Beam Depth for Extreme Fiber Stress in Rectangular Timber Beam Calculator

✖Bending moment is the sum of the moments of that section of all external forces acting on one side of that section.ⓘ Bending Moment [M]			+10% -10%
✖Maximum Fiber Stress can be described as the Maximum tensile or compressive stress in a homogeneous flexure or torsion test specimen. maximum fiber stress occurs at mid-span.ⓘ Maximum Fiber Stress [f_s]			+10% -10%
✖The width of beam is the beam width from edge to edge.ⓘ Width of Beam [b]			+10% -10%

✖Depth of beam is the vertical distance between the uppermost deck and the bottom of the keel, measured at the middle of the overall length.ⓘ Beam Depth for Extreme Fiber Stress in Rectangular Timber Beam [h]

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Formula

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Beam Depth for Extreme Fiber Stress in Rectangular Timber Beam

Formula

`"h" = sqrt((6*"M")/("f"_{"s"}*"b"))`

Example

`"199.92mm"= sqrt((6*"2500N*m")/("2.78MPa"*"135mm"))`

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Beam Depth for Extreme Fiber Stress in Rectangular Timber Beam Solution

STEP 0: Pre-Calculation Summary

Formula Used

Depth of Beam = sqrt((6*Bending Moment)/(Maximum Fiber Stress*Width of Beam))
h = sqrt((6*M)/(f_s*b))
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

Depth of Beam - (Measured in Meter) - Depth of beam is the vertical distance between the uppermost deck and the bottom of the keel, measured at the middle of the overall length.
Bending Moment - (Measured in Newton Meter) - Bending moment is the sum of the moments of that section of all external forces acting on one side of that section.
Maximum Fiber Stress - (Measured in Pascal) - Maximum Fiber Stress can be described as the Maximum tensile or compressive stress in a homogeneous flexure or torsion test specimen. maximum fiber stress occurs at mid-span.
Width of Beam - (Measured in Meter) - The width of beam is the beam width from edge to edge.

STEP 1: Convert Input(s) to Base Unit

Bending Moment: 2500 Newton Meter --> 2500 Newton Meter No Conversion Required
Maximum Fiber Stress: 2.78 Megapascal --> 2780000 Pascal (Check conversion here)
Width of Beam: 135 Millimeter --> 0.135 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = sqrt((6*M)/(f_s*b)) --> sqrt((6*2500)/(2780000*0.135))

Evaluating ... ...

h = 0.199920047968022

STEP 3: Convert Result to Output's Unit

0.199920047968022 Meter -->199.920047968022 Millimeter (Check conversion here)

FINAL ANSWER

199.920047968022 ≈ 199.92 Millimeter <-- Depth of Beam

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Timber Engineering » Timber Beams and Columns » Beams » Beam Depth for Extreme Fiber Stress in Rectangular Timber Beam

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Created by M Naveen

National Institute of Technology (NIT), Warangal

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Coorg Institute of Technology (CIT), Coorg

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< 13 Beams Calculators

Modified Total End Shear for Concentrated Loads

Go Modified Total End Shear = (10*Concentrated Load*(Span of Beam-Distance from Reaction to Concentrated Load)*((Distance from Reaction to Concentrated Load/Depth of Beam)^2))/(9*Span of Beam*(2+(Distance from Reaction to Concentrated Load/Depth of Beam)^2))

Horizontal Shearing Stress in Rectangular Timber Beam given Notch in Lower Face

Go Horizontal Shearing Stress = ((3*Total Shear)/(2*Width of Beam*Depth of Beam above Notch))*(Depth of Beam/Depth of Beam above Notch)

Beam Depth for Extreme Fiber Stress in Rectangular Timber Beam

Go Depth of Beam = sqrt((6*Bending Moment)/(Maximum Fiber Stress*Width of Beam))

Modified Total End Shear for Uniform Loading

Go Modified Total End Shear = (Total Uniformly Distributed Load/2)*(1-((2*Depth of Beam)/Span of Beam))

Horizontal Shearing Stress in Rectangular Timber Beam

Go Horizontal Shearing Stress = (3*Total Shear)/(2*Width of Beam*Depth of Beam)

Beam Depth given Horizontal Shearing Stress

Go Depth of Beam = (3*Total Shear)/(2*Width of Beam*Horizontal Shearing Stress)

