Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature Calculator

✖The direct stress is defined as axial thrust acting per unit area.ⓘ Direct stress [σ]			+10% -10%
✖Euler stress is the stress in column with curvature due to Euler load.ⓘ Euler Stress [σ_E]			+10% -10%
✖Maximum stress at crack tip due to the applied nominal stress.ⓘ Maximum Stress at Crack Tip [σ_max]			+10% -10%
✖The Radius of Gyration or gyradius is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass.ⓘ Radius of Gyration [k_G]			+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%

✖Maximum initial deflection is the degree to which a structural element is displaced under a load.ⓘ Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature [C]

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Formula

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Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature

Formula

`"C" = (1-("σ"/"σ"_{"E"}))*(("σ"_{"max"}/"σ")-1)*("k"_{"G"}^2)/"c"`

Example

`"1497.56mm"=(1-("0.000008MPa"/"0.3MPa"))*(("0.00006MPa"/"0.000008MPa")-1)*(("48mm")^2)/"10mm"`

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Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Maximum initial deflection - (Measured in Meter) - Maximum initial deflection is the degree to which a structural element is displaced under a load.
Direct stress - (Measured in Pascal) - The direct stress is defined as axial thrust acting per unit area.
Euler Stress - (Measured in Pascal) - Euler stress is the stress in column with curvature due to Euler load.
Maximum Stress at Crack Tip - (Measured in Pascal) - Maximum stress at crack tip due to the applied nominal stress.
Radius of Gyration - (Measured in Meter) - The Radius of Gyration or gyradius is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass.
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.

STEP 1: Convert Input(s) to Base Unit

Direct stress: 8E-06 Megapascal --> 8 Pascal (Check conversion here)
Euler Stress: 0.3 Megapascal --> 300000 Pascal (Check conversion here)
Maximum Stress at Crack Tip: 6E-05 Megapascal --> 60 Pascal (Check conversion here)
Radius of Gyration: 48 Millimeter --> 0.048 Meter (Check conversion here)
Distance from Neutral Axis to Extreme Point: 10 Millimeter --> 0.01 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C = (1-(σ/σ_E))*((σ_max/σ)-1)*(k_G^2)/c --> (1-(8/300000))*((60/8)-1)*(0.048^2)/0.01

Evaluating ... ...

C = 1.497560064

STEP 3: Convert Result to Output's Unit

1.497560064 Meter -->1497.560064 Millimeter (Check conversion here)

FINAL ANSWER

1497.560064 ≈ 1497.56 Millimeter <-- Maximum initial deflection

(Calculation completed in 00.004 seconds)

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

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< 8 Deflection Calculators

Distance of Section from Fixed End given Deflection at Section of Column with Eccentric Load

Go Distance b/w fixed end and deflection point = (acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/(sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia)))

Maximum Initial Deflection given Final Deflection at Distance X from End A of Column

Go Maximum initial deflection = Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*sin((pi*Distance of deflection from end A)/Length of column))

Final Deflection at Distance X from end A of Column

Go Deflection of Column = (1/(1-(Crippling Load/Euler Load)))*Maximum initial deflection*sin((pi*Distance of deflection from end A)/Length of column)

Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature

Go Maximum initial deflection = (1-(Direct stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct stress)-1)*(Radius of Gyration^2)/Distance from Neutral Axis to Extreme Point

Maximum Initial Deflection given Initial Deflection at Distance X from A

Go Maximum initial deflection = Initial Deflection/sin((pi*Distance of deflection from end A)/Length of column)

Initial Deflection at Distance X from end A

Go Initial Deflection = Maximum initial deflection*sin((pi*Distance of deflection from end A)/Length of column)

Maximum Initial Deflection given Maximum Deflection for Columns with Initial Curvature

Go Maximum initial deflection = Deflection of Column/(1/(1-(Crippling Load/Euler Load)))

Maximum Deflection for Columns with Initial Curvature

Go Deflection of Column = (1/(1-(Crippling Load/Euler Load)))*Maximum initial deflection

Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature Formula

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 Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature?

Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature calculator uses Maximum initial deflection = (1-(Direct stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct stress)-1)*(Radius of Gyration^2)/Distance from Neutral Axis to Extreme Point to calculate the Maximum initial deflection, The Maximum initial deflection given maximum stress for columns with initial curvature formula is defined as the degree to which a structural element is displaced under a load. Maximum initial deflection is denoted by C symbol.

How to calculate Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature using this online calculator? To use this online calculator for Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature, enter Direct stress (σ), Euler Stress (σ_E), Maximum Stress at Crack Tip (σ_max), Radius of Gyration (k_G) & Distance from Neutral Axis to Extreme Point (c) and hit the calculate button. Here is how the Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature calculation can be explained with given input values -> 1.5E+6 = (1-(8/300000))*((60/8)-1)*(0.048^2)/0.01.

FAQ

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

The Maximum initial deflection given maximum stress for columns with initial curvature formula is defined as the degree to which a structural element is displaced under a load and is represented as C = (1-(σ/σ_E))*((σ_max/σ)-1)*(k_G^2)/c or Maximum initial deflection = (1-(Direct stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct stress)-1)*(Radius of Gyration^2)/Distance from Neutral Axis to Extreme Point. The direct stress is defined as axial thrust acting per unit area, Euler stress is the stress in column with curvature due to Euler load, Maximum stress at crack tip due to the applied nominal stress, The Radius of Gyration or gyradius is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass & Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point.

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

The Maximum initial deflection given maximum stress for columns with initial curvature formula is defined as the degree to which a structural element is displaced under a load is calculated using Maximum initial deflection = (1-(Direct stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct stress)-1)*(Radius of Gyration^2)/Distance from Neutral Axis to Extreme Point. To calculate Maximum Initial Deflection given Maximum Stress for Columns with Initial Curvature, you need Direct stress (σ), Euler Stress (σ_E), Maximum Stress at Crack Tip (σ_max), Radius of Gyration (k_G) & Distance from Neutral Axis to Extreme Point (c). With our tool, you need to enter the respective value for Direct stress, Euler Stress, Maximum Stress at Crack Tip, Radius of Gyration & Distance from Neutral Axis to Extreme Point and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Maximum initial deflection?

In this formula, Maximum initial deflection uses Direct stress, Euler Stress, Maximum Stress at Crack Tip, Radius of Gyration & Distance from Neutral Axis to Extreme Point. We can use 3 other way(s) to calculate the same, which is/are as follows -

Maximum initial deflection = Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*sin((pi*Distance of deflection from end A)/Length of column))
Maximum initial deflection = Initial Deflection/sin((pi*Distance of deflection from end A)/Length of column)
Maximum initial deflection = Deflection of Column/(1/(1-(Crippling Load/Euler Load)))

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