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Distance from Middle Surface given Normal Shearing Stress Formula

GoDistance from Middle Surface given Normal Stress in Thin Shells Formula

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Distance from Middle Surface is the half distance from middle surface to extreme surface, say half the thickness. Check FAQs

z = \sqrt{(\frac{t^{2}}{4}) - (\frac{v xz \cdot t^{3}}{6 \cdot V})}

z - Distance from Middle Surface?t - Shell Thickness?v_xz - Normal Shearing Stress?V - Unit Shear Force?

Distance from Middle Surface given Normal Shearing Stress Example

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Here is how the Distance from Middle Surface given Normal Shearing Stress equation looks like with Values.

Here is how the Distance from Middle Surface given Normal Shearing Stress equation looks like with Units.

Here is how the Distance from Middle Surface given Normal Shearing Stress equation looks like.

0.02 = \sqrt{(\frac{200^{2}}{4}) - (\frac{0.72 \cdot 200^{3}}{6 \cdot 100})}

0.02m = \sqrt{(\frac{{200mm}^{2}}{4}) - (\frac{0.72MPa \cdot {200mm}^{3}}{6 \cdot 100kN})}

0.02 = \sqrt{(\frac{200^{2}}{4}) - (\frac{0.72 \cdot 200^{3}}{6 \cdot 100})}

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Distance from Middle Surface given Normal Shearing Stress Solution

Follow our step by step solution on how to calculate Distance from Middle Surface given Normal Shearing Stress?

FIRST Step Consider the formula

z = \sqrt{(\frac{t^{2}}{4}) - (\frac{v xz \cdot t^{3}}{6 \cdot V})}

Next Step Substitute values of Variables

∴

z = \sqrt{(\frac{{200mm}^{2}}{4}) - (\frac{0.72MPa \cdot {200mm}^{3}}{6 \cdot 100kN})}

Next Step Convert Units

∴

z = \sqrt{(\frac{{0.2m}^{2}}{4}) - (\frac{720000Pa \cdot {0.2m}^{3}}{6 \cdot 100000N})}

Next Step Prepare to Evaluate

∴

z = \sqrt{(\frac{{0.2}^{2}}{4}) - (\frac{720000 \cdot {0.2}^{3}}{6 \cdot 100000})}

LAST Step Evaluate

∴

z = 0.02m

Distance from Middle Surface given Normal Shearing Stress Formula Elements

Variables

Functions

Distance from Middle Surface

Distance from Middle Surface is the half distance from middle surface to extreme surface, say half the thickness.

Symbol: z

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Distance from Middle Surface

Shell Thickness

Shell thickness is the the distance through the shell.

Symbol: t

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Shell Thickness

Normal Shearing Stress

Normal Shearing Stress is the shearing stress produced by the normal shearing force.

Symbol: v_xz

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Normal Shearing Stress

Unit Shear Force

Unit Shear Force is the force acting on the shell surface which cause slipping deformation but with a magnitude of unity.

Symbol: V

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Unit Shear Force

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.

Syntax: sqrt(Number)

Other Formulas to find Distance from Middle Surface

Go Distance from Middle Surface given Normal Stress in Thin Shells

z = (\frac{t^{2}}{12 \cdot M x}) \cdot ((f x \cdot t) - (N x))

Other formulas in Stresses in Thin Shells category

Go Normal Stress in Thin Shells

f x = (\frac{N x}{t}) + (\frac{M x \cdot z}{\frac{t^{3}}{12}})

Go Shearing Stresses on Shells

v xy = ((\frac{T}{t}) + (\frac{D \cdot z \cdot 12}{t^{3}}))

Go Central Shear given Shearing Stress

T = (v xy - (\frac{D \cdot z \cdot 12}{t^{3}})) \cdot t

Go Twisting Moments given Shearing Stress

D = \frac{((v xy \cdot t) - T) \cdot t^{2}}{12 \cdot z}

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

Distance from Middle Surface given Normal Shearing Stress evaluator uses Distance from Middle Surface = sqrt((Shell Thickness^(2)/4)-((Normal Shearing Stress*Shell Thickness^3)/(6*Unit Shear Force))) to evaluate 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 evaluate Distance from Middle Surface given Normal Shearing Stress using this online evaluator? To use this online evaluator 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.

FAQs on Distance from Middle Surface given Normal Shearing Stress

What is the formula to find Distance from Middle Surface given Normal Shearing Stress?

The formula of Distance from Middle Surface given Normal Shearing Stress is expressed as Distance from Middle Surface = sqrt((Shell Thickness^(2)/4)-((Normal Shearing Stress*Shell Thickness^3)/(6*Unit Shear Force))). Here is an example- 0.1 = sqrt((0.2^(2)/4)-((0.72*0.2^3)/(6*100000))).

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

With Shell Thickness (t), Normal Shearing Stress (v_xz) & Unit Shear Force (V) we can find Distance from Middle Surface given Normal Shearing Stress using the formula - Distance from Middle Surface = sqrt((Shell Thickness^(2)/4)-((Normal Shearing Stress*Shell Thickness^3)/(6*Unit Shear Force))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Distance from Middle Surface?

Here are the different ways to Calculate Distance from Middle Surface-

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

Can the Distance from Middle Surface given Normal Shearing Stress be negative?

No, the Distance from Middle Surface given Normal Shearing Stress, measured in Length cannot be negative.

Which unit is used to measure Distance from Middle Surface given Normal Shearing Stress?

Distance from Middle Surface given Normal Shearing Stress is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Distance from Middle Surface given Normal Shearing Stress can be measured.

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Distance from Middle Surface given Normal Shearing Stress Formula

​GoDistance from Middle Surface given Normal Stress in Thin Shells Formula

Distance from Middle Surface given Normal Shearing Stress Example

Distance from Middle Surface given Normal Shearing Stress Solution

Distance from Middle Surface given Normal Shearing Stress Formula Elements

Other Formulas to find Distance from Middle Surface

Other formulas in Stresses in Thin Shells category

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

FAQs on Distance from Middle Surface given Normal Shearing Stress

Variable Name

GoDistance from Middle Surface given Normal Stress in Thin Shells Formula