Lateral Deflection of Equivalent Pin Ended Column at distance x 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 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%

✖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 of Equivalent Pin Ended Column at distance x [e]

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Lateral Deflection of Equivalent Pin Ended Column at distance x Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
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

Maximum Deflection at Mid Height: 219 Millimeter --> 0.219 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 = e_o*sin((pi*x)/L) --> 0.219*sin((pi*2)/3)

Evaluating ... ...

e = 0.189659563428792

STEP 3: Convert Result to Output's Unit

0.189659563428792 Meter -->189.659563428792 Millimeter (Check conversion here)

FINAL ANSWER

189.659563428792 ≈ 189.6596 Millimeter <-- Lateral Deflection

(Calculation completed in 00.004 seconds)

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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

Lateral Deflection of Equivalent Pin Ended Column at distance x Formula

LaTeX Go

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

What is Lateral Deflection?

Lateral deflection is the movement perpendicular to the axial plane of the structure. 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.

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

The calculation of lateral deflection of a column is important to ensure its safety against 'Buckling' which is a sudden, large lateral deflection; which leads to the failure of the column even before it reaches its yield compressive stress.

How to Calculate Lateral Deflection of Equivalent Pin Ended Column at distance x?

Lateral Deflection of Equivalent Pin Ended Column at distance x calculator uses Lateral Deflection = Maximum Deflection at Mid Height*sin((pi*Distance from One End of Pin Ended Column)/Effective Length of Column) to calculate the Lateral Deflection, The Lateral Deflection of Equivalent Pin Ended Column at distance x formula is defined as 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 is denoted by e symbol.

How to calculate Lateral Deflection of Equivalent Pin Ended Column at distance x using this online calculator? To use this online calculator for Lateral Deflection of Equivalent Pin Ended Column at distance x, enter Maximum Deflection at Mid Height (e_o), Distance from One End of Pin Ended Column (x) & Effective Length of Column (L) and hit the calculate button. Here is how the Lateral Deflection of Equivalent Pin Ended Column at distance x calculation can be explained with given input values -> 189659.6 = 0.219*sin((pi*2)/3).

FAQ

What is Lateral Deflection of Equivalent Pin Ended Column at distance x?

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

The Lateral Deflection of Equivalent Pin Ended Column at distance x formula is defined as 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 is calculated using Lateral Deflection = Maximum Deflection at Mid Height*sin((pi*Distance from One End of Pin Ended Column)/Effective Length of Column). To calculate Lateral Deflection of Equivalent Pin Ended Column at distance x, you need Maximum Deflection at Mid Height (e_o), 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 Maximum Deflection at Mid Height, 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.

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