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Maximum Laterally Unbraced Length for Plastic Analysis Formula

GoMaximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams Formula

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Laterally Unbraced Length for Plastic Analysis is the distance between two ends of a member which is prevented from movement and contain plastic hinges. Check FAQs

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

L_pd - Laterally Unbraced Length for Plastic Analysis?r_y - Radius of Gyration about Minor Axis?M₁ - Smaller Moments of Unbraced Beam?M_p - Plastic Moment?F_yc - Minimum Yield Stress of Compression Flange?

Maximum Laterally Unbraced Length for Plastic Analysis Example

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Here is how the Maximum Laterally Unbraced Length for Plastic Analysis equation looks like with Values.

Here is how the Maximum Laterally Unbraced Length for Plastic Analysis equation looks like with Units.

Here is how the Maximum Laterally Unbraced Length for Plastic Analysis equation looks like.

424.4444 = 20 \cdot \frac{3600 + 2200 \cdot (\frac{100}{1000})}{180}

424.4444mm = 20mm \cdot \frac{3600 + 2200 \cdot (\frac{100N*mm}{1000N*mm})}{180MPa}

424.4444 = 20 \cdot \frac{3600 + 2200 \cdot (\frac{100}{1000})}{180}

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Maximum Laterally Unbraced Length for Plastic Analysis Solution

Follow our step by step solution on how to calculate Maximum Laterally Unbraced Length for Plastic Analysis?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

L pd = 20mm \cdot \frac{3600 + 2200 \cdot (\frac{100N*mm}{1000N*mm})}{180MPa}

Next Step Convert Units

∴

L pd = 0.02m \cdot \frac{3600 + 2200 \cdot (\frac{0.1N*m}{1N*m})}{180MPa}

Next Step Prepare to Evaluate

∴

L pd = 0.02 \cdot \frac{3600 + 2200 \cdot (\frac{0.1}{1})}{180}

Next Step Evaluate

∴

L pd = 0.424444444444444m

Next Step Convert to Output's Unit

∴

L pd = 424.444444444444mm

LAST Step Rounding Answer

∴

L pd = 424.4444mm

Maximum Laterally Unbraced Length for Plastic Analysis Formula Elements

Variables

Laterally Unbraced Length for Plastic Analysis

Laterally Unbraced Length for Plastic Analysis is the distance between two ends of a member which is prevented from movement and contain plastic hinges.

Symbol: L_pd

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Laterally Unbraced Length for Plastic Analysis

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

Smaller Moments of Unbraced Beam

Smaller Moments of Unbraced Beam is the smallest moment in the ends of beams which is unbraced.

Symbol: M₁

Measurement: Moment of ForceUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Smaller Moments of Unbraced Beam

Plastic Moment

Plastic Moment is the moment at which the entire cross section has reached its yield stress.

Symbol: M_p

Measurement: Moment of ForceUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Plastic Moment

Minimum Yield Stress of Compression Flange

Minimum Yield Stress of Compression Flange is the yield stress that can be experienced by the compression flange which can at least cause plastic deformation.

Symbol: F_yc

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Minimum Yield Stress of Compression Flange

Other Formulas to find Laterally Unbraced Length for Plastic Analysis

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}

Other formulas in Beams category

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}}

Go Limiting Laterally Unbraced Length for Full Plastic Bending Capacity for Solid Bar and Box Beams

L p = \frac{3750 \cdot (\frac{r y}{M p})}{\sqrt{J \cdot A}}

Go Limiting Laterally Unbraced Length for Inelastic Lateral Buckling

L lim = (\frac{r y \cdot X 1}{F yw - F r}) \cdot \sqrt{1 + \sqrt{1 + (X 2 \cdot {F l}^{2})}}

How to Evaluate Maximum Laterally Unbraced Length for Plastic Analysis?

Maximum Laterally Unbraced Length for Plastic Analysis evaluator uses Laterally Unbraced Length for Plastic Analysis = Radius of Gyration about Minor Axis*(3600+2200*(Smaller Moments of Unbraced Beam/Plastic Moment))/(Minimum Yield Stress of Compression Flange) to evaluate the Laterally Unbraced Length for Plastic Analysis, The Maximum Laterally Unbraced Length for Plastic Analysis formula is defined as the maximum distance between lateral supports in a steel member (such as a beam) where the member can still be analyzed and designed using plastic analysis methods. Laterally Unbraced Length for Plastic Analysis is denoted by L_pd symbol.

How to evaluate Maximum Laterally Unbraced Length for Plastic Analysis using this online evaluator? To use this online evaluator for Maximum Laterally Unbraced Length for Plastic Analysis, enter Radius of Gyration about Minor Axis (r_y), Smaller Moments of Unbraced Beam (M₁), Plastic Moment (M_p) & Minimum Yield Stress of Compression Flange (F_yc) and hit the calculate button.

FAQs on Maximum Laterally Unbraced Length for Plastic Analysis

What is the formula to find Maximum Laterally Unbraced Length for Plastic Analysis?

The formula of Maximum Laterally Unbraced Length for Plastic Analysis is expressed as Laterally Unbraced Length for Plastic Analysis = Radius of Gyration about Minor Axis*(3600+2200*(Smaller Moments of Unbraced Beam/Plastic Moment))/(Minimum Yield Stress of Compression Flange). Here is an example- 424444.4 = 0.02*(3600+2200*(0.1/1))/(180000000).

How to calculate Maximum Laterally Unbraced Length for Plastic Analysis?

With Radius of Gyration about Minor Axis (r_y), Smaller Moments of Unbraced Beam (M₁), Plastic Moment (M_p) & Minimum Yield Stress of Compression Flange (F_yc) we can find Maximum Laterally Unbraced Length for Plastic Analysis using the formula - Laterally Unbraced Length for Plastic Analysis = Radius of Gyration about Minor Axis*(3600+2200*(Smaller Moments of Unbraced Beam/Plastic Moment))/(Minimum Yield Stress of Compression Flange).

What are the other ways to Calculate Laterally Unbraced Length for Plastic Analysis?

Here are the different ways to Calculate Laterally Unbraced Length for Plastic Analysis-

Laterally Unbraced Length for Plastic Analysis=(Radius of Gyration about Minor Axis*(5000+3000*(Smaller Moments of Unbraced Beam/Plastic Moment)))/Yield Stress of Steel

Can the Maximum Laterally Unbraced Length for Plastic Analysis be negative?

No, the Maximum Laterally Unbraced Length for Plastic Analysis, measured in Length cannot be negative.

Which unit is used to measure Maximum Laterally Unbraced Length for Plastic Analysis?

Maximum Laterally Unbraced Length for Plastic Analysis is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Maximum Laterally Unbraced Length for Plastic Analysis can be measured.

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Maximum Laterally Unbraced Length for Plastic Analysis Formula

​GoMaximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams Formula

Maximum Laterally Unbraced Length for Plastic Analysis Example

Maximum Laterally Unbraced Length for Plastic Analysis Solution

Maximum Laterally Unbraced Length for Plastic Analysis Formula Elements

Other Formulas to find Laterally Unbraced Length for Plastic Analysis

Other formulas in Beams category

How to Evaluate Maximum Laterally Unbraced Length for Plastic Analysis?

FAQs on Maximum Laterally Unbraced Length for Plastic Analysis

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GoMaximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams Formula