Beam Width given Extreme Fiber Stress for Rectangular Timber Beam

Go Width of Beam = (6*Bending Moment)/(Maximum Fiber Stress*(Depth of Beam)^2)

Total Shear given Horizontal Shearing Stress

Go Total Shear = (2*Horizontal Shearing Stress*Depth of Beam*Width of Beam)/3

Beam Width given Horizontal Shearing Stress

Go Width of Beam = (3*Total Shear)/(2*Depth of Beam*Horizontal Shearing Stress)

Bending Moment using Extreme Fiber Stress for Rectangular Timber Beam

Go Bending Moment = (Maximum Fiber Stress*Width of Beam*(Depth of Beam)^2)/6

Extreme Fiber Stress in Bending for Rectangular Timber Beam

Go Maximum Fiber Stress = (6*Bending Moment)/(Width of Beam*Depth of Beam^2)

Extreme Fiber Stress for Rectangular Timber Beam given Section Modulus

Go Maximum Fiber Stress = Bending Moment/Section Modulus

Section Modulus given Height and Breadth of Section

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

Beam Depth for Extreme Fiber Stress in Rectangular Timber Beam Formula

Depth of Beam = sqrt((6*Bending Moment)/(Maximum Fiber Stress*Width of Beam))
h = sqrt((6*M)/(f_s*b))

What is Extreme Fiber Stress?

Extreme Fiber Stress can be defined as the stress per unit of area in an extreme fiber of a structural member subjected to bending.

What is Timber Beam?

Timber Beam, also known as Lumber is the raw wood material that is custom designed and machine cut into dimensional boards according to their width, thickness, and length. Timber Beam is predominantly used for the purpose of structural construction, and several other needs.

How to Calculate Beam Depth for Extreme Fiber Stress in Rectangular Timber Beam?

Beam Depth for Extreme Fiber Stress in Rectangular Timber Beam calculator uses Depth of Beam = sqrt((6*Bending Moment)/(Maximum Fiber Stress*Width of Beam)) to calculate the Depth of Beam, The Beam Depth for Extreme Fiber Stress in Rectangular Timber Beam is defined as the depth in an extreme fiber of a rectangular timber beam when subjected to bending. Depth of Beam is denoted by h symbol.

How to calculate Beam Depth for Extreme Fiber Stress in Rectangular Timber Beam using this online calculator? To use this online calculator for Beam Depth for Extreme Fiber Stress in Rectangular Timber Beam, enter Bending Moment (M), Maximum Fiber Stress (f_s) & Width of Beam (b) and hit the calculate button. Here is how the Beam Depth for Extreme Fiber Stress in Rectangular Timber Beam calculation can be explained with given input values -> 199920 = sqrt((6*2500)/(2780000*0.135)).

FAQ

What is Beam Depth for Extreme Fiber Stress in Rectangular Timber Beam?

The Beam Depth for Extreme Fiber Stress in Rectangular Timber Beam is defined as the depth in an extreme fiber of a rectangular timber beam when subjected to bending and is represented as h = sqrt((6*M)/(f_s*b)) or Depth of Beam = sqrt((6*Bending Moment)/(Maximum Fiber Stress*Width of Beam)). Bending moment is the sum of the moments of that section of all external forces acting on one side of that section, Maximum Fiber Stress can be described as the Maximum tensile or compressive stress in a homogeneous flexure or torsion test specimen. maximum fiber stress occurs at mid-span & The width of beam is the beam width from edge to edge.

How to calculate Beam Depth for Extreme Fiber Stress in Rectangular Timber Beam?

The Beam Depth for Extreme Fiber Stress in Rectangular Timber Beam is defined as the depth in an extreme fiber of a rectangular timber beam when subjected to bending is calculated using Depth of Beam = sqrt((6*Bending Moment)/(Maximum Fiber Stress*Width of Beam)). To calculate Beam Depth for Extreme Fiber Stress in Rectangular Timber Beam, you need Bending Moment (M), Maximum Fiber Stress (f_s) & Width of Beam (b). With our tool, you need to enter the respective value for Bending Moment, Maximum Fiber 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.

How many ways are there to calculate Depth of Beam?

In this formula, Depth of Beam uses Bending Moment, Maximum Fiber Stress & Width of Beam. We can use 1 other way(s) to calculate the same, which is/are as follows -

Depth of Beam = (3*Total Shear)/(2*Width of Beam*Horizontal Shearing Stress)

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