Beam Width for Uniform Strength in Bending Stress Calculator

✖Load on Beam is the external force or weight applied to the beam, potentially causing deformation or stress.ⓘ Load on Beam [w]			+10% -10%
✖Length of Beam is the dimension that measures the span or extent along the longitudinal axis, from one end to another.ⓘ Length of Beam [L]			+10% -10%
✖Allowable Bending Stress is the maximum stress a material can endure without exceeding its elastic limit under bending deformation.ⓘ Allowable Bending Stress [f]			+10% -10%
✖Depth of Beam is the vertical measurement between its upper and lower surfaces, perpendicular to its length and width.ⓘ Depth of Beam [d_Beam]			+10% -10%

✖Width of Beam is the horizontal dimension between its opposite surfaces or edges, perpendicular to its depth and length.ⓘ Beam Width for Uniform Strength in Bending Stress [b_Beam]

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Formula

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Beam Width for Uniform Strength in Bending Stress

Formula

`"b"_{"Beam"} = 3*"w"*"L"/(2*"f"*"d"_{"Beam"}^2)`

Example

`"312.5mm"=3*"50kN"*"5000mm"/(2*"120MPa"*("100mm")^2)`

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Beam Width for Uniform Strength in Bending Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Width of Beam = 3*Load on Beam*Length of Beam/(2*Allowable Bending Stress*Depth of Beam^2)
b_Beam = 3*w*L/(2*f*d_Beam^2)
This formula uses 5 Variables

Variables Used

Width of Beam - (Measured in Millimeter) - Width of Beam is the horizontal dimension between its opposite surfaces or edges, perpendicular to its depth and length.
Load on Beam - (Measured in Newton) - Load on Beam is the external force or weight applied to the beam, potentially causing deformation or stress.
Length of Beam - (Measured in Millimeter) - Length of Beam is the dimension that measures the span or extent along the longitudinal axis, from one end to another.
Allowable Bending Stress - (Measured in Megapascal) - Allowable Bending Stress is the maximum stress a material can endure without exceeding its elastic limit under bending deformation.
Depth of Beam - (Measured in Millimeter) - Depth of Beam is the vertical measurement between its upper and lower surfaces, perpendicular to its length and width.

STEP 1: Convert Input(s) to Base Unit

Load on Beam: 50 Kilonewton --> 50000 Newton (Check conversion here)
Length of Beam: 5000 Millimeter --> 5000 Millimeter No Conversion Required
Allowable Bending Stress: 120 Megapascal --> 120 Megapascal No Conversion Required
Depth of Beam: 100 Millimeter --> 100 Millimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

b_Beam = 3*w*L/(2*f*d_Beam^2) --> 3*50000*5000/(2*120*100^2)

Evaluating ... ...

b_Beam = 312.5

STEP 3: Convert Result to Output's Unit

0.3125 Meter -->312.5 Millimeter (Check conversion here)

FINAL ANSWER

312.5 Millimeter <-- Width of Beam

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Strength of Materials » Bending Stress » Section Modulus for Various Shapes » Beam Width for Uniform Strength in Bending Stress

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Created by Rachana B V

The National Institute of Engineering (NIE), Mysuru

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Gautam Buddha University (GBU), Greater Noida

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< 15 Section Modulus for Various Shapes Calculators

Inner Depth of Hollow Rectangular Shape

Go Inner Depth of Hollow Rectangular Section = (((6*Section Modulus*Outer Depth of Hollow Rectangular Section)+(Outer Breadth of Hollow Rectangular Section*Outer Depth of Hollow Rectangular Section^3))/(Inner Breadth of Hollow Rectangular Section))^(1/3)

Outer Breadth of Hollow Rectangular Shape

Go Outer Breadth of Hollow Rectangular Section = ((6*Section Modulus*Outer Depth of Hollow Rectangular Section)+(Inner Breadth of Hollow Rectangular Section*Inner Depth of Hollow Rectangular Section^3))/(Outer Depth of Hollow Rectangular Section^(3))

Section Modulus of Hollow Rectangular Shape

Go Section Modulus = ((Outer Breadth of Hollow Rectangular Section*Outer Depth of Hollow Rectangular Section^3)-(Inner Breadth of Hollow Rectangular Section*Inner Depth of Hollow Rectangular Section^3))/(6*Outer Depth of Hollow Rectangular Section)

Inner Breadth of Hollow Rectangular Shape

Go Inner Breadth of Hollow Rectangular Section = ((6*Section Modulus*Outer Depth of Hollow Rectangular Section)+(Outer Breadth of Hollow Rectangular Section*Outer Depth of Hollow Rectangular Section^3))/(Inner Depth of Hollow Rectangular Section^3)

