Depth of Beam 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%
✖Width of Beam is the horizontal dimension between its opposite surfaces or edges, perpendicular to its depth and length.ⓘ Width of Beam [b_Beam]			+10% -10%

✖Depth of Beam is the vertical measurement between its upper and lower surfaces, perpendicular to its length and width.ⓘ Depth of Beam for Uniform Strength in Bending Stress [d_Beam]

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Formula

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Depth of Beam for Uniform Strength in Bending Stress

Formula

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

Example

`"100.0801mm"=sqrt((3*"50kN"*"5000mm")/("120MPa"*2*"312mm"))`

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Depth of Beam for Uniform Strength in Bending Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Depth of Beam = sqrt((3*Load on Beam*Length of Beam)/(Allowable Bending Stress*2*Width of Beam))
d_Beam = sqrt((3*w*L)/(f*2*b_Beam))
This formula uses 1 Functions, 5 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

Depth of Beam - (Measured in Meter) - Depth of Beam is the vertical measurement between its upper and lower surfaces, perpendicular to its length and width.
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 Meter) - 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 Pascal) - Allowable Bending Stress is the maximum stress a material can endure without exceeding its elastic limit under bending deformation.
Width of Beam - (Measured in Meter) - Width of Beam is the horizontal dimension between its opposite surfaces or edges, perpendicular to its depth and length.

STEP 1: Convert Input(s) to Base Unit

Load on Beam: 50 Kilonewton --> 50000 Newton (Check conversion here)
Length of Beam: 5000 Millimeter --> 5 Meter (Check conversion here)
Allowable Bending Stress: 120 Megapascal --> 120000000 Pascal (Check conversion here)
Width of Beam: 312 Millimeter --> 0.312 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_Beam = sqrt((3*w*L)/(f*2*b_Beam)) --> sqrt((3*50000*5)/(120000000*2*0.312))

Evaluating ... ...

d_Beam = 0.100080096128179

STEP 3: Convert Result to Output's Unit

0.100080096128179 Meter -->100.080096128179 Millimeter (Check conversion here)

FINAL ANSWER

100.080096128179 ≈ 100.0801 Millimeter <-- Depth 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 » Depth of Beam 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

Depth of Beam for Uniform Strength in Bending Stress Formula

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

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 Depth of Beam for Uniform Strength in Bending Stress?

Depth of Beam for Uniform Strength in Bending Stress calculator uses Depth of Beam = sqrt((3*Load on Beam*Length of Beam)/(Allowable Bending Stress*2*Width of Beam)) to calculate the Depth of Beam, The Depth of Beam for Uniform Strength in Bending Stress formula is defined as the vertical dimension that ensures consistent stress distribution. Depth of Beam is denoted by d_Beam symbol.

How to calculate Depth of Beam for Uniform Strength in Bending Stress using this online calculator? To use this online calculator for Depth of Beam for Uniform Strength in Bending Stress, enter Load on Beam (w), Length of Beam (L), Allowable Bending Stress (f) & Width of Beam (b_Beam) and hit the calculate button. Here is how the Depth of Beam for Uniform Strength in Bending Stress calculation can be explained with given input values -> 100080.1 = sqrt((3*50000*5)/(120000000*2*0.312)).

FAQ

What is Depth of Beam for Uniform Strength in Bending Stress?

The Depth of Beam for Uniform Strength in Bending Stress formula is defined as the vertical dimension that ensures consistent stress distribution and is represented as d_Beam = sqrt((3*w*L)/(f*2*b_Beam)) or Depth of Beam = sqrt((3*Load on Beam*Length of Beam)/(Allowable Bending Stress*2*Width of Beam)). 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 & Width of Beam is the horizontal dimension between its opposite surfaces or edges, perpendicular to its depth and length.

How to calculate Depth of Beam for Uniform Strength in Bending Stress?

The Depth of Beam for Uniform Strength in Bending Stress formula is defined as the vertical dimension that ensures consistent stress distribution is calculated using Depth of Beam = sqrt((3*Load on Beam*Length of Beam)/(Allowable Bending Stress*2*Width of Beam)). To calculate Depth of Beam for Uniform Strength in Bending Stress, you need Load on Beam (w), Length of Beam (L), Allowable Bending Stress (f) & Width of Beam (b_Beam). With our tool, you need to enter the respective value for Load on Beam, Length of Beam, Allowable Bending Stress & Width 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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