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

✖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.ⓘ Lateral Deflection [e]			+10% -10%
✖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.ⓘ Distance from One End of Pin Ended Column [x]			+10% -10%
✖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.ⓘ Effective Length of Column [L]			+10% -10%

✖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.ⓘ Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column [e_o]

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Formula

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

Formula

`"e"_{"o"} = "e"/sin((pi*"x")/"L")`

Example

`"219.3931mm"="190mm"/sin((pi*"2000mm")/"3000mm")`

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

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Deflection at Mid Height = Lateral Deflection/sin((pi*Distance from One End of Pin Ended Column)/Effective Length of Column)
e_o = e/sin((pi*x)/L)
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sin(Angle)

Variables Used

Maximum Deflection at Mid Height - (Measured in Meter) - 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.
Lateral Deflection - (Measured in Meter) - 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.
Distance from One End of Pin Ended Column - (Measured in Meter) - 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.
Effective Length of Column - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Lateral Deflection: 190 Millimeter --> 0.19 Meter (Check conversion here)
Distance from One End of Pin Ended Column: 2000 Millimeter --> 2 Meter (Check conversion here)
Effective Length of Column: 3000 Millimeter --> 3 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

e_o = e/sin((pi*x)/L) --> 0.19/sin((pi*2)/3)

Evaluating ... ...

e_o = 0.219393102292058

STEP 3: Convert Result to Output's Unit

0.219393102292058 Meter -->219.393102292058 Millimeter (Check conversion here)

FINAL ANSWER

219.393102292058 ≈ 219.3931 Millimeter <-- Maximum Deflection at Mid Height

(Calculation completed in 00.006 seconds)

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Home » Engineering » Civil » Columns » Columns of Special Materials » Reinforced Concrete Columns » Equivalent Column Concept » Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column

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Created by Swarnima Singh

NIT Jaipur (mnitj), jaipur

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< 5 Equivalent Column Concept Calculators

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

Go Maximum Deflection at Mid Height = Lateral Deflection/sin((pi*Distance from One End of Pin Ended Column)/Effective Length of Column)

Lateral Deflection of Equivalent Pin Ended Column at distance x

Go Lateral Deflection = Maximum Deflection at Mid Height*sin((pi*Distance from One End of Pin Ended Column)/Effective Length of Column)

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

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

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

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

Curvature of Column Based on Column Mode of Failure

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

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

Maximum Deflection at Mid Height = Lateral Deflection/sin((pi*Distance from One End of Pin Ended Column)/Effective Length of Column)
e_o = e/sin((pi*x)/L)

What is Maximum Deflection?

Maximum deflection occurs at the farthest point from the support. In the case of two support points, it will be at the midpoint between them regardless of the location of the point loads. Where there are more than two supports then it will be at a midpoint between the section which has the most load.

Why is the calculation of Maximum Deflection of a Column important?

Maximum Deflection is a crucial consideration in the design of a structure and failure to apply due attention to it can be catastrophic.

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

Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column calculator uses Maximum Deflection at Mid Height = Lateral Deflection/sin((pi*Distance from One End of Pin Ended Column)/Effective Length of Column) to calculate 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 calculate Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column using this online calculator? To use this online calculator 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. Here is how the Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column calculation can be explained with given input values -> 219393.1 = 0.19/sin((pi*2)/3).

FAQ

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

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 and is represented as e_o = e/sin((pi*x)/L) or Maximum Deflection at Mid Height = Lateral Deflection/sin((pi*Distance from One End of Pin Ended Column)/Effective Length of Column). 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, 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 & 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.

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

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 is calculated using Maximum Deflection at Mid Height = Lateral Deflection/sin((pi*Distance from One End of Pin Ended Column)/Effective Length of Column). To calculate Maximum Deflection at Mid Height given Lateral Deflection of Pin Ended Column, you need Lateral Deflection (e), Distance from One End of Pin Ended Column (x) & Effective Length of Column (L). With our tool, you need to enter the respective value for Lateral Deflection, Distance from One End of Pin Ended Column & Effective Length of Column 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 Deflection at Mid Height?

In this formula, Maximum Deflection at Mid Height uses Lateral Deflection, Distance from One End of Pin Ended Column & Effective Length of Column. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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