Depth of Beam for Uniform Strength in Bending Stress

Go Depth of Beam = sqrt((3*Load on Beam*Length of Beam)/(Allowable Bending Stress*2*Width of Beam))

Inner Diameter of Hollow Circular Shape in Bending Stress

Go Inner Diameter of Shaft = ((Outer Diameter of Shaft^4)-(32*Section Modulus*Outer Diameter of Shaft/pi))^(1/4)

Section Modulus of Hollow Circular Shape

Go Section Modulus = (pi*(Outer Diameter of Shaft^4-Inner Diameter of Shaft^4))/(32*Outer Diameter of Shaft)

Load on Beam for Uniform Strength in Bending Stress

Go Load on Beam = (Allowable Bending Stress*(2*Width of Beam*Depth of Beam^2))/(3*Length of Beam)

Beam Width for Uniform Strength in Bending Stress

Go Width of Beam = 3*Load on Beam*Length of Beam/(2*Allowable Bending Stress*Depth of Beam^2)

Allowable Bending Stress

Go Allowable Bending Stress = 3*Load on Beam*Length of Beam/(2*Width of Beam*Depth of Beam^2)

Depth of Rectangular Shape given Section Modulus

Go Depth of Cross Section = sqrt((6*Section Modulus)/Width of Cross Section)

Breadth of Rectangular Shape given Section Modulus

Go Width of Cross Section = (6*Section Modulus)/Depth of Cross Section^2

Section Modulus of Rectangular Shape

Go Section Modulus = (Width of Cross Section*Depth of Cross Section^2)/6

Diameter of Circular Shape given Section Modulus

Go Diameter of Circular Shaft = ((32*Section Modulus)/pi)^(1/3)

Section Modulus of Circular Shape

Go Section Modulus = (pi*Diameter of Circular Shaft^3)/32

Beam Width for Uniform Strength in Bending Stress Formula

Width of Beam = 3*Load on Beam*Length of Beam/(2*Allowable Bending Stress*Depth of Beam^2)
b_Beam = 3*w*L/(2*f*d_Beam^2)

What is the purpose of calculating the Beam Width for Uniform Strength in Bending Stress?

The purpose is to determine the minimum width necessary to prevent uneven stress distribution and potential structural failure.

How to Calculate Beam Width for Uniform Strength in Bending Stress?

Beam Width for Uniform Strength in Bending Stress calculator uses Width of Beam = 3*Load on Beam*Length of Beam/(2*Allowable Bending Stress*Depth of Beam^2) to calculate the Width of Beam, The Beam Width for Uniform Strength in Bending Stress formula is defined as the required width ensuring consistent stress distribution under applied load. Width of Beam is denoted by b_Beam symbol.

How to calculate Beam Width for Uniform Strength in Bending Stress using this online calculator? To use this online calculator for Beam Width for Uniform Strength in Bending Stress, enter Load on Beam (w), Length of Beam (L), Allowable Bending Stress (f) & Depth of Beam (d_Beam) and hit the calculate button. Here is how the Beam Width for Uniform Strength in Bending Stress calculation can be explained with given input values -> 31250 = 3*50*5/(2*120000000*0.1^2).

FAQ

What is Beam Width for Uniform Strength in Bending Stress?

The Beam Width for Uniform Strength in Bending Stress formula is defined as the required width ensuring consistent stress distribution under applied load and is represented as b_Beam = 3*w*L/(2*f*d_Beam^2) or Width of Beam = 3*Load on Beam*Length of Beam/(2*Allowable Bending Stress*Depth of Beam^2). Load on Beam is the external force or weight applied to the beam, potentially causing deformation or stress, Length of Beam is the dimension that measures the span or extent along the longitudinal axis, from one end to another, Allowable Bending Stress is the maximum stress a material can endure without exceeding its elastic limit under bending deformation & Depth of Beam is the vertical measurement between its upper and lower surfaces, perpendicular to its length and width.

How to calculate Beam Width for Uniform Strength in Bending Stress?

The Beam Width for Uniform Strength in Bending Stress formula is defined as the required width ensuring consistent stress distribution under applied load is calculated using Width of Beam = 3*Load on Beam*Length of Beam/(2*Allowable Bending Stress*Depth of Beam^2). To calculate Beam Width for Uniform Strength in Bending Stress, you need Load on Beam (w), Length of Beam (L), Allowable Bending Stress (f) & Depth of Beam (d_Beam). With our tool, you need to enter the respective value for Load on Beam, Length of Beam, Allowable Bending Stress & Depth of Beam 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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