Distance from Middle Surface given Normal Shearing Stress Calculator

✖Shell thickness is the the distance through the shell.ⓘ Shell Thickness [t]			+10% -10%
✖Normal Shearing Stress is the shearing stress produced by the normal shearing force.ⓘ Normal Shearing Stress [v_xz]			+10% -10%
✖Unit Shear Force is the force acting on the shell surface which cause slipping deformation but with a magnitude of unity.ⓘ Unit Shear Force [V]			+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 Shearing Stress [z]

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Formula

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Distance from Middle Surface given Normal Shearing Stress

Formula

`"z" = sqrt(("t"^(2)/4)-(("v"_{"xz"}*"t"^3)/(6*"V")))`

Example

`"0.02m"=sqrt((("200mm")^(2)/4)-(("0.72MPa"*("200mm")^3)/(6*"100kN")))`

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Distance from Middle Surface given Normal Shearing Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Distance from Middle Surface = sqrt((Shell Thickness^(2)/4)-((Normal Shearing Stress*Shell Thickness^3)/(6*Unit Shear Force)))
z = sqrt((t^(2)/4)-((v_xz*t^3)/(6*V)))
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

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.
Normal Shearing Stress - (Measured in Pascal) - Normal Shearing Stress is the shearing stress produced by the normal shearing force.
Unit Shear Force - (Measured in Newton) - Unit Shear Force is the force acting on the shell surface which cause slipping deformation but with a magnitude of unity.

STEP 1: Convert Input(s) to Base Unit

Shell Thickness: 200 Millimeter --> 0.2 Meter (Check conversion here)
Normal Shearing Stress: 0.72 Megapascal --> 720000 Pascal (Check conversion here)
Unit Shear Force: 100 Kilonewton --> 100000 Newton (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z = sqrt((t^(2)/4)-((v_xz*t^3)/(6*V))) --> sqrt((0.2^(2)/4)-((720000*0.2^3)/(6*100000)))

Evaluating ... ...

z = 0.02

STEP 3: Convert Result to Output's Unit

0.02 Meter --> No Conversion Required

FINAL ANSWER

0.02 Meter <-- Distance from Middle Surface

(Calculation completed in 00.004 seconds)

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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Meerut Institute of Engineering and Technology (MIET), Meerut

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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))

Distance from Middle Surface given Normal Shearing Stress Formula

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

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 Distance from Middle Surface given Normal Shearing Stress?

Distance from Middle Surface given Normal Shearing Stress calculator uses Distance from Middle Surface = sqrt((Shell Thickness^(2)/4)-((Normal Shearing Stress*Shell Thickness^3)/(6*Unit Shear Force))) to calculate the Distance from Middle Surface, The Distance from Middle Surface given Normal Shearing Stress formula is defined as the relationship between the unit normal force and normal shearing stress. Distance from Middle Surface is denoted by z symbol.

How to calculate Distance from Middle Surface given Normal Shearing Stress using this online calculator? To use this online calculator for Distance from Middle Surface given Normal Shearing Stress, enter Shell Thickness (t), Normal Shearing Stress (v_xz) & Unit Shear Force (V) and hit the calculate button. Here is how the Distance from Middle Surface given Normal Shearing Stress calculation can be explained with given input values -> 0.1 = sqrt((0.2^(2)/4)-((0.72*0.2^3)/(6*100000))).

FAQ

What is Distance from Middle Surface given Normal Shearing Stress?

The Distance from Middle Surface given Normal Shearing Stress formula is defined as the relationship between the unit normal force and normal shearing stress and is represented as z = sqrt((t^(2)/4)-((v_xz*t^3)/(6*V))) or Distance from Middle Surface = sqrt((Shell Thickness^(2)/4)-((Normal Shearing Stress*Shell Thickness^3)/(6*Unit Shear Force))). Shell thickness is the the distance through the shell, Normal Shearing Stress is the shearing stress produced by the normal shearing force & Unit Shear Force is the force acting on the shell surface which cause slipping deformation but with a magnitude of unity.

How to calculate Distance from Middle Surface given Normal Shearing Stress?

The Distance from Middle Surface given Normal Shearing Stress formula is defined as the relationship between the unit normal force and normal shearing stress is calculated using Distance from Middle Surface = sqrt((Shell Thickness^(2)/4)-((Normal Shearing Stress*Shell Thickness^3)/(6*Unit Shear Force))). To calculate Distance from Middle Surface given Normal Shearing Stress, you need Shell Thickness (t), Normal Shearing Stress (v_xz) & Unit Shear Force (V). With our tool, you need to enter the respective value for Shell Thickness, Normal Shearing Stress & Unit Shear 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, Normal Shearing Stress & Unit Shear Force. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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