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))
dBeam = sqrt((3*w*L)/(f*2*bBeam))
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
dBeam = sqrt((3*w*L)/(f*2*bBeam)) --> sqrt((3*50000*5)/(120000000*2*0.312))
Evaluating ... ...
dBeam = 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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The National Institute of Engineering (NIE), Mysuru
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Section Modulus for Various Shapes Calculators

Section Modulus of Hollow Rectangular Shape
​ LaTeX ​ 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)
Depth of Rectangular Shape given Section Modulus
​ LaTeX ​ Go Depth of Cross Section = sqrt((6*Section Modulus)/Width of Cross Section)
Breadth of Rectangular Shape given Section Modulus
​ LaTeX ​ Go Width of Cross Section = (6*Section Modulus)/Depth of Cross Section^2
Section Modulus of Rectangular Shape
​ LaTeX ​ Go Section Modulus = (Width of Cross Section*Depth of Cross Section^2)/6

Depth of Beam for Uniform Strength in Bending Stress Formula

​LaTeX ​Go
Depth of Beam = sqrt((3*Load on Beam*Length of Beam)/(Allowable Bending Stress*2*Width of Beam))
dBeam = sqrt((3*w*L)/(f*2*bBeam))

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 dBeam 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 (bBeam) 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 dBeam = sqrt((3*w*L)/(f*2*bBeam)) 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 (bBeam). 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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