Normal Stress in Thin Shells Calculator

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

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Formula

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Normal Stress in Thin Shells

Formula

`"f"_{"x"} = ("N"_{"x"}/"t")+(("M"_{"x"}*"z")/("t"^(3)/12))`

Example

`"2.700075MPa"=("15N"/"200mm")+(("90kN*m"*"0.02m")/(("200mm")^(3)/12))`

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Normal Stress in Thin Shells Solution

STEP 0: Pre-Calculation Summary

Formula Used

Normal Stress on Thin Shells = (Unit Normal Force/Shell Thickness)+((Unit Bending Moment*Distance from Middle Surface)/(Shell Thickness^(3)/12))
f_x = (N_x/t)+((M_x*z)/(t^(3)/12))
This formula uses 5 Variables

Variables Used

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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Unit Normal Force: 15 Newton --> 15 Newton No Conversion Required
Shell Thickness: 200 Millimeter --> 0.2 Meter (Check conversion here)
Unit Bending Moment: 90 Kilonewton Meter --> 90000 Newton Meter (Check conversion here)
Distance from Middle Surface: 0.02 Meter --> 0.02 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_x = (N_x/t)+((M_x*z)/(t^(3)/12)) --> (15/0.2)+((90000*0.02)/(0.2^(3)/12))

Evaluating ... ...

f_x = 2700075

STEP 3: Convert Result to Output's Unit

2700075 Pascal -->2.700075 Megapascal (Check conversion here)

FINAL ANSWER

2.700075 Megapascal <-- Normal Stress on Thin Shells

(Calculation completed in 00.004 seconds)

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< 7 Stresses in Thin Shells Calculators

Distance from Middle Surface given Normal Stress in Thin Shells

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

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

Twisting Moments given Shearing Stress

Go Twisting Moments on Shells = (((Shearing Stress on Shells*Shell Thickness)-Central Shear)*Shell Thickness^2)/(12*Distance from Middle Surface)

Shearing Stresses on Shells

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

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 Shearing Stress

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

Normal Shearing Stresses

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

Normal Stress in Thin Shells Formula

Normal Stress on Thin Shells = (Unit Normal Force/Shell Thickness)+((Unit Bending Moment*Distance from Middle Surface)/(Shell Thickness^(3)/12))
f_x = (N_x/t)+((M_x*z)/(t^(3)/12))

What are Thin Shells?

A thin shell is defined as a shell with a thickness which is small compared to its other dimensions and in which deformations are not large compared to thickness. Thin-shell structures are lightweight constructions using shell elements. These elements, typically curved, are assembled to make large structures. Typical applications include aircraft fuselages, boat hulls, and the roofs of large buildings.

What are the forces acting on Shells?

The internal forces and moments exist at every point on the middle surface of the shell element. They represent the resultants of different normal and shear stresses over the element thickness. The internal forces have the units of force per unit length and the internal moments have the units of moment per unit length.

How to Calculate Normal Stress in Thin Shells?

Normal Stress in Thin Shells calculator uses Normal Stress on Thin Shells = (Unit Normal Force/Shell Thickness)+((Unit Bending Moment*Distance from Middle Surface)/(Shell Thickness^(3)/12)) to calculate the Normal Stress on Thin Shells, The Normal Stress in Thin Shells formula is defined as the perpendicular stress formed on the shell surface due to the normal force acting on it and the force is assumed to be uniformly distributed along the surface of the thin shell. Normal Stress on Thin Shells is denoted by f_x symbol.

How to calculate Normal Stress in Thin Shells using this online calculator? To use this online calculator for Normal Stress in Thin Shells, enter Unit Normal Force (N_x), Shell Thickness (t), Unit Bending Moment (M_x) & Distance from Middle Surface (z) and hit the calculate button. Here is how the Normal Stress in Thin Shells calculation can be explained with given input values -> 0.0027 = (15/0.2)+((90000*0.02)/(0.2^(3)/12)).

FAQ

What is Normal Stress in Thin Shells?

The Normal Stress in Thin Shells formula is defined as the perpendicular stress formed on the shell surface due to the normal force acting on it and the force is assumed to be uniformly distributed along the surface of the thin shell and is represented as f_x = (N_x/t)+((M_x*z)/(t^(3)/12)) or Normal Stress on Thin Shells = (Unit Normal Force/Shell Thickness)+((Unit Bending Moment*Distance from Middle Surface)/(Shell Thickness^(3)/12)). Unit Normal Force is the force acting perpendicular to the surface in contact with each other whose magnitude is unity, 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 & Distance from Middle Surface is the half distance from middle surface to extreme surface, say half the thickness.

How to calculate Normal Stress in Thin Shells?

The Normal Stress in Thin Shells formula is defined as the perpendicular stress formed on the shell surface due to the normal force acting on it and the force is assumed to be uniformly distributed along the surface of the thin shell is calculated using Normal Stress on Thin Shells = (Unit Normal Force/Shell Thickness)+((Unit Bending Moment*Distance from Middle Surface)/(Shell Thickness^(3)/12)). To calculate Normal Stress in Thin Shells, you need Unit Normal Force (N_x), Shell Thickness (t), Unit Bending Moment (M_x) & Distance from Middle Surface (z). With our tool, you need to enter the respective value for Unit Normal Force, Shell Thickness, Unit Bending Moment & Distance from Middle Surface and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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