Curvature of Column Based on Column Mode of Failure 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%
✖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%

✖Curvature of Column based on column's mode of failure.ⓘ Curvature of Column Based on Column Mode of Failure [Φ_m]

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Formula

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Curvature of Column Based on Column Mode of Failure

Formula

`"Φ"_{"m"} = "e"_{"o"}*pi^2/"L"^2`

Example

`"0.24016"="219mm"*pi^2/("3000mm")^2`

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Curvature of Column Based on Column Mode of Failure Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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

Maximum Deflection at Mid Height: 219 Millimeter --> 0.219 Meter (Check conversion here)
Effective Length of Column: 3000 Millimeter --> 3 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Φ_m = e_o*pi^2/L^2 --> 0.219*pi^2/3^2

Evaluating ... ...

Φ_m = 0.240160373759841

STEP 3: Convert Result to Output's Unit

0.240160373759841 --> No Conversion Required

FINAL ANSWER

0.240160373759841 ≈ 0.24016 <-- Curvature 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 » Curvature of Column Based on Column Mode of Failure

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Created by Ayush Singh

Gautam Buddha University (GBU), Greater Noida

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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

Curvature of Column Based on Column Mode of Failure Formula

Curvature of Column = Maximum Deflection at Mid Height*pi^2/Effective Length of Column^2
Φ_m = e_o*pi^2/L^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 column to an axially loaded equivalent pin-ended column with greater length.

How to Calculate Curvature of Column Based on Column Mode of Failure?

Curvature of Column Based on Column Mode of Failure calculator uses Curvature of Column = Maximum Deflection at Mid Height*pi^2/Effective Length of Column^2 to calculate the Curvature of Column, The Curvature of Column Based on Column Mode of Failure formula is defined as the ratio of lateral deflection of the column to the square of the length of the equivalent pin-ended column. Curvature of Column is denoted by Φ_m symbol.

How to calculate Curvature of Column Based on Column Mode of Failure using this online calculator? To use this online calculator for Curvature of Column Based on Column Mode of Failure, enter Maximum Deflection at Mid Height (e_o) & Effective Length of Column (L) and hit the calculate button. Here is how the Curvature of Column Based on Column Mode of Failure calculation can be explained with given input values -> 0.24016 = 0.219*pi^2/3^2.

FAQ

What is Curvature of Column Based on Column Mode of Failure?

The Curvature of Column Based on Column Mode of Failure formula is defined as the ratio of lateral deflection of the column to the square of the length of the equivalent pin-ended column and is represented as Φ_m = e_o*pi^2/L^2 or Curvature of Column = Maximum Deflection at Mid Height*pi^2/Effective Length of Column^2. 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 & 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 Curvature of Column Based on Column Mode of Failure?

The Curvature of Column Based on Column Mode of Failure formula is defined as the ratio of lateral deflection of the column to the square of the length of the equivalent pin-ended column is calculated using Curvature of Column = Maximum Deflection at Mid Height*pi^2/Effective Length of Column^2. To calculate Curvature of Column Based on Column Mode of Failure, you need Maximum Deflection at Mid Height (e_o) & Effective Length of Column (L). With our tool, you need to enter the respective value for Maximum Deflection at Mid Height & 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.

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