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

GoDeflection at Section of Column with Eccentric Load Formula

GoDeflection at Section of Column with Eccentric Load given Moment at Section Formula

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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. Check FAQs

δ c = (\frac{M}{P}) - (e load + δ)

δ_c - Deflection of Column?M - Moment of Force?P - Eccentric Load on Column?e_load - Eccentricity of Load?δ - Deflection of Free End?

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

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

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

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

996.388 = (\frac{48}{40}) - (2.5 + 201.112)

996.388mm = (\frac{48N*m}{40N}) - (2.5mm + 201.112mm)

996.388 = (\frac{48}{40}) - (2.5 + 201.112)

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

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

FIRST Step Consider the formula

δ c = (\frac{M}{P}) - (e load + δ)

Next Step Substitute values of Variables

∴

δ c = (\frac{48N*m}{40N}) - (2.5mm + 201.112mm)

Next Step Convert Units

∴

δ c = (\frac{48N*m}{40N}) - (0.0025m + 0.2011m)

Next Step Prepare to Evaluate

∴

δ c = (\frac{48}{40}) - (0.0025 + 0.2011)

Next Step Evaluate

∴

δ c = 0.996388m

LAST Step Convert to Output's Unit

∴

δ c = 996.388mm

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

Variables

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

Note: Value should be greater than 0.

Formulas to find Deflection of Column

Moment of Force

Moment of force also known as torque, measures the tendency of a force to rotate an object around a point or axis, calculated as the product of the force and the perpendicular distance.

Symbol: M

Measurement: TorqueUnit: N*m

Note: Value should be greater than 0.

Formulas to find Moment of Force

Eccentric Load on Column

Eccentric load on column refers to a load that is applied at a point away from the centroidal axis of the column’s cross-section where loading introduces both axial stress and bending stress.

Symbol: P

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Eccentric Load on Column

Eccentricity of Load

Eccentricity of load refers to the offset of a load from the centroid of a structural element, such as a beam or column.

Symbol: e_load

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Eccentricity of Load

Deflection of Free End

Deflection of free end of a beam refers to the displacement or movement of the beam’s free end from its original position due to applied loads or crippling load at the free end.

Symbol: δ

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Deflection of Free End

Other Formulas to find Deflection of Column

Go Deflection at Section of Column with Eccentric Load

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

Go Deflection at Section of Column with Eccentric Load given Moment at Section

δ c = - (\frac{M}{P}) + δ + e

Other formulas in Columns With Eccentric Load category

Go Moment at Section of Column with Eccentric Load

M = P \cdot (δ + e load - δ c)

Go Eccentricity given Moment at Section of Column with Eccentric Load

e = (\frac{M}{P}) - δ + δ c

Go Eccentric Load given Deflection at Section of Column with Eccentric Load

P = ({(\frac{a \cos (1 - (\frac{δ c}{δ + e load}))}{x})}^{2}) \cdot (ε column \cdot I)

Go Modulus of Elasticity given Deflection at Section of Column with Eccentric Load

ε column = (\frac{P}{I \cdot ({(\frac{a \cos (1 - (\frac{δ c}{δ + e load}))}{x})}^{2})})

How to Evaluate Deflection at Free End given Moment at Section of Column with Eccentric load?

Deflection at Free End given Moment at Section of Column with Eccentric load evaluator uses Deflection of Column = (Moment of Force/Eccentric Load on Column)-(Eccentricity of Load+Deflection of Free End) to evaluate the Deflection of Column, Deflection at Free End given Moment at Section of Column with Eccentric load formula is defined as a measure of the lateral movement of the free end of a column when an eccentric load is applied, taking into account the moment at a section of the column and the load's eccentricity. Deflection of Column is denoted by δ_c symbol.

How to evaluate Deflection at Free End given Moment at Section of Column with Eccentric load using this online evaluator? To use this online evaluator for Deflection at Free End given Moment at Section of Column with Eccentric load, enter Moment of Force (M), Eccentric Load on Column (P), Eccentricity of Load (e_load) & Deflection of Free End (δ) and hit the calculate button.

FAQs on Deflection at Free End given Moment at Section of Column with Eccentric load

What is the formula to find Deflection at Free End given Moment at Section of Column with Eccentric load?

The formula of Deflection at Free End given Moment at Section of Column with Eccentric load is expressed as Deflection of Column = (Moment of Force/Eccentric Load on Column)-(Eccentricity of Load+Deflection of Free End). Here is an example- 1.2E+6 = (48/40)-(0.0025+0.201112).

How to calculate Deflection at Free End given Moment at Section of Column with Eccentric load?

With Moment of Force (M), Eccentric Load on Column (P), Eccentricity of Load (e_load) & Deflection of Free End (δ) we can find Deflection at Free End given Moment at Section of Column with Eccentric load using the formula - Deflection of Column = (Moment of Force/Eccentric Load on Column)-(Eccentricity of Load+Deflection of Free End).

What are the other ways to Calculate Deflection of Column?

Here are the different ways to Calculate Deflection of Column-

Deflection of Column=(Deflection of Free End+Eccentricity of Column)*(1-cos(Distance b/w Fixed End and Deflection Point*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))))
Deflection of Column=-(Moment of Force/Eccentric Load on Column)+Deflection of Free End+Eccentricity of Column

Can the Deflection at Free End given Moment at Section of Column with Eccentric load be negative?

No, the Deflection at Free End given Moment at Section of Column with Eccentric load, measured in Length cannot be negative.

Which unit is used to measure Deflection at Free End given Moment at Section of Column with Eccentric load?

Deflection at Free End given Moment at Section of Column with Eccentric load is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Deflection at Free End given Moment at Section of Column with Eccentric load can be measured.

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

​GoDeflection at Section of Column with Eccentric Load Formula

​GoDeflection at Section of Column with Eccentric Load given Moment at Section Formula

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

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

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

Other Formulas to find Deflection of Column

Other formulas in Columns With Eccentric Load category

How to Evaluate Deflection at Free End given Moment at Section of Column with Eccentric load?

FAQs on Deflection at Free End given Moment at Section of Column with Eccentric load

Variable Name

GoDeflection at Section of Column with Eccentric Load Formula

GoDeflection at Section of Column with Eccentric Load given Moment at Section Formula