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)))
ฯƒE = ฯƒ/(1-((C*c/(rleast^2))/((ฯƒmax/ฯƒ)-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) - The direct stress is defined as axial thrust acting per unit area.
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 is used for structural calculations.
Maximum Stress at Crack Tip - (Measured in Pascal) - Maximum stress at crack tip due to the applied nominal stress.
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: 10 Millimeter --> 0.01 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
ฯƒE = ฯƒ/(1-((C*c/(rleast^2))/((ฯƒmax/ฯƒ)-1))) --> 8/(1-((0.3*0.01/(0.04702^2))/((60/8)-1)))
Evaluating ... ...
ฯƒE = 10.1106838012212
STEP 3: Convert Result to Output's Unit
10.1106838012212 Pascal -->1.01106838012212E-05 Megapascal (Check conversion here)
FINAL ANSWER
1.01106838012212E-05 โ‰ˆ 1E-5 Megapascal <-- Euler Stress
(Calculation completed in 00.004 seconds)

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19 Columns With Initial Curvature Calculators

Radius of Gyration given Maximum Stress for Columns with Initial Curvature
Go Radius of Gyration = sqrt((Maximum initial deflection*Distance from Neutral Axis to Extreme Point)/(1-(Direct stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct stress)-1))
Euler Stress given Maximum Stress for Columns with Initial Curvature
Go 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)))
Maximum Stress for Columns with Initial Curvature
Go Maximum Stress at Crack Tip = (((Maximum initial deflection*Distance from Neutral Axis to Extreme Point/(Least Radius of Gyration Column^2))/(1-(Direct stress/Euler Stress)))+1)*Direct stress
Length of Column given Final Deflection at Distance X from End A of Column
Go Length of column = (pi*Distance of deflection from end A)/(asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum initial deflection)))
Value of Distance 'X' given Final Deflection at Distance X from end A of Column
Go Distance of deflection from end A = (asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum initial deflection)))*Length of column/pi
Distance from Neutral Axis of Extreme Layer given Maximum Stress for Columns
Go Distance from Neutral Axis to Extreme Point = (1-(Direct stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct stress)-1)*(Radius of Gyration^2)/Maximum initial deflection
Crippling Load given Final Deflection at Distance X from end A of Column
Go Crippling Load = (1-(Maximum initial deflection*sin((pi*Distance of deflection from end A)/Length of column)/Deflection of Column))*Euler Load
Euler Load given Final Deflection at Distance X from end A of Column
Go Euler Load = Crippling Load/(1-(Maximum initial deflection*sin((pi*Distance of deflection from end A)/Length of column)/Deflection of Column))
Length of Column given Initial Deflection at Distance X from end A
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
Go Distance of deflection from end A = (asin(Initial Deflection/Maximum initial deflection))*Length of column/pi
Length of Column given Euler Load
Go Length of column = sqrt(((pi^2)*Modulus of elasticity of column*Moment of Inertia)/(Euler Load))
Modulus of Elasticity given Euler Load
Go Modulus of elasticity of column = (Euler Load*(Length of column^2))/((pi^2)*Moment of Inertia)
Moment of Inertia given Euler Load
Go Moment of Inertia = (Euler Load*(Length of column^2))/((pi^2)*Modulus of elasticity of column)
Euler Load
Go Euler Load = ((pi^2)*Modulus of elasticity of column*Moment of Inertia)/(Length of column^2)
Crippling Load given Maximum Deflection for Columns with Initial Curvature
Go Crippling Load = (1-(Maximum initial deflection/Deflection of Column))*Euler Load
Euler Load given Maximum Deflection for Columns with Initial Curvature
Go Euler Load = Crippling Load/(1-(Maximum initial deflection/Deflection of Column))
Crippling Load given Factor of Safety
Go Crippling Load = (1-(1/Factor of Safety))*Euler Load
Factor of Safety given Euler Load
Go Factor of Safety = 1/(1-(Crippling Load/Euler Load))
Euler Load given Factor of Safety
Go Euler Load = Crippling Load/(1-(1/Factor of Safety))

Euler Stress given Maximum Stress for Columns with Initial Curvature Formula

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)))
ฯƒE = ฯƒ/(1-((C*c/(rleast^2))/((ฯƒmax/ฯƒ)-1)))

What is buckling or crippling load?

Buckling Load is the highest load at which the column will buckle. Crippling load is the max load beyond that load, it cant use further it becomes disable to use.

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 stress caused in columns with curvature due to Euler load. Euler Stress is denoted by ฯƒE 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 (ฯƒ), Maximum initial deflection (C), Distance from Neutral Axis to Extreme Point (c), Least Radius of Gyration Column (rleast) & Maximum Stress at Crack Tip (ฯƒmax) 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*0.01/(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 stress caused in columns with curvature due to Euler load and is represented as ฯƒE = ฯƒ/(1-((C*c/(rleast^2))/((ฯƒmax/ฯƒ)-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))). The direct stress is defined as axial thrust acting per unit area, 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 is used for structural calculations & Maximum stress at crack tip due to the applied nominal stress.
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 stress caused in columns with curvature due to Euler load 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 (ฯƒ), Maximum initial deflection (C), Distance from Neutral Axis to Extreme Point (c), Least Radius of Gyration Column (rleast) & Maximum Stress at Crack Tip (ฯƒmax). 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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