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Length of Equivalent Pin Ended Column given Max Deflection at Mid Height Formula

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The Effective Length of Column can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration. Check FAQs

L = \sqrt{\frac{e o \cdot π^{2}}{Φ m}}

L - Effective Length of Column?e_o - Maximum Deflection at Mid Height?Φ_m - Curvature of Column?π - Archimedes' constant?

Length of Equivalent Pin Ended Column given Max Deflection at Mid Height Example

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Here is how the Length of Equivalent Pin Ended Column given Max Deflection at Mid Height equation looks like with Values.

Here is how the Length of Equivalent Pin Ended Column given Max Deflection at Mid Height equation looks like with Units.

Here is how the Length of Equivalent Pin Ended Column given Max Deflection at Mid Height equation looks like.

3001.0022 = \sqrt{\frac{219 \cdot {3.1416}^{2}}{0.24}}

3001.0022mm = \sqrt{\frac{219mm \cdot {3.1416}^{2}}{0.24}}

3001.0022 = \sqrt{\frac{219 \cdot {3.1416}^{2}}{0.24}}

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Length of Equivalent Pin Ended Column given Max Deflection at Mid Height Solution

Follow our step by step solution on how to calculate Length of Equivalent Pin Ended Column given Max Deflection at Mid Height?

FIRST Step Consider the formula

L = \sqrt{\frac{e o \cdot π^{2}}{Φ m}}

Next Step Substitute values of Variables

∴

L = \sqrt{\frac{219mm \cdot π^{2}}{0.24}}

Next Step Substitute values of Constants

∴

L = \sqrt{\frac{219mm \cdot {3.1416}^{2}}{0.24}}

Next Step Convert Units

∴

L = \sqrt{\frac{0.219m \cdot {3.1416}^{2}}{0.24}}

Next Step Prepare to Evaluate

∴

L = \sqrt{\frac{0.219 \cdot {3.1416}^{2}}{0.24}}

Next Step Evaluate

∴

L = 3.00100216860869m

Next Step Convert to Output's Unit

∴

L = 3001.00216860869mm

LAST Step Rounding Answer

∴

L = 3001.0022mm

Length of Equivalent Pin Ended Column given Max Deflection at Mid Height Formula Elements

Variables

Constants

Functions

Effective Length of Column

The Effective Length of Column can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Length of Column

Maximum Deflection at Mid Height

The Maximum Deflection at Mid Height of the equivalent pin-ended column is the largest value of deflected curve calculated at the mid-height of the equivalent pin-ended column.

Symbol: e_o

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Maximum Deflection at Mid Height

Curvature of Column

Curvature of Column based on column's mode of failure.

Symbol: Φ_m

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Curvature of Column

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Equivalent Column Concept category

Go Lateral Deflection of Equivalent Pin Ended Column at distance x

e = e o \cdot \sin (\frac{π \cdot x}{L})

Go Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column

e o = \frac{e}{\sin (\frac{π \cdot x}{L})}

Go Maximum Deflection at Mid-Height of Equivalent Pin-Ended Column

e o = Φ m \cdot \frac{{(L)}^{2}}{π^{2}}

Go Curvature of Column Based on Column Mode of Failure

Φ m = e o \cdot \frac{π^{2}}{L^{2}}

How to Evaluate Length of Equivalent Pin Ended Column given Max Deflection at Mid Height?

Length of Equivalent Pin Ended Column given Max Deflection at Mid Height evaluator uses Effective Length of Column = sqrt((Maximum Deflection at Mid Height*pi^2)/Curvature of Column) to evaluate the Effective Length of Column, The Length of Equivalent Pin Ended Column given Max Deflection at Mid Height formula is defined as the ratio of the maximum deflection at the mid-height of the equivalent column to the curvature of the column based on the column’s mode of failure. Effective Length of Column is denoted by L symbol.

How to evaluate Length of Equivalent Pin Ended Column given Max Deflection at Mid Height using this online evaluator? To use this online evaluator for Length of Equivalent Pin Ended Column given Max Deflection at Mid Height, enter Maximum Deflection at Mid Height (e_o) & Curvature of Column (Φ_m) and hit the calculate button.

FAQs on Length of Equivalent Pin Ended Column given Max Deflection at Mid Height

What is the formula to find Length of Equivalent Pin Ended Column given Max Deflection at Mid Height?

The formula of Length of Equivalent Pin Ended Column given Max Deflection at Mid Height is expressed as Effective Length of Column = sqrt((Maximum Deflection at Mid Height*pi^2)/Curvature of Column). Here is an example- 3E+6 = sqrt((0.219*pi^2)/0.24).

How to calculate Length of Equivalent Pin Ended Column given Max Deflection at Mid Height?

With Maximum Deflection at Mid Height (e_o) & Curvature of Column (Φ_m) we can find Length of Equivalent Pin Ended Column given Max Deflection at Mid Height using the formula - Effective Length of Column = sqrt((Maximum Deflection at Mid Height*pi^2)/Curvature of Column). This formula also uses Archimedes' constant and Square Root Function function(s).

Can the Length of Equivalent Pin Ended Column given Max Deflection at Mid Height be negative?

No, the Length of Equivalent Pin Ended Column given Max Deflection at Mid Height, measured in Length cannot be negative.

Which unit is used to measure Length of Equivalent Pin Ended Column given Max Deflection at Mid Height?

Length of Equivalent Pin Ended Column given Max Deflection at Mid Height is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Length of Equivalent Pin Ended Column given Max Deflection at Mid Height can be measured.

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Length of Equivalent Pin Ended Column given Max Deflection at Mid Height Formula

Length of Equivalent Pin Ended Column given Max Deflection at Mid Height Example

Length of Equivalent Pin Ended Column given Max Deflection at Mid Height Solution

Length of Equivalent Pin Ended Column given Max Deflection at Mid Height Formula Elements

Other formulas in Equivalent Column Concept category

How to Evaluate Length of Equivalent Pin Ended Column given Max Deflection at Mid Height?

FAQs on Length of Equivalent Pin Ended Column given Max Deflection at Mid Height

Variable Name