Maximum Initial Deflection 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%
✖Euler stress is the stress in column with curvature due to Euler load.ⓘ Euler Stress [σ_E]			+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%
✖Radius of Gyration is the radial distance from the axis of rotation at which the entire area or mass can be assumed to be concentrated to produce the same moment of inertia.ⓘ 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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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) - 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.
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 is the highest stress concentration that occurs at the tip of a crack in a material under load.
Radius of Gyration - (Measured in Meter) - Radius of Gyration is the radial distance from the axis of rotation at which the entire area or mass can be assumed to be concentrated to produce the same moment of inertia.
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: 312 Millimeter --> 0.312 Meter (Check conversion here)
Distance from Neutral Axis to Extreme Point: 49.91867 Millimeter --> 0.04991867 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)*(0.312^2)/0.04991867

Evaluating ... ...

C = 12.6749996953044

STEP 3: Convert Result to Output's Unit

12.6749996953044 Meter -->12674.9996953044 Millimeter (Check conversion here)

FINAL ANSWER

12674.9996953044 ≈ 12675 Millimeter <-- Maximum Initial Deflection

(Calculation completed in 00.020 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Mechanical » Columns With Initial Curvature » Maximum Initial Deflection 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)

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

LaTeX Go

What is Maximum Deflection?

Maximum Deflection refers to the largest displacement or deformation experienced by a structural element (such as a beam or column) under an applied load. It occurs at the point along the length of the element where the bending or deformation is greatest.

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 a measure of the maximum initial deflection that occurs in columns with initial curvature when subjected to maximum stress, taking into account the effects of initial curvature on the column's behavior. 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 -> 300000 = (1-(8/300000))*((60/8)-1)*(0.312^2)/0.04991867.

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 a measure of the maximum initial deflection that occurs in columns with initial curvature when subjected to maximum stress, taking into account the effects of initial curvature on the column's behavior 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. 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, Euler stress is the stress in column with curvature due to Euler load, Maximum Stress at Crack Tip is the highest stress concentration that occurs at the tip of a crack in a material under load, Radius of Gyration is the radial distance from the axis of rotation at which the entire area or mass can be assumed to be concentrated to produce the same moment of inertia & 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 a measure of the maximum initial deflection that occurs in columns with initial curvature when subjected to maximum stress, taking into account the effects of initial curvature on the column's behavior 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 = 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)))*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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