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Deflection at Free End given Deflection at Section of Column with Eccentric load Formula

GoDeflection at Free End of Column with Eccentric load Formula

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Deflection of Free End is the deflection caused due to crippling load at the free end. Check FAQs

a crippling = (\frac{δ c}{1 - \cos (x \cdot \sqrt{\frac{P}{ε column \cdot I}})}) - e load

a_crippling - Deflection of Free End?δ_c - Deflection of Column?x - Distance b/w fixed end and deflection point?P - Eccentric load on column?ε_column - Modulus of elasticity of column?I - Moment of Inertia?e_load - Eccentricity of Load?

Deflection at Free End given Deflection at Section of Column with Eccentric load Example

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Here is how the Deflection at Free End given Deflection at Section of Column with Eccentric load equation looks like with Values.

Here is how the Deflection at Free End given Deflection at Section of Column with Eccentric load equation looks like with Units.

Here is how the Deflection at Free End given Deflection at Section of Column with Eccentric load equation looks like.

201.112 = (\frac{12}{1 - \cos (1000 \cdot \sqrt{\frac{40}{2 \cdot 0.0002}})}) - 2.5

201.112mm = (\frac{12mm}{1 - \cos (1000mm \cdot \sqrt{\frac{40N}{2MPa \cdot 0.0002kg·m²}})}) - 2.5mm

201.112 = (\frac{12}{1 - \cos (1000 \cdot \sqrt{\frac{40}{2 \cdot 0.0002}})}) - 2.5

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Deflection at Free End given Deflection at Section of Column with Eccentric load Solution

Follow our step by step solution on how to calculate Deflection at Free End given Deflection at Section of Column with Eccentric load?

FIRST Step Consider the formula

a crippling = (\frac{δ c}{1 - \cos (x \cdot \sqrt{\frac{P}{ε column \cdot I}})}) - e load

Next Step Substitute values of Variables

∴

a crippling = (\frac{12mm}{1 - \cos (1000mm \cdot \sqrt{\frac{40N}{2MPa \cdot 0.0002kg·m²}})}) - 2.5mm

Next Step Convert Units

∴

a crippling = (\frac{0.012m}{1 - \cos (1m \cdot \sqrt{\frac{40N}{2E+6Pa \cdot 0.0002kg·m²}})}) - 0.0025m

Next Step Prepare to Evaluate

∴

a crippling = (\frac{0.012}{1 - \cos (1 \cdot \sqrt{\frac{40}{2E+6 \cdot 0.0002}})}) - 0.0025

Next Step Evaluate

∴

a crippling = 0.201111961236572m

Next Step Convert to Output's Unit

∴

a crippling = 201.111961236572mm

LAST Step Rounding Answer

∴

a crippling = 201.112mm

Deflection at Free End given Deflection at Section of Column with Eccentric load Formula Elements

Variables

Functions

Deflection of Free End

Deflection of Free End is the deflection caused due to crippling load at the free end.

Symbol: a_crippling

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Deflection of Free End

Deflection of Column

Deflection of column refers to the degree to which a column bends or displaces under the influence of external forces such as weight, wind, or seismic activity.

Symbol: δ_c

Measurement: LengthUnit: mm