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

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

GoMoment of Inertia given Deflection at Free End of 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{{(a \frac{sech (\frac{(σ max - (\frac{P}{A sectional})) \cdot S}{P \cdot e})}{l e})}^{2}}{\frac{P}{ε column}}

I - Moment of Inertia?σ_max - Maximum Stress at Crack Tip?P - Eccentric Load on Column?A_sectional - Cross-Sectional Area of Column?S - Section Modulus for Column?e - Eccentricity of Column?l_e - Effective Column Length?ε_column - Modulus of Elasticity of Column?

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

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Here is how the Moment of Inertia given Maximum Stress for Column with Eccentric Load equation looks like with Values.

Here is how the Moment of Inertia given Maximum Stress for Column with Eccentric Load equation looks like with Units.

Here is how the Moment of Inertia given Maximum Stress for Column with Eccentric Load equation looks like.

1.3E+8 = \frac{{(a \frac{sech (\frac{(6E-5 - (\frac{40}{0.6667})) \cdot 13}{40 \cdot 15000})}{200})}^{2}}{\frac{40}{2}}

1.3E+8kg·m² = \frac{{(a \frac{sech (\frac{(6E-5MPa - (\frac{40N}{0.6667m²})) \cdot 13m³}{40N \cdot 15000mm})}{200mm})}^{2}}{\frac{40N}{2MPa}}

1.3E+8 = \frac{{(a \frac{sech (\frac{(6E-5 - (\frac{40}{0.6667})) \cdot 13}{40 \cdot 15000})}{200})}^{2}}{\frac{40}{2}}

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

Follow our step by step solution on how to calculate Moment of Inertia given Maximum Stress for Column with Eccentric Load?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

I = \frac{{(a \frac{sech (\frac{(6E-5MPa - (\frac{40N}{0.6667m²})) \cdot 13m³}{40N \cdot 15000mm})}{200mm})}^{2}}{\frac{40N}{2MPa}}

Next Step Convert Units

∴

I = \frac{{(a \frac{sech (\frac{(60Pa - (\frac{40N}{0.6667m²})) \cdot 13m³}{40N \cdot 15m})}{0.2m})}^{2}}{\frac{40N}{2E+6Pa}}

Next Step Prepare to Evaluate

∴

I = \frac{{(a \frac{sech (\frac{(60 - (\frac{40}{0.6667})) \cdot 13}{40 \cdot 15})}{0.2})}^{2}}{\frac{40}{2E+6}}

Next Step Evaluate

∴

I = 126805754.82365kg·m²

LAST Step Rounding Answer

∴

I = 1.3E+8kg·m²

Moment of Inertia given Maximum Stress for 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

Maximum Stress at Crack Tip

Maximum stress at crack tip refers to the highest stress concentration that occurs at the very tip of a crack in a material.

Symbol: σ_max

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Maximum Stress at Crack Tip

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

Cross-Sectional Area of Column

Cross-sectional area of column is the area of the shape we get when we cut through the column perpendicular to its length, helps in determining the column’s ability to bear loads and resist stresses.

Symbol: A_sectional

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Cross-Sectional Area of Column

Section Modulus for Column

Section modulus for column is a geometric property of a cross-section that measures the ability of a section to resist bending and is crucial for determining the bending stress in structural elements.

Symbol: S

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Section Modulus for Column

Eccentricity of Column

Eccentricity of column refers to the distance between the line of action of the applied load and the centroidal axis of the column’s cross-section.

Symbol: e

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Eccentricity of Column

Effective Column Length

Effective column length, often that represents the length of a column that influences its buckling behavior.

Symbol: l_e

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Column Length

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

sech

The hyperbolic secant function is a hyperbolic function that is the reciprocal of the hyperbolic cosine function.

Syntax: sech(Number)

asech

The hyperbolic secant function is defined as sech(x) = 1/cosh(x), where cosh(x) is the hyperbolic cosine function.

Syntax: asech(Number)

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 Deflection at Free End of Column with Eccentric Load

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

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

How to Evaluate Moment of Inertia given Maximum Stress for Column with Eccentric Load?

Moment of Inertia given Maximum Stress for Column with Eccentric Load evaluator uses 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)) to evaluate the Moment of Inertia, Moment of Inertia given Maximum Stress for Column with Eccentric Load formula is defined as a measure of the resistance of a column to bending under an eccentric load, taking into account the maximum stress, sectional area, and eccentricity of the load, providing a critical parameter in structural analysis and design. Moment of Inertia is denoted by I symbol.

How to evaluate Moment of Inertia given Maximum Stress for Column with Eccentric Load using this online evaluator? To use this online evaluator for Moment of Inertia given Maximum Stress for Column with Eccentric Load, enter Maximum Stress at Crack Tip (σ_max), Eccentric Load on Column (P), Cross-Sectional Area of Column (A_sectional), Section Modulus for Column (S), Eccentricity of Column (e), Effective Column Length (l_e) & Modulus of Elasticity of Column (ε_column) and hit the calculate button.

FAQs on Moment of Inertia given Maximum Stress for Column with Eccentric Load

What is the formula to find Moment of Inertia given Maximum Stress for Column with Eccentric Load?

The formula of Moment of Inertia given Maximum Stress for Column with Eccentric Load is expressed as 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)). Here is an example- 1.1E+6 = ((asech(((60-(40/0.66671))*13)/(40*15))/(0.2))^2)/(40/(2000000)).

How to calculate Moment of Inertia given Maximum Stress for Column with Eccentric Load?

With Maximum Stress at Crack Tip (σ_max), Eccentric Load on Column (P), Cross-Sectional Area of Column (A_sectional), Section Modulus for Column (S), Eccentricity of Column (e), Effective Column Length (l_e) & Modulus of Elasticity of Column (ε_column) we can find Moment of Inertia given Maximum Stress for Column with Eccentric Load using the formula - 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)). This formula also uses Hyperbolic Secant (sech), Inverse Trigonometric Secant (asech) 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=Eccentric Load on Column/(Modulus of Elasticity of Column*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2))

Can the Moment of Inertia given Maximum Stress for Column with Eccentric Load be negative?

No, the Moment of Inertia given Maximum Stress for Column with Eccentric Load, measured in Moment of Inertia cannot be negative.

Which unit is used to measure Moment of Inertia given Maximum Stress for Column with Eccentric Load?

Moment of Inertia given Maximum Stress for 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 Maximum Stress for Column with Eccentric Load can be measured.

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

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

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

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

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

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

FAQs on Moment of Inertia given Maximum Stress for Column with Eccentric Load

Variable Name

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

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