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

GoMaximum Laterally Unbraced Length for Plastic Analysis 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 = \frac{r y \cdot (5000 + 3000 \cdot (\frac{M 1}{M p}))}{F y}

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_y - Yield Stress of Steel?

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

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Here is how the Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams equation looks like with Values.

Here is how the Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams equation looks like with Units.

Here is how the Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams equation looks like.

424 = \frac{20 \cdot (5000 + 3000 \cdot (\frac{100}{1000}))}{250}

424mm = \frac{20mm \cdot (5000 + 3000 \cdot (\frac{100N*mm}{1000N*mm}))}{250MPa}

424 = \frac{20 \cdot (5000 + 3000 \cdot (\frac{100}{1000}))}{250}

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

Follow our step by step solution on how to calculate Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

L pd = \frac{20mm \cdot (5000 + 3000 \cdot (\frac{100N*mm}{1000N*mm}))}{250MPa}

Next Step Convert Units

∴

L pd = \frac{0.02m \cdot (5000 + 3000 \cdot (\frac{0.1N*m}{1N*m}))}{250MPa}

Next Step Prepare to Evaluate

∴

L pd = \frac{0.02 \cdot (5000 + 3000 \cdot (\frac{0.1}{1}))}{250}

Next Step Evaluate

∴

L pd = 0.424m

LAST Step Convert to Output's Unit

∴

L pd = 424mm

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

Yield Stress of Steel

Yield Stress of Steel is the stress at which the material begins to deform plastically, meaning it will not return to its original shape when the applied force is removed.

Symbol: F_y

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Yield Stress of Steel

Other Formulas to find Laterally Unbraced Length for Plastic Analysis

Go Maximum Laterally Unbraced Length for Plastic Analysis

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

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 in Solid Bars and Box Beams?

Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams evaluator uses 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 to evaluate the Laterally Unbraced Length for Plastic Analysis, The Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams formula is defined as the limiting lateral unbraced length of beams which are boxed in shape and of solid bars when plastic hinges are present. Laterally Unbraced Length for Plastic Analysis is denoted by L_pd symbol.

How to evaluate Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams using this online evaluator? To use this online evaluator for Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams, enter Radius of Gyration about Minor Axis (r_y), Smaller Moments of Unbraced Beam (M₁), Plastic Moment (M_p) & Yield Stress of Steel (F_y) and hit the calculate button.

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

What is the formula to find Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams?

The formula of Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams is expressed as 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. Here is an example- 424000 = (0.02*(5000+3000*(0.1/1)))/250000000.

How to calculate Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams?

With Radius of Gyration about Minor Axis (r_y), Smaller Moments of Unbraced Beam (M₁), Plastic Moment (M_p) & Yield Stress of Steel (F_y) we can find Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams using the formula - 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.

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*(3600+2200*(Smaller Moments of Unbraced Beam/Plastic Moment))/(Minimum Yield Stress of Compression Flange)

Can the Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams be negative?

No, the Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams, measured in Length cannot be negative.

Which unit is used to measure Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams?

Maximum Laterally Unbraced Length for Plastic Analysis in Solid Bars and Box Beams 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 in Solid Bars and Box Beams can be measured.

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

​GoMaximum Laterally Unbraced Length for Plastic Analysis Formula

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

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

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

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

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GoMaximum Laterally Unbraced Length for Plastic Analysis Formula