitude is unity, Normal Stress on Thin Shells is the stress caused on the thin shell due to the normal force (axial load) on the surface & Unit Normal Force is the force acting perpendicular to the surface in contact with each other whose magnitude is unity.

How to calculate Distance from Middle Surface given Normal Stress in Thin Shells?

The Distance from Middle Surface given Normal Stress in Thin Shells formula is defined as the relation between the unit normal force and stress and the bending moment on the shell surface is calculated using Distance from Middle Surface = (Shell Thickness^(2)/(12*Unit Bending Moment))*((Normal Stress on Thin Shells*Shell Thickness)-(Unit Normal Force)). To calculate Distance from Middle Surface given Normal Stress in Thin Shells, you need Shell Thickness (t), Unit Bending Moment (M_x), Normal Stress on Thin Shells (f_x) & Unit Normal Force (N_x). With our tool, you need to enter the respective value for Shell Thickness, Unit Bending Moment, Normal Stress on Thin Shells & Unit Normal Force 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 Distance from Middle Surface?

In this formula, Distance from Middle Surface uses Shell Thickness, Unit Bending Moment, Normal Stress on Thin Shells & Unit Normal Force. We can use 1 other way(s) to calculate the same, which is/are as follows -

Distance from Middle Surface = sqrt((Shell Thickness^(2)/4)-((Normal Shearing Stress*Shell Thickness^3)/(6*Unit Shear Force)))

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