Relative Slenderness of Web and Flange Calculator

✖Web Depth is the distance between the starting and end of the web ignoring the fillets at both sides.ⓘ Web Depth [d_c]			+10% -10%
✖Web Thickness is the thickness of the web section in the member of I section.ⓘ Web Thickness [t_w]			+10% -10%
✖Maximum Unbraced Length also known as the unsupported length, is the largest distance along a structural member between the brace points.ⓘ Maximum Unbraced Length [l_max]			+10% -10%
✖Width of Compression Flange is the portion of the slab that acts integrally with the beam and extends on either side of the beam forming the compression zone.ⓘ Width of Compression Flange [b_f]			+10% -10%

✖Slenderness of Web and Flange of a structural element is a measure of its susceptibility to buckling under compressive stress.ⓘ Relative Slenderness of Web and Flange [r_wf]

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Relative Slenderness of Web and Flange

Formula

`"r"_{"wf"} = ("d"_{"c"}/"t"_{"w"})/("l"_{"max"}/"b"_{"f"})`

Example

`"1.077564"=("46mm"/"100mm")/("1921mm"/"4500mm")`

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Relative Slenderness of Web and Flange Solution

STEP 0: Pre-Calculation Summary

Formula Used

Slenderness of Web and Flange = (Web Depth/Web Thickness)/(Maximum Unbraced Length/Width of Compression Flange)
r_wf = (d_c/t_w)/(l_max/b_f)
This formula uses 5 Variables

Variables Used

Slenderness of Web and Flange - Slenderness of Web and Flange of a structural element is a measure of its susceptibility to buckling under compressive stress.
Web Depth - (Measured in Meter) - Web Depth is the distance between the starting and end of the web ignoring the fillets at both sides.
Web Thickness - (Measured in Meter) - Web Thickness is the thickness of the web section in the member of I section.
Maximum Unbraced Length - (Measured in Meter) - Maximum Unbraced Length also known as the unsupported length, is the largest distance along a structural member between the brace points.
Width of Compression Flange - (Measured in Meter) - Width of Compression Flange is the portion of the slab that acts integrally with the beam and extends on either side of the beam forming the compression zone.

STEP 1: Convert Input(s) to Base Unit

Web Depth: 46 Millimeter --> 0.046 Meter (Check conversion here)
Web Thickness: 100 Millimeter --> 0.1 Meter (Check conversion here)
Maximum Unbraced Length: 1921 Millimeter --> 1.921 Meter (Check conversion here)
Width of Compression Flange: 4500 Millimeter --> 4.5 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_wf = (d_c/t_w)/(l_max/b_f) --> (0.046/0.1)/(1.921/4.5)

Evaluating ... ...

r_wf = 1.07756376887038

STEP 3: Convert Result to Output's Unit

1.07756376887038 --> No Conversion Required

FINAL ANSWER

1.07756376887038 ≈ 1.077564 <-- Slenderness of Web and Flange

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Design of Steel Structures » Webs under Concentrated Loads » Relative Slenderness of Web and Flange

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has created this Calculator and 500+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< 16 Webs under Concentrated Loads Calculators

Reaction of Concentrated Load applied at least Half of Depth of Beam

Go Concentrated Load of Reaction = 67.5*Web Thickness^2*(1+3*(Bearing or Plate Length/Depth of Section)*(Web Thickness/Flange Thickness)^1.5)*sqrt(Yield Stress of Steel/(Web Thickness/Flange Thickness))

Reaction of Concentrated Load when Applied at distance at least Half of Beam Depth

Go Concentrated Load of Reaction = 34*Web Thickness^2*(1+3*(Bearing or Plate Length/Depth of Section)*(Web Thickness/Flange Thickness)^1.5)*sqrt(Yield Stress of Steel/(Web Thickness/Flange Thickness))

Beam Depth for given Column Load

Go Depth of Section = (Bearing or Plate Length*(3*(Web Thickness/Flange Thickness)^1.5))/((Concentrated Load of Reaction/((67.5*Web Thickness^(3/2))*sqrt(Yield Stress of Steel*Flange Thickness))-1))

Length of Bearing for Applied Load at least Half of Depth of Beam

Go Bearing or Plate Length = (Concentrated Load of Reaction/((67.5*Web Thickness^(3/2))*sqrt(Yield Stress of Steel*Flange Thickness))-1)*Depth of Section/(3*(Web Thickness/Flange Thickness)^1.5)

Length of Bearing if Column Load is at Distance of Half Beam Depth

Go Bearing or Plate Length = (Concentrated Load of Reaction/((34*Web Thickness^(3/2))*sqrt(Yield Stress of Steel*Flange Thickness))-1)*Depth of Section/(3*(Web Thickness/Flange Thickness)^1.5)

Stress when Concentrated Load is Applied Close to Beam End

Go Compressive Stress = Concentrated Load of Reaction/(Web Thickness*(Bearing or Plate Length+2.5*Distance from Flange to Web Fillet))

Web Thickness for given Stress Due to Load near Beam End

Go Web Thickness = Concentrated Load of Reaction/(Compressive Stress*(Bearing or Plate Length+2.5*Distance from Flange to Web Fillet))

Stress for Concentrated Load Applied at Distance Larger than Depth of Beam

Go Compressive Stress = Concentrated Load of Reaction/(Web Thickness*(Bearing or Plate Length+5*Distance from Flange to Web Fillet))

