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

✖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 [e_o]			+10% -10%
✖Curvature of Column based on column's mode of failure.ⓘ Curvature of Column [Φ_m]			+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.ⓘ Length of Equivalent Pin Ended Column given Max Deflection at Mid Height [L]

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

Formula

`"L" = sqrt(("e"_{"o"}*pi^2)/"Φ"_{"m"})`

Example

`"3001.002mm"=sqrt(("219mm"*pi^2)/"0.24")`

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

STEP 0: Pre-Calculation Summary

Formula Used

Effective Length of Column = sqrt((Maximum Deflection at Mid Height*pi^2)/Curvature of Column)
L = sqrt((e_o*pi^2)/Φ_m)
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sqrt(Number)

Variables Used

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

STEP 1: Convert Input(s) to Base Unit

Maximum Deflection at Mid Height: 219 Millimeter --> 0.219 Meter (Check conversion here)
Curvature of Column: 0.24 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = sqrt((e_o*pi^2)/Φ_m) --> sqrt((0.219*pi^2)/0.24)

Evaluating ... ...

L = 3.00100216860869

STEP 3: Convert Result to Output's Unit

3.00100216860869 Meter -->3001.00216860869 Millimeter (Check conversion here)

FINAL ANSWER

3001.00216860869 ≈ 3001.002 Millimeter <-- Effective Length of Column

(Calculation completed in 00.004 seconds)

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

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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

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

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

What is the Equivalent Column Concept?

It is accepted that the deflected axis of any column may be represented by a portion of the column deflected shape of an axially loaded pin-ended column. Therefore, for a given column subjected to end moments, an equivalent column exists and the column-deflected shape of the equivalent pin-ended column can be represented by a sinusoidal curve.

What are the Different Modes of Failure of RC Columns?

There are three modes of failure of concrete columns (compression members) i.e. failure due to pure compression, combined compression and elastic instability. This concept is adopted in order to reduce uni-axially loaded column to an axially loaded equivalent pin-ended column with greater length.

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

Length of Equivalent Pin Ended Column given Max Deflection at Mid Height calculator uses Effective Length of Column = sqrt((Maximum Deflection at Mid Height*pi^2)/Curvature of Column) to calculate 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 calculate Length of Equivalent Pin Ended Column given Max Deflection at Mid Height using this online calculator? To use this online calculator 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. Here is how the Length of Equivalent Pin Ended Column given Max Deflection at Mid Height calculation can be explained with given input values -> 3E+6 = sqrt((0.219*pi^2)/0.24).

FAQ

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

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 and is represented as L = sqrt((e_o*pi^2)/Φ_m) or Effective Length of Column = sqrt((Maximum Deflection at Mid Height*pi^2)/Curvature of Column). 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 & Curvature of Column based on column's mode of failure.

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

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 is calculated using Effective Length of Column = sqrt((Maximum Deflection at Mid Height*pi^2)/Curvature of Column). To calculate Length of Equivalent Pin Ended Column given Max Deflection at Mid Height, you need Maximum Deflection at Mid Height (e_o) & Curvature of Column (Φ_m). With our tool, you need to enter the respective value for Maximum Deflection at Mid Height & Curvature of Column and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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