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Moment of Inertia given Deflection at Free End of Column with Eccentric Load Formula

GoMoment of Inertia given Deflection at Section of Column with Eccentric Load Formula

GoMoment of Inertia given Maximum Stress for Column with Eccentric Load Formula

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Moment of inertia also known as the rotational inertia or angular mass, is a measure of an object’s resistance to changes in its rotational motion around a specific axis. Check FAQs

I = \frac{P}{ε column \cdot ({(\frac{a r c \sec ((\frac{δ}{e load}) + 1)}{L})}^{2})}

I - Moment of Inertia?P - Eccentric Load on Column?ε_column - Modulus of Elasticity of Column?δ - Deflection of Free End?e_load - Eccentricity of Load?L - Column Length?

Moment of Inertia given Deflection at Free End of Column with Eccentric Load Example

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

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

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

0.0002 = \frac{40}{2 \cdot ({(\frac{a r c \sec ((\frac{201.112}{2.5}) + 1)}{5000})}^{2})}

0.0002kg·m² = \frac{40N}{2MPa \cdot ({(\frac{a r c \sec ((\frac{201.112mm}{2.5mm}) + 1)}{5000mm})}^{2})}

0.0002 = \frac{40}{2 \cdot ({(\frac{a r c \sec ((\frac{201.112}{2.5}) + 1)}{5000})}^{2})}

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Strength of Materials » fx Moment of Inertia given Deflection at Free End of Column with Eccentric Load

Moment of Inertia given Deflection at Free End of Column with Eccentric Load Solution

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

FIRST Step Consider the formula

I = \frac{P}{ε column \cdot ({(\frac{a r c \sec ((\frac{δ}{e load}) + 1)}{L})}^{2})}

Next Step Substitute values of Variables

∴

I = \frac{40N}{2MPa \cdot ({(\frac{a r c \sec ((\frac{201.112mm}{2.5mm}) + 1)}{5000mm})}^{2})}

Next Step Convert Units

∴

I = \frac{40N}{2E+6Pa \cdot ({(\frac{a r c \sec ((\frac{0.2011m}{0.0025m}) + 1)}{5m})}^{2})}

Next Step Prepare to Evaluate

∴

I = \frac{40}{2E+6 \cdot ({(\frac{a r c \sec ((\frac{0.2011}{0.0025}) + 1)}{5})}^{2})}

Next Step Evaluate

∴

I = 0.000205847923844933kg·m²

LAST Step Rounding Answer

∴

I = 0.0002kg·m²

Moment of Inertia given Deflection at Free End of Column with Eccentric Load Formula Elements

Variables

Functions

Moment of Inertia

Moment of inertia also known as the rotational inertia or angular mass, is a measure of an object’s resistance to changes in its rotational motion around a specific axis.

Symbol: I

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of Inertia

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

Modulus of Elasticity of Column

Modulus of elasticity of column is a measure of a material’s stiffness or rigidity, is defined as the ratio of longitudinal stress to longitudinal strain within the elastic limit of a material.

Symbol: ε_column

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity of Column

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

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

Column Length

Column length refers to the distance between its two ends, typically measured from the base to the top, crucial as it influences the column’s stability and load-bearing capacity.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Column Length

sec

Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine.

Syntax: sec(Angle)

arcsec

Inverse trigonometric secant – Unary function.

Syntax: arcsec(x)

Other Formulas to find Moment of Inertia

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

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

Go Moment of Inertia given Maximum Stress for Column with Eccentric Load

I = \frac{{(a \frac{sech (\frac{(σ max - (\frac{P}{A sectional})) \cdot S}{P \cdot e})}{l e})}^{2}}{\frac{P}{ε column}}

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 Moment of Inertia given Deflection at Free End of Column with Eccentric Load?