Length of Bearing when Load applied at Distance Larger than Depth of Beam

Go Bearing or Plate Length = (Concentrated Load of Reaction/(Compressive Stress*Web Thickness))-5*Distance from Flange to Web Fillet

Web Thickness for Given Stress

Go Web Thickness = Concentrated Load of Reaction/(Compressive Stress*(Bearing or Plate Length+5*Distance from Flange to Web Fillet))

Reaction of Concentrated Load given Allowable Compressive Stress

Go Concentrated Load of Reaction = Compressive Stress*Web Thickness*(Bearing or Plate Length+5*Distance from Flange to Web Fillet)

Relative Slenderness of Web and Flange

Go Slenderness of Web and Flange = (Web Depth/Web Thickness)/(Maximum Unbraced Length/Width of Compression Flange)

Slenderness of Web and Flange given Stiffeners and Concentrated Load

Go Slenderness of Web and Flange = ((((Concentrated Load of Reaction*Clear Distance between Flanges)/(6800*Web Thickness^3))-1)/0.4)^(1/3)

Required Stiffeners if Concentrated Load exceeds Load of Reaction R

Go Concentrated Load of Reaction = ((6800*Web Thickness^3)/Clear Distance between Flanges)*(1+(0.4*Slenderness of Web and Flange^3))

Clear Distance from Flanges for Concentrated Load with Stiffeners

Go Clear Distance between Flanges = ((6800*Web Thickness^3)/Concentrated Load of Reaction)*(1+(0.4*Slenderness of Web and Flange^3))

Web Depth Clear of fillets

Go Web Depth = Depth of Section-2*Distance from Flange to Web Fillet

Relative Slenderness of Web and Flange Formula

Slenderness of Web and Flange = (Web Depth/Web Thickness)/(Maximum Unbraced Length/Width of Compression Flange)
r_wf = (d_c/t_w)/(l_max/b_f)

What are Flange and Web Slenderness?

Web slenderness and flange slenderness were varied from a fairly compact range to highly slender values. The optimized values for flange and web slenderness were determined for each unbraced length ratio and a relationship between unbraced length and optimum flange slenderness values was established.

What is Web Crippling?

Web Crippling is similar to web buckling, but it happens in the web of the beam when it's subjected to compressive stress. The reaction at support developed due to high concentrated point load on the beam leads to the development of high compressive stresses in the thin web close to the upper flange or lower flange. As a result of this, the thin web may develop a fold at a place close to the flange and this is called web crippling.

How to Calculate Relative Slenderness of Web and Flange?

Relative Slenderness of Web and Flange calculator uses Slenderness of Web and Flange = (Web Depth/Web Thickness)/(Maximum Unbraced Length/Width of Compression Flange) to calculate the Slenderness of Web and Flange, The Relative Slenderness of Web and Flange formula is defined as the ratio of slenderness of web and flange separately. The concentrated load limits depend on this value to decide whether web stiffeners are required or not, for the prevention of sideways web buckling. Slenderness of Web and Flange is denoted by r_wf symbol.

How to calculate Relative Slenderness of Web and Flange using this online calculator? To use this online calculator for Relative Slenderness of Web and Flange, enter Web Depth (d_c), Web Thickness (t_w), Maximum Unbraced Length (l_max) & Width of Compression Flange (b_f) and hit the calculate button. Here is how the Relative Slenderness of Web and Flange calculation can be explained with given input values -> 1.639771 = (0.046/0.1)/(1.921/4.5).

FAQ

What is Relative Slenderness of Web and Flange?

The Relative Slenderness of Web and Flange formula is defined as the ratio of slenderness of web and flange separately. The concentrated load limits depend on this value to decide whether web stiffeners are required or not, for the prevention of sideways web buckling and is represented as r_wf = (d_c/t_w)/(l_max/b_f) or Slenderness of Web and Flange = (Web Depth/Web Thickness)/(Maximum Unbraced Length/Width of Compression Flange). Web Depth is the distance between the starting and end of the web ignoring the fillets at both sides, Web Thickness is the thickness of the web section in the member of I section, Maximum Unbraced Length also known as the unsupported length, is the largest distance along a structural member between the brace points & Width of Compression Flange is the portion of the slab that acts integrally with the beam and extends on either side of the beam forming the compression zone.

How to calculate Relative Slenderness of Web and Flange?

The Relative Slenderness of Web and Flange formula is defined as the ratio of slenderness of web and flange separately. The concentrated load limits depend on this value to decide whether web stiffeners are required or not, for the prevention of sideways web buckling is calculated using Slenderness of Web and Flange = (Web Depth/Web Thickness)/(Maximum Unbraced Length/Width of Compression Flange). To calculate Relative Slenderness of Web and Flange, you need Web Depth (d_c), Web Thickness (t_w), Maximum Unbraced Length (l_max) & Width of Compression Flange (b_f). With our tool, you need to enter the respective value for Web Depth, Web Thickness, Maximum Unbraced Length & Width of Compression Flange and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Slenderness of Web and Flange?

In this formula, Slenderness of Web and Flange uses Web Depth, Web Thickness, Maximum Unbraced Length & Width of Compression Flange. We can use 1 other way(s) to calculate the same, which is/are as follows -

Slenderness of Web and Flange = ((((Concentrated Load of Reaction*Clear Distance between Flanges)/(6800*Web Thickness^3))-1)/0.4)^(1/3)

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