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

✖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.ⓘ 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 of Equivalent Pin-Ended Column [e_o]

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

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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

Curvature of Column: 0.24 --> No Conversion Required
Effective Length of Column: 3000 Millimeter --> 3 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

e_o = Φ_m*(L)^2/pi^2 --> 0.24*(3)^2/pi^2

Evaluating ... ...

e_o = 0.21885375666745

STEP 3: Convert Result to Output's Unit

0.21885375666745 Meter -->218.85375666745 Millimeter (Check conversion here)

FINAL ANSWER

218.85375666745 ≈ 218.8538 Millimeter <-- Maximum Deflection at Mid Height

(Calculation completed in 00.004 seconds)

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

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Created by Ayush Singh

Gautam Buddha University (GBU), Greater Noida

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Coorg Institute of Technology (CIT), Coorg

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< Equivalent Column Concept Calculators

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

LaTeX 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

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

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

LaTeX 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

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

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

LaTeX Go

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

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 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 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 columns to an axially loaded equivalent pin-ended column with greater length.

How to Calculate Maximum Deflection at Mid-Height of Equivalent Pin-Ended Column?

Maximum Deflection at Mid-Height of Equivalent Pin-Ended Column calculator uses Maximum Deflection at Mid Height = Curvature of Column*(Effective Length of Column)^2/pi^2 to calculate the Maximum Deflection at Mid Height, The Maximum Deflection at Mid-Height of Equivalent Pin-Ended Column formula is defined as the ratio of the length of the equivalent pin-ended column to the constant pie whole multiplied by the curvature of the column based on the column’s mode of failure. Maximum Deflection at Mid Height is denoted by e_o symbol.

How to calculate Maximum Deflection at Mid-Height of Equivalent Pin-Ended Column using this online calculator? To use this online calculator for Maximum Deflection at Mid-Height of Equivalent Pin-Ended Column, enter Curvature of Column (Φ_m) & Effective Length of Column (L) and hit the calculate button. Here is how the Maximum Deflection at Mid-Height of Equivalent Pin-Ended Column calculation can be explained with given input values -> 218853.8 = 0.24*(3)^2/pi^2.

FAQ

What is Maximum Deflection at Mid-Height of Equivalent Pin-Ended Column?

The Maximum Deflection at Mid-Height of Equivalent Pin-Ended Column formula is defined as the ratio of the length of the equivalent pin-ended column to the constant pie whole multiplied by the curvature of the column based on the column’s mode of failure and is represented as e_o = Φ_m*(L)^2/pi^2 or Maximum Deflection at Mid Height = Curvature of Column*(Effective Length of Column)^2/pi^2. Curvature of Column based on column's mode of failure & 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 of Equivalent Pin-Ended Column?

The Maximum Deflection at Mid-Height of Equivalent Pin-Ended Column formula is defined as the ratio of the length of the equivalent pin-ended column to the constant pie whole multiplied by the curvature of the column based on the column’s mode of failure is calculated using Maximum Deflection at Mid Height = Curvature of Column*(Effective Length of Column)^2/pi^2. To calculate Maximum Deflection at Mid-Height of Equivalent Pin-Ended Column, you need Curvature of Column (Φ_m) & Effective Length of Column (L). With our tool, you need to enter the respective value for Curvature of 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 Curvature of 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 = Lateral Deflection/sin((pi*Distance from One End of Pin Ended Column)/Effective Length of Column)

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