Moment of Inertia given Deflection at Free End of Column with Eccentric Load evaluator uses Moment of Inertia = Eccentric Load on Column/(Modulus of Elasticity of Column*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2)) to evaluate the Moment of Inertia, Moment of Inertia given Deflection at Free End of Column with Eccentric Load formula is defined as a measure of the tendency of an object to resist changes in its rotation, specifically in columns subjected to eccentric loads, providing valuable insights into the structural integrity of such systems. Moment of Inertia is denoted by I symbol.

How to evaluate Moment of Inertia given Deflection at Free End of Column with Eccentric Load using this online evaluator? To use this online evaluator for Moment of Inertia given Deflection at Free End of Column with Eccentric Load, enter Eccentric Load on Column (P), Modulus of Elasticity of Column (ε_column), Deflection of Free End (δ), Eccentricity of Load (e_load) & Column Length (L) and hit the calculate button.

FAQs on Moment of Inertia given Deflection at Free End of Column with Eccentric Load

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

The formula of Moment of Inertia given Deflection at Free End of Column with Eccentric Load is expressed as Moment of Inertia = Eccentric Load on Column/(Modulus of Elasticity of Column*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2)). Here is an example- 0.000248 = 40/(2000000*(((arcsec((0.201112/0.0025)+1))/5)^2)).

How to calculate Moment of Inertia given Deflection at Free End of Column with Eccentric Load?

With Eccentric Load on Column (P), Modulus of Elasticity of Column (ε_column), Deflection of Free End (δ), Eccentricity of Load (e_load) & Column Length (L) we can find Moment of Inertia given Deflection at Free End of Column with Eccentric Load using the formula - Moment of Inertia = Eccentric Load on Column/(Modulus of Elasticity of Column*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2)). This formula also uses Secant (sec), Inverse Trigonometric Secant (arcsec) function(s).

What are the other ways to Calculate Moment of Inertia?

Here are the different ways to Calculate Moment of Inertia-

Moment of Inertia=(Eccentric Load on Column/(Modulus of Elasticity of Column*(((acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/Distance b/w Fixed End and Deflection Point)^2)))
Moment of Inertia=((asech(((Maximum Stress at Crack Tip-(Eccentric Load on Column/Cross-Sectional Area of Column))*Section Modulus for Column)/(Eccentric Load on Column*Eccentricity of Column))/(Effective Column Length))^2)/(Eccentric Load on Column/(Modulus of Elasticity of Column))

Can the Moment of Inertia given Deflection at Free End of Column with Eccentric Load be negative?

No, the Moment of Inertia given Deflection at Free End of Column with Eccentric Load, measured in Moment of Inertia cannot be negative.

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

Moment of Inertia given Deflection at Free End of Column with Eccentric Load is usually measured using the Kilogram Square Meter[kg·m²] for Moment of Inertia. Kilogram Square Centimeter[kg·m²], Kilogram Square Millimeter[kg·m²], Gram Square Centimeter[kg·m²] are the few other units in which Moment of Inertia given Deflection at Free End of Column with Eccentric Load can be measured.

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Moment of Inertia given Deflection at Free End of Column with Eccentric Load Formula

​GoMoment of Inertia given Deflection at Section of Column with Eccentric Load Formula

​GoMoment of Inertia given Maximum Stress for Column with Eccentric Load Formula

Moment of Inertia given Deflection at Free End of Column with Eccentric Load Example

Moment of Inertia given Deflection at Free End of Column with Eccentric Load Solution

Moment of Inertia given Deflection at Free End of Column with Eccentric Load Formula Elements

Other Formulas to find Moment of Inertia

Other formulas in Columns With Eccentric Load category

How to Evaluate Moment of Inertia given Deflection at Free End of Column with Eccentric Load?

FAQs on Moment of Inertia given Deflection at Free End of Column with Eccentric Load

Variable Name

GoMoment of Inertia given Deflection at Section of Column with Eccentric Load Formula

GoMoment of Inertia given Maximum Stress for Column with Eccentric Load Formula