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Critical Elastic Moment for Box Sections and Solid Bars Formula

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Critical Elastic Moment for Box Section is the maximum moment a box-section beam can withstand before it reaches the elastic buckling stage. Check FAQs

M bs = \frac{57000 \cdot C b \cdot \sqrt{J \cdot A}}{\frac{L}{r y}}

M_bs - Critical Elastic Moment for Box Section?C_b - Moment Gradient Factor?J - Torsional Constant?A - Cross Sectional Area in Steel Structures?L - Unbraced Length of Member?r_y - Radius of Gyration about Minor Axis?

Critical Elastic Moment for Box Sections and Solid Bars Example

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Here is how the Critical Elastic Moment for Box Sections and Solid Bars equation looks like with Values.

Here is how the Critical Elastic Moment for Box Sections and Solid Bars equation looks like with Units.

Here is how the Critical Elastic Moment for Box Sections and Solid Bars equation looks like.

69.7095 = \frac{57000 \cdot 1.96 \cdot \sqrt{21.9 \cdot 6400}}{\frac{12}{20}}

69.7095N*m = \frac{57000 \cdot 1.96 \cdot \sqrt{21.9 \cdot 6400mm²}}{\frac{12m}{20mm}}

69.7095 = \frac{57000 \cdot 1.96 \cdot \sqrt{21.9 \cdot 6400}}{\frac{12}{20}}

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Critical Elastic Moment for Box Sections and Solid Bars Solution

Follow our step by step solution on how to calculate Critical Elastic Moment for Box Sections and Solid Bars?

FIRST Step Consider the formula

M bs = \frac{57000 \cdot C b \cdot \sqrt{J \cdot A}}{\frac{L}{r y}}

Next Step Substitute values of Variables

∴

M bs = \frac{57000 \cdot 1.96 \cdot \sqrt{21.9 \cdot 6400mm²}}{\frac{12m}{20mm}}

Next Step Convert Units

∴

M bs = \frac{57000 \cdot 1.96 \cdot \sqrt{21.9 \cdot 0.0064m²}}{\frac{12m}{0.02m}}

Next Step Prepare to Evaluate

∴

M bs = \frac{57000 \cdot 1.96 \cdot \sqrt{21.9 \cdot 0.0064}}{\frac{12}{0.02}}

Next Step Evaluate

∴

M bs = 69.7094604081828N*m

LAST Step Rounding Answer

∴

M bs = 69.7095N*m

Critical Elastic Moment for Box Sections and Solid Bars Formula Elements

Variables

Functions

Critical Elastic Moment for Box Section

Critical Elastic Moment for Box Section is the maximum moment a box-section beam can withstand before it reaches the elastic buckling stage.

Symbol: M_bs

Measurement: Moment of ForceUnit: N*m

Note: Value can be positive or negative.

Formulas to find Critical Elastic Moment for Box Section

Moment Gradient Factor

Moment Gradient Factor is rate at which moment is changing with length of beam.

Symbol: C_b

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Moment Gradient Factor

Torsional Constant

Torsional Constant is a geometrical property of a bar's cross-section which is involved in the relationship between the angle of twist and applied torque along the axis of the bar.

Symbol: J

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Torsional Constant

Cross Sectional Area in Steel Structures

Cross Sectional Area in Steel Structures is the area of a particular section of a structural element, such as a beam or column, when cut perpendicular to its longitudinal axis.

Symbol: A

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Cross Sectional Area in Steel Structures

Unbraced Length of Member

Unbraced Length of Member is the distance between two points along a structural member where lateral support is provided.

Symbol: L

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Unbraced Length of Member

Radius of Gyration about Minor Axis

Radius of Gyration about Minor Axis is the root mean square distance of the object's parts from either its center of mass or a given minor axis, depending on the relevant application.

