Maximum Bending Stress in Plastic State Calculator

✖Maximum Bending Moment is the maximum amount of stress a beam can withstand before it starts to bend or deform under external loads.ⓘ Maximum Bending Moment [M]			+10% -10%
✖Depth Yielded Plastically is the distance along the beam where the stress exceeds the yield strength of the material during bending.ⓘ Depth Yielded Plastically [y]			+10% -10%
✖Material Constant is a measure of the stiffness of a material, used to calculate the bending stress and deflection of beams under various loads.ⓘ Material Constant [n]			+10% -10%
✖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.ⓘ Nth Moment of Inertia [I_n]			+10% -10%

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

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Maximum Bending Stress in Plastic State Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Bending Stress in Plastic State = (Maximum Bending Moment*Depth Yielded Plastically^Material Constant)/Nth Moment of Inertia
σ = (M*y^n)/I_n
This formula uses 5 Variables

Variables Used

Maximum Bending Stress in Plastic State - (Measured in Pascal) - Maximum Bending Stress in Plastic State is the maximum stress a beam can withstand in its plastic state without undergoing deformation or breaking.
Maximum Bending Moment - (Measured in Newton Meter) - Maximum Bending Moment is the maximum amount of stress a beam can withstand before it starts to bend or deform under external loads.
Depth Yielded Plastically - (Measured in Millimeter) - Depth Yielded Plastically is the distance along the beam where the stress exceeds the yield strength of the material during bending.
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.
Nth Moment of Inertia - (Measured in Kilogram Square Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Maximum Bending Moment: 1500000000 Newton Millimeter --> 1500000 Newton Meter (Check conversion here)
Depth Yielded Plastically: 0.5 Millimeter --> 0.5 Millimeter No Conversion Required
Material Constant: 0.25 --> No Conversion Required
Nth Moment of Inertia: 12645542471 Kilogram Square Millimeter --> 12645.542471 Kilogram Square Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ = (M*y^n)/I_n --> (1500000*0.5^0.25)/12645.542471

Evaluating ... ...

σ = 99.7461853276133

STEP 3: Convert Result to Output's Unit

99.7461853276133 Pascal -->9.97461853276134E-05 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

9.97461853276134E-05 ≈ 1E-4 Newton per Square Millimeter <-- Maximum Bending Stress in Plastic State

(Calculation completed in 00.020 seconds)

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< Nonlinear Behavior of Beams Calculators

Radius of Curvature given Bending Stress

LaTeX Go Radius of Curvature = ((Elastoplastic Modulus*Depth Yielded Plastically^Material Constant)/Maximum Bending Stress in Plastic State)^(1/Material Constant)

Nth Moment of Inertia

LaTeX Go Nth Moment of Inertia = (Breadth of Rectangular Beam*Depth of Rectangular Beam^(Material Constant+2))/((Material Constant+2)*2^(Material Constant+1))

Maximum Bending Stress in Plastic State

LaTeX Go Maximum Bending Stress in Plastic State = (Maximum Bending Moment*Depth Yielded Plastically^Material Constant)/Nth Moment of Inertia

Radius of Curvature given Bending Moment

LaTeX Go Radius of Curvature = ((Elastoplastic Modulus*Nth Moment of Inertia)/Maximum Bending Moment)^(1/Material Constant)

Maximum Bending Stress in Plastic State Formula

LaTeX Go

Maximum Bending Stress in Plastic State = (Maximum Bending Moment*Depth Yielded Plastically^Material Constant)/Nth Moment of Inertia
σ = (M*y^n)/I_n

What is Maximum Bending Stress?

Maximum Bending Stress is the highest stress experienced at the outermost fibers of a beam's cross-section when subjected to bending. It occurs at the farthest points from the neutral axis, where tensile and compressive stresses are greatest. This stress is directly related to the bending moment and the beam’s geometry and material properties. Ensuring the maximum bending stress remains within the material’s allowable limits is essential in design to prevent structural failure, as excessive stress can lead to cracking or permanent deformation.

How to Calculate Maximum Bending Stress in Plastic State?

Maximum Bending Stress in Plastic State calculator uses Maximum Bending Stress in Plastic State = (Maximum Bending Moment*Depth Yielded Plastically^Material Constant)/Nth Moment of Inertia to calculate 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 calculate Maximum Bending Stress in Plastic State using this online calculator? To use this online calculator 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. Here is how the Maximum Bending Stress in Plastic State calculation can be explained with given input values -> 1E-10 = (1500000*0.0005^0.25)/12645.542471.

FAQ

What is 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 and is represented as σ = (M*y^n)/I_n or Maximum Bending Stress in Plastic State = (Maximum Bending Moment*Depth Yielded Plastically^Material Constant)/Nth Moment of Inertia. Maximum Bending Moment is the maximum amount of stress a beam can withstand before it starts to bend or deform under external loads, Depth Yielded Plastically is the distance along the beam where the stress exceeds the yield strength of the material during bending, Material Constant is a measure of the stiffness of a material, used to calculate the bending stress and deflection of beams under various loads & 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.

How to calculate 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 is calculated using Maximum Bending Stress in Plastic State = (Maximum Bending Moment*Depth Yielded Plastically^Material Constant)/Nth Moment of Inertia. To calculate Maximum Bending Stress in Plastic State, you need Maximum Bending Moment (M), Depth Yielded Plastically (y), Material Constant (n) & Nth Moment of Inertia (I_n). With our tool, you need to enter the respective value for Maximum Bending Moment, Depth Yielded Plastically, Material Constant & Nth Moment of Inertia 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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