Slenderness Ratio for Beams Calculator

✖The effective length is given in terms of the unsupported length of the beam. Unsupported length is the distance between supports and adequate bracing is not installed elsewhere in the span.ⓘ Effective Length [L_e]			+10% -10%
✖Depth of Cross Section (Height), in (mm) defines the geometrical measure from head to foot or from base to top of the section considered.ⓘ Depth of Cross Section [d]			+10% -10%
✖Width of Cross Section defines the geometric measurement or extent of the member from side to side.ⓘ Width of Cross Section [w]			+10% -10%

✖Slenderness ratio, or simply slenderness is an aspect ratio, the quotient between the height and the width of a building.ⓘ Slenderness Ratio for Beams [R_B]

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Formula

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Slenderness Ratio for Beams

Formula

`"R"_{"B"} = sqrt(("L"_{"e"}*"d")/("w")^2)`

Example

`"13.52799"=sqrt(("2380mm"*"200mm")/("51mm")^2)`

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Slenderness Ratio for Beams Solution

STEP 0: Pre-Calculation Summary

Formula Used

Slenderness Ratio = sqrt((Effective Length*Depth of Cross Section)/(Width of Cross Section)^2)
R_B = sqrt((L_e*d)/(w)^2)
This formula uses 1 Functions, 4 Variables

Functions Used

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., sqrt(Number)

Variables Used

Slenderness Ratio - Slenderness ratio, or simply slenderness is an aspect ratio, the quotient between the height and the width of a building.
Effective Length - (Measured in Millimeter) - The effective length is given in terms of the unsupported length of the beam. Unsupported length is the distance between supports and adequate bracing is not installed elsewhere in the span.
Depth of Cross Section - (Measured in Millimeter) - Depth of Cross Section (Height), in (mm) defines the geometrical measure from head to foot or from base to top of the section considered.
Width of Cross Section - (Measured in Millimeter) - Width of Cross Section defines the geometric measurement or extent of the member from side to side.

STEP 1: Convert Input(s) to Base Unit

Effective Length: 2380 Millimeter --> 2380 Millimeter No Conversion Required
Depth of Cross Section: 200 Millimeter --> 200 Millimeter No Conversion Required
Width of Cross Section: 51 Millimeter --> 51 Millimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_B = sqrt((L_e*d)/(w)^2) --> sqrt((2380*200)/(51)^2)

Evaluating ... ...

R_B = 13.5279908318905

STEP 3: Convert Result to Output's Unit

13.5279908318905 --> No Conversion Required

FINAL ANSWER

13.5279908318905 ≈ 13.52799 <-- Slenderness Ratio

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Timber Engineering » Adjustment Factors for Design Values » Column Stability and Buckling Stiffness Factor » Slenderness Ratio for Beams

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Coorg Institute of Technology (CIT), Coorg

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< 2 Column Stability and Buckling Stiffness Factor Calculators

Buckling Stiffness Factor

Go Buckling Stiffness Factor = 1+((Stiffness Factor for Wood*Effective Length)/(Stiffness Factor for Lumber*Modulus of Elasticity))

Slenderness Ratio for Beams

Go Slenderness Ratio = sqrt((Effective Length*Depth of Cross Section)/(Width of Cross Section)^2)

Slenderness Ratio for Beams Formula

Slenderness Ratio = sqrt((Effective Length*Depth of Cross Section)/(Width of Cross Section)^2)
R_B = sqrt((L_e*d)/(w)^2)

What is Slenderness Ratio?

Slenderness is a measure of the propensity of a column to buckle in a structure. In architecture, the slenderness ratio, or simply slenderness is an aspect ratio, the quotient between the height and the width of a building.

What does High Slenderness Ratio mean?

A higher slenderness ratio means a lower critical stress that will cause buckling. Conversely, a lower slenderness ratio results in a higher critical stress (but still within the elastic range of the material). Column sections with large r-values are more resistant to buckling.

How to Calculate Slenderness Ratio for Beams?

Slenderness Ratio for Beams calculator uses Slenderness Ratio = sqrt((Effective Length*Depth of Cross Section)/(Width of Cross Section)^2) to calculate the Slenderness Ratio, The Slenderness Ratio for Beams formula is defined as the ratio of the length of a structural member (such as a column or beam) to its least radius of gyration. Slenderness Ratio is denoted by R_B symbol.

How to calculate Slenderness Ratio for Beams using this online calculator? To use this online calculator for Slenderness Ratio for Beams, enter Effective Length (L_e), Depth of Cross Section (d) & Width of Cross Section (w) and hit the calculate button. Here is how the Slenderness Ratio for Beams calculation can be explained with given input values -> 13.52799 = sqrt((2.38*0.2)/(0.051)^2).

FAQ

What is Slenderness Ratio for Beams?

The Slenderness Ratio for Beams formula is defined as the ratio of the length of a structural member (such as a column or beam) to its least radius of gyration and is represented as R_B = sqrt((L_e*d)/(w)^2) or Slenderness Ratio = sqrt((Effective Length*Depth of Cross Section)/(Width of Cross Section)^2). The effective length is given in terms of the unsupported length of the beam. Unsupported length is the distance between supports and adequate bracing is not installed elsewhere in the span, Depth of Cross Section (Height), in (mm) defines the geometrical measure from head to foot or from base to top of the section considered & Width of Cross Section defines the geometric measurement or extent of the member from side to side.

How to calculate Slenderness Ratio for Beams?

The Slenderness Ratio for Beams formula is defined as the ratio of the length of a structural member (such as a column or beam) to its least radius of gyration is calculated using Slenderness Ratio = sqrt((Effective Length*Depth of Cross Section)/(Width of Cross Section)^2). To calculate Slenderness Ratio for Beams, you need Effective Length (L_e), Depth of Cross Section (d) & Width of Cross Section (w). With our tool, you need to enter the respective value for Effective Length, Depth of Cross Section & Width of Cross Section and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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