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Lateral Deflection of Equivalent Pin Ended Column at distance x Formula

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Lateral Deflection is the deflection of an equivalent pin-headed column in the lateral direction due to any applied load case. The deflection is taken at any distance 'x' from one end of the column. Check FAQs

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

e - Lateral Deflection?e_o - Maximum Deflection at Mid Height?x - Distance from One End of Pin Ended Column?L - Effective Length of Column?π - Archimedes' constant?

Lateral Deflection of Equivalent Pin Ended Column at distance x Example

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Here is how the Lateral Deflection of Equivalent Pin Ended Column at distance x equation looks like with Values.

Here is how the Lateral Deflection of Equivalent Pin Ended Column at distance x equation looks like with Units.

Here is how the Lateral Deflection of Equivalent Pin Ended Column at distance x equation looks like.

189.6596 = 219 \cdot \sin (\frac{3.1416 \cdot 2000}{3000})

189.6596mm = 219mm \cdot \sin (\frac{3.1416 \cdot 2000mm}{3000mm})

189.6596 = 219 \cdot \sin (\frac{3.1416 \cdot 2000}{3000})

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Lateral Deflection of Equivalent Pin Ended Column at distance x Solution

Follow our step by step solution on how to calculate Lateral Deflection of Equivalent Pin Ended Column at distance x?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

e = 219mm \cdot \sin (\frac{π \cdot 2000mm}{3000mm})

Next Step Substitute values of Constants

∴

e = 219mm \cdot \sin (\frac{3.1416 \cdot 2000mm}{3000mm})

Next Step Convert Units

∴

e = 0.219m \cdot \sin (\frac{3.1416 \cdot 2m}{3m})

Next Step Prepare to Evaluate

∴

e = 0.219 \cdot \sin (\frac{3.1416 \cdot 2}{3})

Next Step Evaluate

∴

e = 0.189659563428792m

Next Step Convert to Output's Unit

∴

e = 189.659563428792mm

LAST Step Rounding Answer

∴

e = 189.6596mm

Lateral Deflection of Equivalent Pin Ended Column at distance x Formula Elements

Variables

Constants

Functions

Lateral Deflection

Lateral Deflection is the deflection of an equivalent pin-headed column in the lateral direction due to any applied load case. The deflection is taken at any distance 'x' from one end of the column.

Symbol: e

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Lateral Deflection

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

Distance from One End of Pin Ended Column

The Distance from One End of Pin Ended Column is the distance calculated from one end of the equivalent axially loaded pin-ended column, where the lateral deflection is to be obtained.

Symbol: x

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance from One End of Pin Ended Column

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

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

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

Other formulas in Equivalent Column Concept category

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}}

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

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

How to Evaluate Lateral Deflection of Equivalent Pin Ended Column at distance x?

Lateral Deflection of Equivalent Pin Ended Column at distance x evaluator uses Lateral Deflection = Maximum Deflection at Mid Height*sin((pi*Distance from One End of Pin Ended Column)/Effective Length of Column) to evaluate the Lateral Deflection, The Lateral Deflection of Equivalent Pin Ended Column at distance x formula is defined as the deflection of an equivalent pin-headed column in the lateral direction due to any applied load case. The deflection is taken at any distance 'x' from one end of the column. Lateral Deflection is denoted by e symbol.

How to evaluate Lateral Deflection of Equivalent Pin Ended Column at distance x using this online evaluator? To use this online evaluator for Lateral Deflection of Equivalent Pin Ended Column at distance x, enter Maximum Deflection at Mid Height (e_o), Distance from One End of Pin Ended Column (x) & Effective Length of Column (L) and hit the calculate button.

FAQs on Lateral Deflection of Equivalent Pin Ended Column at distance x

What is the formula to find Lateral Deflection of Equivalent Pin Ended Column at distance x?

The formula of Lateral Deflection of Equivalent Pin Ended Column at distance x is expressed as Lateral Deflection = Maximum Deflection at Mid Height*sin((pi*Distance from One End of Pin Ended Column)/Effective Length of Column). Here is an example- 189659.6 = 0.219*sin((pi*2)/3).

How to calculate Lateral Deflection of Equivalent Pin Ended Column at distance x?

With Maximum Deflection at Mid Height (e_o), Distance from One End of Pin Ended Column (x) & Effective Length of Column (L) we can find Lateral Deflection of Equivalent Pin Ended Column at distance x using the formula - Lateral Deflection = Maximum Deflection at Mid Height*sin((pi*Distance from One End of Pin Ended Column)/Effective Length of Column). This formula also uses Archimedes' constant and Sine (sin) function(s).

Can the Lateral Deflection of Equivalent Pin Ended Column at distance x be negative?

No, the Lateral Deflection of Equivalent Pin Ended Column at distance x, measured in Length cannot be negative.

Which unit is used to measure Lateral Deflection of Equivalent Pin Ended Column at distance x?

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

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Lateral Deflection of Equivalent Pin Ended Column at distance x Formula

Lateral Deflection of Equivalent Pin Ended Column at distance x Example

Lateral Deflection of Equivalent Pin Ended Column at distance x Solution

Lateral Deflection of Equivalent Pin Ended Column at distance x Formula Elements

Other formulas in Equivalent Column Concept category

How to Evaluate Lateral Deflection of Equivalent Pin Ended Column at distance x?

FAQs on Lateral Deflection of Equivalent Pin Ended Column at distance x

Variable Name