Symbol: r_y

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Gyration about Minor Axis

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 Beams category

Go Maximum Laterally Unbraced Length for Plastic Analysis

L pd = r y \cdot \frac{3600 + 2200 \cdot (\frac{M 1}{M p})}{F yc}

Go Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams

L pd = \frac{r y \cdot (5000 + 3000 \cdot (\frac{M 1}{M p}))}{F y}

Go Plastic Moment

M p = F yw \cdot Z p

Go Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for I and Channel Sections

L p = \frac{300 \cdot r y}{\sqrt{F yf}}

How to Evaluate Critical Elastic Moment for Box Sections and Solid Bars?

Critical Elastic Moment for Box Sections and Solid Bars evaluator uses Critical Elastic Moment for Box Section = (57000*Moment Gradient Factor*sqrt(Torsional Constant*Cross Sectional Area in Steel Structures))/(Unbraced Length of Member/Radius of Gyration about Minor Axis) to evaluate the Critical Elastic Moment for Box Section, The Critical Elastic Moment for Box Sections and Solid Bars formula is defined as the maximum limit of the moment a box beam or solid bar can withstand, any further moment can make the beam or member in failure. It is the maximum moment a box-section beam can withstand before it reaches the elastic buckling stage. Elastic buckling is a condition where a structural member deforms significantly due to instability under compressive stresses, but the material has not yet yielded. Critical Elastic Moment for Box Section is denoted by M_bs symbol.

How to evaluate Critical Elastic Moment for Box Sections and Solid Bars using this online evaluator? To use this online evaluator for Critical Elastic Moment for Box Sections and Solid Bars, enter Moment Gradient Factor (C_b), Torsional Constant (J), Cross Sectional Area in Steel Structures (A), Unbraced Length of Member (L) & Radius of Gyration about Minor Axis (r_y) and hit the calculate button.

FAQs on Critical Elastic Moment for Box Sections and Solid Bars

What is the formula to find Critical Elastic Moment for Box Sections and Solid Bars?

The formula of Critical Elastic Moment for Box Sections and Solid Bars is expressed as Critical Elastic Moment for Box Section = (57000*Moment Gradient Factor*sqrt(Torsional Constant*Cross Sectional Area in Steel Structures))/(Unbraced Length of Member/Radius of Gyration about Minor Axis). Here is an example- 69.70946 = (57000*1.96*sqrt(21.9*0.0064))/(12/0.02).

How to calculate Critical Elastic Moment for Box Sections and Solid Bars?

With Moment Gradient Factor (C_b), Torsional Constant (J), Cross Sectional Area in Steel Structures (A), Unbraced Length of Member (L) & Radius of Gyration about Minor Axis (r_y) we can find Critical Elastic Moment for Box Sections and Solid Bars using the formula - Critical Elastic Moment for Box Section = (57000*Moment Gradient Factor*sqrt(Torsional Constant*Cross Sectional Area in Steel Structures))/(Unbraced Length of Member/Radius of Gyration about Minor Axis). This formula also uses Square Root (sqrt) function(s).

Can the Critical Elastic Moment for Box Sections and Solid Bars be negative?

Yes, the Critical Elastic Moment for Box Sections and Solid Bars, measured in Moment of Force can be negative.

Which unit is used to measure Critical Elastic Moment for Box Sections and Solid Bars?

Critical Elastic Moment for Box Sections and Solid Bars is usually measured using the Newton Meter[N*m] for Moment of Force. Kilonewton Meter[N*m], Millinewton Meter[N*m], Micronewton Meter[N*m] are the few other units in which Critical Elastic Moment for Box Sections and Solid Bars can be measured.

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Critical Elastic Moment for Box Sections and Solid Bars Formula

Critical Elastic Moment for Box Sections and Solid Bars Example

Critical Elastic Moment for Box Sections and Solid Bars Solution

Critical Elastic Moment for Box Sections and Solid Bars Formula Elements

Other formulas in Beams category

How to Evaluate Critical Elastic Moment for Box Sections and Solid Bars?

FAQs on Critical Elastic Moment for Box Sections and Solid Bars

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