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Section Modulus given Maximum Stress for Column with Eccentric Load Formula

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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. Check FAQs

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

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

Section Modulus given Maximum Stress for Column with Eccentric Load Example

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Here is how the Section Modulus given Maximum Stress for Column with Eccentric Load equation looks like with Values.

Here is how the Section Modulus given Maximum Stress for Column with Eccentric Load equation looks like with Units.

Here is how the Section Modulus given Maximum Stress for Column with Eccentric Load equation looks like.

77111.6031 = \frac{\frac{40 \cdot 15000 \cdot \sec (200 \cdot \sqrt{\frac{40}{2 \cdot 0.0002}})}{2}}{6E-5 - (\frac{40}{0.6667})}

77111.6031m³ = \frac{\frac{40N \cdot 15000mm \cdot \sec (200mm \cdot \sqrt{\frac{40N}{2MPa \cdot 0.0002kg·m²}})}{2}}{6E-5MPa - (\frac{40N}{0.6667m²})}

77111.6031 = \frac{\frac{40 \cdot 15000 \cdot \sec (200 \cdot \sqrt{\frac{40}{2 \cdot 0.0002}})}{2}}{6E-5 - (\frac{40}{0.6667})}

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Section Modulus given Maximum Stress for Column with Eccentric Load Solution

Follow our step by step solution on how to calculate Section Modulus given Maximum Stress for Column with Eccentric Load?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

S = \frac{\frac{40N \cdot 15000mm \cdot \sec (200mm \cdot \sqrt{\frac{40N}{2MPa \cdot 0.0002kg·m²}})}{2}}{6E-5MPa - (\frac{40N}{0.6667m²})}

Next Step Convert Units

∴

S = \frac{\frac{40N \cdot 15m \cdot \sec (0.2m \cdot \sqrt{\frac{40N}{2E+6Pa \cdot 0.0002kg·m²}})}{2}}{60Pa - (\frac{40N}{0.6667m²})}

Next Step Prepare to Evaluate

∴

S = \frac{\frac{40 \cdot 15 \cdot \sec (0.2 \cdot \sqrt{\frac{40}{2E+6 \cdot 0.0002}})}{2}}{60 - (\frac{40}{0.6667})}

Next Step Evaluate

∴

S = 77111.6031328573m³

LAST Step Rounding Answer

∴

S = 77111.6031m³

Section Modulus given Maximum Stress for Column with Eccentric Load Formula Elements

Variables

Functions

Section Modulus for Column

Symbol: S

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Section Modulus for Column

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 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

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

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

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)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

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 Section Modulus given Maximum Stress for Column with Eccentric Load?

Section Modulus given Maximum Stress for Column with Eccentric Load evaluator uses Section Modulus for Column = ((Eccentric Load on Column*Eccentricity of Column*sec(Effective Column Length*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))))/2)/(Maximum Stress at Crack Tip-(Eccentric Load on Column/Cross-Sectional Area of Column)) to evaluate the Section Modulus for Column, Section Modulus given Maximum Stress for Column with Eccentric Load formula is defined as a measure of the ability of a column to resist bending due to an eccentric load, taking into account the maximum stress, load, and sectional properties of the column. Section Modulus for Column is denoted by S symbol.

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

FAQs on Section Modulus given Maximum Stress for Column with Eccentric Load

What is the formula to find Section Modulus given Maximum Stress for Column with Eccentric Load?

The formula of Section Modulus given Maximum Stress for Column with Eccentric Load is expressed as Section Modulus for Column = ((Eccentric Load on Column*Eccentricity of Column*sec(Effective Column Length*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))))/2)/(Maximum Stress at Crack Tip-(Eccentric Load on Column/Cross-Sectional Area of Column)). Here is an example- 9.568227 = ((40*15*sec(0.2*sqrt(40/(2000000*0.000168))))/2)/(60-(40/0.66671)).

How to calculate Section Modulus given Maximum Stress for Column with Eccentric Load?

With Eccentric Load on Column (P), Eccentricity of Column (e), Effective Column Length (l_e), Modulus of Elasticity of Column (ε_column), Moment of Inertia (I), Maximum Stress at Crack Tip (σ_max) & Cross-Sectional Area of Column (A_sectional) we can find Section Modulus given Maximum Stress for Column with Eccentric Load using the formula - Section Modulus for Column = ((Eccentric Load on Column*Eccentricity of Column*sec(Effective Column Length*sqrt(Eccentric Load on Column/(Modulus of Elasticity of Column*Moment of Inertia))))/2)/(Maximum Stress at Crack Tip-(Eccentric Load on Column/Cross-Sectional Area of Column)). This formula also uses Secant (sec), Square Root (sqrt) function(s).

Can the Section Modulus given Maximum Stress for Column with Eccentric Load be negative?

No, the Section Modulus given Maximum Stress for Column with Eccentric Load, measured in Volume cannot be negative.

Which unit is used to measure Section Modulus given Maximum Stress for Column with Eccentric Load?

Section Modulus given Maximum Stress for Column with Eccentric Load is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Section Modulus given Maximum Stress for Column with Eccentric Load can be measured.

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Section Modulus given Maximum Stress for Column with Eccentric Load Formula

Section Modulus given Maximum Stress for Column with Eccentric Load Example

Section Modulus given Maximum Stress for Column with Eccentric Load Solution

Section Modulus given Maximum Stress for Column with Eccentric Load Formula Elements

Other formulas in Columns With Eccentric Load category

How to Evaluate Section Modulus given Maximum Stress for Column with Eccentric Load?

FAQs on Section Modulus given Maximum Stress for Column with Eccentric Load

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