Euler Stress given Maximum Stress for Columns with Initial Curvature Calculator

✖Direct Stress refers to the internal resistance offered by a material to an external force or load, acting perpendicularly to the cross-sectional area of the material.ⓘ Direct Stress [σ]			+10% -10%
✖Maximum Initial Deflection is the degree to which a structural element is displaced under a load.ⓘ Maximum Initial Deflection [C]			+10% -10%
✖Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point.ⓘ Distance from Neutral Axis to Extreme Point [c]			+10% -10%
✖Least Radius of Gyration Column is the smallest value of the radius of gyration, it is used for structural calculations.ⓘ Least Radius of Gyration Column [r_least]			+10% -10%
✖Maximum Stress at Crack Tip is the highest stress concentration that occurs at the tip of a crack in a material under load.ⓘ Maximum Stress at Crack Tip [σ_max]			+10% -10%

✖Euler stress is the stress in column with curvature due to Euler load.ⓘ Euler Stress given Maximum Stress for Columns with Initial Curvature [σ_E]

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Euler Stress given Maximum Stress for Columns with Initial Curvature Solution

STEP 0: Pre-Calculation Summary

Formula Used

Euler Stress = Direct Stress/(1-((Maximum Initial Deflection*Distance from Neutral Axis to Extreme Point/(Least Radius of Gyration Column^2))/((Maximum Stress at Crack Tip/Direct Stress)-1)))
σ_E = σ/(1-((C*c/(r_least^2))/((σ_max/σ)-1)))
This formula uses 6 Variables

Variables Used

Euler Stress - (Measured in Pascal) - Euler stress is the stress in column with curvature due to Euler load.
Direct Stress - (Measured in Pascal) - Direct Stress refers to the internal resistance offered by a material to an external force or load, acting perpendicularly to the cross-sectional area of the material.
Maximum Initial Deflection - (Measured in Meter) - Maximum Initial Deflection is the degree to which a structural element is displaced under a load.
Distance from Neutral Axis to Extreme Point - (Measured in Meter) - Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point.
Least Radius of Gyration Column - (Measured in Meter) - Least Radius of Gyration Column is the smallest value of the radius of gyration, it is used for structural calculations.
Maximum Stress at Crack Tip - (Measured in Pascal) - Maximum Stress at Crack Tip is the highest stress concentration that occurs at the tip of a crack in a material under load.

STEP 1: Convert Input(s) to Base Unit

Direct Stress: 8E-06 Megapascal --> 8 Pascal (Check conversion here)
Maximum Initial Deflection: 300 Millimeter --> 0.3 Meter (Check conversion here)
Distance from Neutral Axis to Extreme Point: 49.91867 Millimeter --> 0.04991867 Meter (Check conversion here)
Least Radius of Gyration Column: 47.02 Millimeter --> 0.04702 Meter (Check conversion here)
Maximum Stress at Crack Tip: 6E-05 Megapascal --> 60 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_E = σ/(1-((C*c/(r_least^2))/((σ_max/σ)-1))) --> 8/(1-((0.3*0.04991867/(0.04702^2))/((60/8)-1)))

Evaluating ... ...

σ_E = -190.064285317512

STEP 3: Convert Result to Output's Unit

-190.064285317512 Pascal -->-0.000190064285317512 Megapascal (Check conversion here)

FINAL ANSWER

-0.000190064285317512 ≈ -0.00019 Megapascal <-- Euler Stress

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Mechanical » Columns With Initial Curvature » Euler Stress given Maximum Stress for Columns with Initial Curvature

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< Columns With Initial Curvature Calculators

Length of Column given Initial Deflection at Distance X from end A

LaTeX Go Length of Column = (pi*Distance of Deflection from end A)/(asin(Initial Deflection/Maximum Initial Deflection))

Value of Distance 'X' given Initial Deflection at Distance X from end A

LaTeX Go Distance of Deflection from end A = (asin(Initial Deflection/Maximum Initial Deflection))*Length of Column/pi

Modulus of Elasticity given Euler Load

LaTeX Go Modulus of Elasticity of Column = (Euler Load*(Length of Column^2))/(pi^2*Moment of Inertia)

Euler Load

LaTeX Go Euler Load = ((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Length of Column^2)

Euler Stress given Maximum Stress for Columns with Initial Curvature Formula

LaTeX Go

What is Euler Stress?

