Width of Beam at Considered Level given Shear Stress for Circular Section Solution

STEP 0: Pre-Calculation Summary
Formula Used
Width of Beam Section = (Shear Force on Beam*2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))/(Moment of Inertia of Area of Section*Shear Stress in Beam)
B = (Fs*2/3*(R^2-y^2)^(3/2))/(I*𝜏beam)
This formula uses 6 Variables
Variables Used
Width of Beam Section - (Measured in Meter) - Width of Beam Section is the width of the rectangular cross-section of the beam parallel to the axis in consideration.
Shear Force on Beam - (Measured in Newton) - Shear Force on Beam is the force which causes shear deformation to occur in the shear plane.
Radius of Circular Section - (Measured in Meter) - The Radius of Circular Section is the distance from center of circle to the the circle.
Distance from Neutral Axis - (Measured in Meter) - Distance from Neutral Axis is the distance of the considered layer from the neutral layer.
Moment of Inertia of Area of Section - (Measured in Meter⁴) - Moment of Inertia of Area of Section is the second moment of the area of the section about the neutral axis.
Shear Stress in Beam - (Measured in Pascal) - Shear Stress in Beam is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.
STEP 1: Convert Input(s) to Base Unit
Shear Force on Beam: 4.8 Kilonewton --> 4800 Newton (Check conversion here)
Radius of Circular Section: 1200 Millimeter --> 1.2 Meter (Check conversion here)
Distance from Neutral Axis: 5 Millimeter --> 0.005 Meter (Check conversion here)
Moment of Inertia of Area of Section: 0.00168 Meter⁴ --> 0.00168 Meter⁴ No Conversion Required
Shear Stress in Beam: 6 Megapascal --> 6000000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
B = (Fs*2/3*(R^2-y^2)^(3/2))/(I*𝜏beam) --> (4800*2/3*(1.2^2-0.005^2)^(3/2))/(0.00168*6000000)
Evaluating ... ...
B = 0.548557142919147
STEP 3: Convert Result to Output's Unit
0.548557142919147 Meter -->548.557142919147 Millimeter (Check conversion here)
FINAL ANSWER
548.557142919147 548.5571 Millimeter <-- Width of Beam Section
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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5 Shear Stress in Circular Section Calculators

Shear Stress Distribution for Circular Section
Go Maximum Shear Stress on Beam = (Shear Force on Beam*2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))/(Moment of Inertia of Area of Section*Width of Beam Section)
Width of Beam at Considered Level given Shear Stress for Circular Section
Go Width of Beam Section = (Shear Force on Beam*2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))/(Moment of Inertia of Area of Section*Shear Stress in Beam)
Shear Force in Circular Section
Go Shear Force on Beam = (Shear Stress in Beam*Moment of Inertia of Area of Section*Width of Beam Section)/(2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))
Shear Force using Maximum Shear Stress
Go Shear Force on Beam = (3*Moment of Inertia of Area of Section*Maximum Shear Stress on Beam)/Radius of Circular Section^2
Width of Beam at Considered Level given Radius of Circular Section
Go Width of Beam Section = 2*sqrt(Radius of Circular Section^2-Distance from Neutral Axis^2)

Width of Beam at Considered Level given Shear Stress for Circular Section Formula

Width of Beam Section = (Shear Force on Beam*2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))/(Moment of Inertia of Area of Section*Shear Stress in Beam)
B = (Fs*2/3*(R^2-y^2)^(3/2))/(I*𝜏beam)

What is shear stress and strain?

When a force acts parallel to the surface of an object, it exerts a shear stress. Let's consider a rod under uniaxial tension. The rod elongates under this tension to a new length, and the normal strain is a ratio of this small deformation to the rod's original length.

How to Calculate Width of Beam at Considered Level given Shear Stress for Circular Section?

Width of Beam at Considered Level given Shear Stress for Circular Section calculator uses Width of Beam Section = (Shear Force on Beam*2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))/(Moment of Inertia of Area of Section*Shear Stress in Beam) to calculate the Width of Beam Section, The Width of beam at considered level given Shear stress for circular section formula is defined as how wide the beam is. Width of Beam Section is denoted by B symbol.

How to calculate Width of Beam at Considered Level given Shear Stress for Circular Section using this online calculator? To use this online calculator for Width of Beam at Considered Level given Shear Stress for Circular Section, enter Shear Force on Beam (Fs), Radius of Circular Section (R), Distance from Neutral Axis (y), Moment of Inertia of Area of Section (I) & Shear Stress in Beam (𝜏beam) and hit the calculate button. Here is how the Width of Beam at Considered Level given Shear Stress for Circular Section calculation can be explained with given input values -> 548557.1 = (4800*2/3*(1.2^2-0.005^2)^(3/2))/(0.00168*6000000).

FAQ

What is Width of Beam at Considered Level given Shear Stress for Circular Section?
The Width of beam at considered level given Shear stress for circular section formula is defined as how wide the beam is and is represented as B = (Fs*2/3*(R^2-y^2)^(3/2))/(I*𝜏beam) or Width of Beam Section = (Shear Force on Beam*2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))/(Moment of Inertia of Area of Section*Shear Stress in Beam). Shear Force on Beam is the force which causes shear deformation to occur in the shear plane, The Radius of Circular Section is the distance from center of circle to the the circle, Distance from Neutral Axis is the distance of the considered layer from the neutral layer, Moment of Inertia of Area of Section is the second moment of the area of the section about the neutral axis & Shear Stress in Beam is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.
How to calculate Width of Beam at Considered Level given Shear Stress for Circular Section?
The Width of beam at considered level given Shear stress for circular section formula is defined as how wide the beam is is calculated using Width of Beam Section = (Shear Force on Beam*2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))/(Moment of Inertia of Area of Section*Shear Stress in Beam). To calculate Width of Beam at Considered Level given Shear Stress for Circular Section, you need Shear Force on Beam (Fs), Radius of Circular Section (R), Distance from Neutral Axis (y), Moment of Inertia of Area of Section (I) & Shear Stress in Beam (𝜏beam). With our tool, you need to enter the respective value for Shear Force on Beam, Radius of Circular Section, Distance from Neutral Axis, Moment of Inertia of Area of Section & Shear Stress in 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 Width of Beam Section?
In this formula, Width of Beam Section uses Shear Force on Beam, Radius of Circular Section, Distance from Neutral Axis, Moment of Inertia of Area of Section & Shear Stress in Beam. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Width of Beam Section = 2*sqrt(Radius of Circular Section^2-Distance from Neutral Axis^2)
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