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Maximum Bending Stress in Plastic State Formula

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Maximum Bending Stress in Plastic State is the maximum stress a beam can withstand in its plastic state without undergoing deformation or breaking. Check FAQs

σ = \frac{M \cdot y^{n}}{I n}

σ - Maximum Bending Stress in Plastic State?M - Maximum Bending Moment?y - Depth Yielded Plastically?n - Material Constant?I_n - Nth Moment of Inertia?

Maximum Bending Stress in Plastic State Example

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Here is how the Maximum Bending Stress in Plastic State equation looks like with Values.

Here is how the Maximum Bending Stress in Plastic State equation looks like with Units.

Here is how the Maximum Bending Stress in Plastic State equation looks like.

1E-4 = \frac{1.5E+9 \cdot {0.5}^{0.25}}{1.3E+10}

1E-4N/mm² = \frac{1.5E+9N*mm \cdot {0.5mm}^{0.25}}{1.3E+10kg*mm²}

1E-4 = \frac{1.5E+9 \cdot {0.5}^{0.25}}{1.3E+10}

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Maximum Bending Stress in Plastic State Solution

Follow our step by step solution on how to calculate Maximum Bending Stress in Plastic State?

FIRST Step Consider the formula

σ = \frac{M \cdot y^{n}}{I n}

Next Step Substitute values of Variables

∴

σ = \frac{1.5E+9N*mm \cdot {0.5mm}^{0.25}}{1.3E+10kg*mm²}

Next Step Convert Units

∴

σ = \frac{1.5E+6N*m \cdot {0.5mm}^{0.25}}{12645.5425kg·m²}

Next Step Prepare to Evaluate

∴

σ = \frac{1.5E+6 \cdot {0.5}^{0.25}}{12645.5425}

Next Step Evaluate

∴

σ = 99.7461853276133Pa

Next Step Convert to Output's Unit

∴

σ = 9.97461853276134E-05N/mm²

LAST Step Rounding Answer

∴

σ = 1E-4N/mm²

Maximum Bending Stress in Plastic State Formula Elements

Variables

Maximum Bending Stress in Plastic State

Maximum Bending Stress in Plastic State is the maximum stress a beam can withstand in its plastic state without undergoing deformation or breaking.

Symbol: σ

Measurement: StressUnit: N/mm²

Note: Value can be positive or negative.

Formulas to find Maximum Bending Stress in Plastic State

Maximum Bending Moment

Maximum Bending Moment is the maximum amount of stress a beam can withstand before it starts to bend or deform under external loads.

Symbol: M

Measurement: Moment of ForceUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Maximum Bending Moment

Depth Yielded Plastically

Depth Yielded Plastically is the distance along the beam where the stress exceeds the yield strength of the material during bending.

Symbol: y

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth Yielded Plastically

Material Constant

Material Constant is a measure of the stiffness of a material, used to calculate the bending stress and deflection of beams under various loads.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Material Constant

Nth Moment of Inertia

Nth Moment of Inertia is a measure of the distribution of the beam's mass around its axis of rotation, used in bending beam analysis.

Symbol: I_n

Measurement: Moment of InertiaUnit: kg*mm²

Note: Value should be greater than 0.

Formulas to find Nth Moment of Inertia

Other formulas in Nonlinear Behavior of Beams category

Go Nth Moment of Inertia

I n = \frac{b \cdot d^{n + 2}}{(n + 2) \cdot 2^{n + 1}}

Go Radius of Curvature given Bending Stress

R = {(\frac{H \cdot y^{n}}{σ})}^{\frac{1}{n}}

Go Radius of Curvature given Bending Moment

R = {(\frac{H \cdot I n}{M})}^{\frac{1}{n}}

How to Evaluate Maximum Bending Stress in Plastic State?

Maximum Bending Stress in Plastic State evaluator uses Maximum Bending Stress in Plastic State = (Maximum Bending Moment*Depth Yielded Plastically^Material Constant)/Nth Moment of Inertia to evaluate the Maximum Bending Stress in Plastic State, Maximum Bending Stress in Plastic State formula is defined as a measure of the maximum stress a material can withstand without deforming plastically when subjected to bending forces, providing a critical value for designing and analyzing beams and other structural elements. Maximum Bending Stress in Plastic State is denoted by σ symbol.

How to evaluate Maximum Bending Stress in Plastic State using this online evaluator? To use this online evaluator for Maximum Bending Stress in Plastic State, enter Maximum Bending Moment (M), Depth Yielded Plastically (y), Material Constant (n) & Nth Moment of Inertia (I_n) and hit the calculate button.

FAQs on Maximum Bending Stress in Plastic State

What is the formula to find Maximum Bending Stress in Plastic State?

The formula of Maximum Bending Stress in Plastic State is expressed as Maximum Bending Stress in Plastic State = (Maximum Bending Moment*Depth Yielded Plastically^Material Constant)/Nth Moment of Inertia. Here is an example- 1E-10 = (1500000*0.0005^0.25)/12645.542471.

How to calculate Maximum Bending Stress in Plastic State?

With Maximum Bending Moment (M), Depth Yielded Plastically (y), Material Constant (n) & Nth Moment of Inertia (I_n) we can find Maximum Bending Stress in Plastic State using the formula - Maximum Bending Stress in Plastic State = (Maximum Bending Moment*Depth Yielded Plastically^Material Constant)/Nth Moment of Inertia.

Can the Maximum Bending Stress in Plastic State be negative?

Yes, the Maximum Bending Stress in Plastic State, measured in Stress can be negative.

Which unit is used to measure Maximum Bending Stress in Plastic State?

Maximum Bending Stress in Plastic State is usually measured using the Newton per Square Millimeter[N/mm²] for Stress. Pascal[N/mm²], Newton per Square Meter[N/mm²], Kilonewton per Square Meter[N/mm²] are the few other units in which Maximum Bending Stress in Plastic State can be measured.

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Maximum Bending Stress in Plastic State Formula

Maximum Bending Stress in Plastic State Example

Maximum Bending Stress in Plastic State Solution

Maximum Bending Stress in Plastic State Formula Elements

Other formulas in Nonlinear Behavior of Beams category

How to Evaluate Maximum Bending Stress in Plastic State?

FAQs on Maximum Bending Stress in Plastic State

Variable Name