Euler Stress refers to the critical compressive stress at which a slender column will buckle. It is derived from the Euler’s Critical Load and is used to express the buckling condition in terms of stress rather than load.

How to Calculate Euler Stress given Maximum Stress for Columns with Initial Curvature?

Euler Stress given Maximum Stress for Columns with Initial Curvature calculator uses Euler Stress = Direct Stress/(1-((Maximum Initial Deflection*Distance from Neutral Axis to Extreme Point/(Least Radius of Gyration Column^2))/((Maximum Stress at Crack Tip/Direct Stress)-1))) to calculate the Euler Stress, The Euler Stress given Maximum Stress for Columns with Initial Curvature formula is defined as a measure of the maximum stress a column can withstand before buckling, taking into account the initial curvature of the column, which affects its load-carrying capacity and stability. Euler Stress is denoted by σ_E symbol.

How to calculate Euler Stress given Maximum Stress for Columns with Initial Curvature using this online calculator? To use this online calculator for Euler Stress given Maximum Stress for Columns with Initial Curvature, enter Direct Stress (σ), Maximum Initial Deflection (C), Distance from Neutral Axis to Extreme Point (c), Least Radius of Gyration Column (r_least) & Maximum Stress at Crack Tip (σ_max) and hit the calculate button. Here is how the Euler Stress given Maximum Stress for Columns with Initial Curvature calculation can be explained with given input values -> 1E-11 = 8/(1-((0.3*0.04991867/(0.04702^2))/((60/8)-1))).

FAQ

What is Euler Stress given Maximum Stress for Columns with Initial Curvature?

The Euler Stress given Maximum Stress for Columns with Initial Curvature formula is defined as a measure of the maximum stress a column can withstand before buckling, taking into account the initial curvature of the column, which affects its load-carrying capacity and stability and is represented as σ_E = σ/(1-((C*c/(r_least^2))/((σ_max/σ)-1))) or Euler Stress = Direct Stress/(1-((Maximum Initial Deflection*Distance from Neutral Axis to Extreme Point/(Least Radius of Gyration Column^2))/((Maximum Stress at Crack Tip/Direct Stress)-1))). Direct Stress refers to the internal resistance offered by a material to an external force or load, acting perpendicularly to the cross-sectional area of the material, Maximum Initial Deflection is the degree to which a structural element is displaced under a load, Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point, Least Radius of Gyration Column is the smallest value of the radius of gyration, it is used for structural calculations & Maximum Stress at Crack Tip is the highest stress concentration that occurs at the tip of a crack in a material under load.

How to calculate Euler Stress given Maximum Stress for Columns with Initial Curvature?

The Euler Stress given Maximum Stress for Columns with Initial Curvature formula is defined as a measure of the maximum stress a column can withstand before buckling, taking into account the initial curvature of the column, which affects its load-carrying capacity and stability is calculated using Euler Stress = Direct Stress/(1-((Maximum Initial Deflection*Distance from Neutral Axis to Extreme Point/(Least Radius of Gyration Column^2))/((Maximum Stress at Crack Tip/Direct Stress)-1))). To calculate Euler Stress given Maximum Stress for Columns with Initial Curvature, you need Direct Stress (σ), Maximum Initial Deflection (C), Distance from Neutral Axis to Extreme Point (c), Least Radius of Gyration Column (r_least) & Maximum Stress at Crack Tip (σ_max). With our tool, you need to enter the respective value for Direct Stress, Maximum Initial Deflection, Distance from Neutral Axis to Extreme Point, Least Radius of Gyration Column & Maximum Stress at Crack Tip 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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