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

GoMaximum Deflection at Mid-Height of Equivalent Pin-Ended Column Formula

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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. Check FAQs

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

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

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

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Here is how the Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column equation looks like with Values.

Here is how the Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column equation looks like with Units.

Here is how the Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column equation looks like.

219.3931 = \frac{190}{\sin (\frac{3.1416 \cdot 2000}{3000})}

219.3931mm = \frac{190mm}{\sin (\frac{3.1416 \cdot 2000mm}{3000mm})}

219.3931 = \frac{190}{\sin (\frac{3.1416 \cdot 2000}{3000})}

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

Follow our step by step solution on how to calculate Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

e o = \frac{190mm}{\sin (\frac{π \cdot 2000mm}{3000mm})}

Next Step Substitute values of Constants

∴

e o = \frac{190mm}{\sin (\frac{3.1416 \cdot 2000mm}{3000mm})}

Next Step Convert Units

∴

e o = \frac{0.19m}{\sin (\frac{3.1416 \cdot 2m}{3m})}

Next Step Prepare to Evaluate

∴

e o = \frac{0.19}{\sin (\frac{3.1416 \cdot 2}{3})}

Next Step Evaluate

∴

e o = 0.219393102292058m

Next Step Convert to Output's Unit

∴

e o = 219.393102292058mm

LAST Step Rounding Answer

∴

e o = 219.3931mm

Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column Formula Elements

Variables

Constants

Functions

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

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

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 to find Maximum Deflection at Mid Height

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

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

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

Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column evaluator uses Maximum Deflection at Mid Height = Lateral Deflection/sin((pi*Distance from One End of Pin Ended Column)/Effective Length of Column) to evaluate the Maximum Deflection at Mid Height, The Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column formula is defined as the largest lateral deflection suffered by the column at its mid-height level. The column being talked about here is the axial pin-ended column with greater length. Maximum Deflection at Mid Height is denoted by e_o symbol.

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

FAQs on Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column

What is the formula to find Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column?

The formula of Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column is expressed as Maximum Deflection at Mid Height = Lateral Deflection/sin((pi*Distance from One End of Pin Ended Column)/Effective Length of Column). Here is an example- 219393.1 = 0.19/sin((pi*2)/3).

How to calculate Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column?

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

What are the other ways to Calculate Maximum Deflection at Mid Height?

Here are the different ways to Calculate Maximum Deflection at Mid Height-

Maximum Deflection at Mid Height=Curvature of Column*(Effective Length of Column)^2/pi^2

Can the Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column be negative?

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

Which unit is used to measure Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column?

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

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

​GoMaximum Deflection at Mid-Height of Equivalent Pin-Ended Column Formula

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

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

Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column Formula Elements

Other Formulas to find Maximum Deflection at Mid Height

Other formulas in Equivalent Column Concept category

How to Evaluate Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column?

FAQs on Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column

Variable Name

GoMaximum Deflection at Mid-Height of Equivalent Pin-Ended Column Formula