Maximum Shear Stress in I Section Solution

STEP 0: Pre-Calculation Summary
Formula Used
Maximum Shear Stress on Beam = Shear Force on Beam/(Moment of Inertia of Area of Section*Thickness of Beam Web)*((Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/8+(Thickness of Beam Web*Inner Depth of I Section^2)/8)
𝜏max = Fs/(I*b)*((B*(D^2-d^2))/8+(b*d^2)/8)
This formula uses 7 Variables
Variables Used
Maximum Shear Stress on Beam - (Measured in Pascal) - Maximum Shear Stress on Beam that acts coplanar with a cross-section of material arises due to shear forces.
Shear Force on Beam - (Measured in Newton) - Shear Force on Beam is the force which causes shear deformation to occur in the shear plane.
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.
Thickness of Beam Web - (Measured in Meter) - Thickness of Beam Web is the thickness of the vertical piece that connects the two flanges.
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.
Outer Depth of I section - (Measured in Meter) - The Outer Depth of I section is a measure of distance, the distance between the outer bars of the I-section.
Inner Depth of I Section - (Measured in Meter) - Inner Depth of I Section is a measure of distance, the distance between the inner bars of the I-section.
STEP 1: Convert Input(s) to Base Unit
Shear Force on Beam: 4.8 Kilonewton --> 4800 Newton (Check conversion here)
Moment of Inertia of Area of Section: 0.00168 Meter⁴ --> 0.00168 Meter⁴ No Conversion Required
Thickness of Beam Web: 7 Millimeter --> 0.007 Meter (Check conversion here)
Width of Beam Section: 100 Millimeter --> 0.1 Meter (Check conversion here)
Outer Depth of I section: 9000 Millimeter --> 9 Meter (Check conversion here)
Inner Depth of I Section: 450 Millimeter --> 0.45 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
𝜏max = Fs/(I*b)*((B*(D^2-d^2))/8+(b*d^2)/8) --> 4800/(0.00168*0.007)*((0.1*(9^2-0.45^2))/8+(0.007*0.45^2)/8)
Evaluating ... ...
𝜏max = 412304464.285714
STEP 3: Convert Result to Output's Unit
412304464.285714 Pascal -->412.304464285714 Megapascal (Check conversion here)
FINAL ANSWER
412.304464285714 β‰ˆ 412.3045 Megapascal <-- Maximum Shear Stress on Beam
(Calculation completed in 00.008 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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Indian Institute of Information Technology (IIIT), Guwahati
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18 Shear Stress Distribution in Web Calculators

Shear Force in Web
Go Shear Force on Beam = (Moment of Inertia of Area of Section*Thickness of Beam Web*Shear Stress in Beam)/((Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/8+Thickness of Beam Web/2*(Inner Depth of I Section^2/4-Distance from Neutral Axis^2))
Moment of Inertia of I-Section given Shear Stress of Web
Go Moment of Inertia of Area of Section = Shear Force on Beam/(Shear Stress in Beam*Thickness of Beam Web)*(Width of Beam Section/8*(Outer Depth of I section^2-Inner Depth of I Section^2)+Thickness of Beam Web/2*(Inner Depth of I Section^2/4-Distance from Neutral Axis^2))
Shear Stress in Web
Go Shear Stress in Beam = Shear Force on Beam/(Moment of Inertia of Area of Section*Thickness of Beam Web)*(Width of Beam Section/8*(Outer Depth of I section^2-Inner Depth of I Section^2)+Thickness of Beam Web/2*(Inner Depth of I Section^2/4-Distance from Neutral Axis^2))
Thickness of Web given Shear Stress of Web
Go Thickness of Beam Web = (Shear Force on Beam*Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/(8* Moment of Inertia of Area of Section*Shear Stress in Beam-Shear Force on Beam*(Inner Depth of I Section^2-4*Distance from Neutral Axis^2))
Maximum Shear Stress in I Section
Go Maximum Shear Stress on Beam = Shear Force on Beam/(Moment of Inertia of Area of Section*Thickness of Beam Web)*((Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/8+(Thickness of Beam Web*Inner Depth of I Section^2)/8)
Maximum Shear Force in I Section
Go Shear Force on Beam = (Maximum Shear Stress on Beam*Moment of Inertia of Area of Section*Thickness of Beam Web)/((Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/8+(Thickness of Beam Web*Inner Depth of I Section^2)/8)
Moment of Inertia of I-Section given Maximum Shear Stress and Force
Go Moment of Inertia of Area of Section = Shear Force on Beam/(Shear Stress in Beam*Thickness of Beam Web)*((Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/8+(Thickness of Beam Web*Inner Depth of I Section^2)/8)
Thickness of Web given Maximum Shear Stress and Force
Go Thickness of Beam Web = (Width of Beam Section*Shear Force on Beam*(Outer Depth of I section^2-Inner Depth of I Section^2))/(8* Moment of Inertia of Area of Section*Shear Stress in Beam-Shear Force on Beam*Inner Depth of I Section^2)
Moment of Inertia of Section given Shear Stress at Junction of Top of Web
Go Moment of Inertia of Area of Section = (Shear Force on Beam*Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/(8*Shear Stress in Beam*Thickness of Beam Web)
Thickness of Web given Shear Stress at Junction of Top of Web
Go Thickness of Beam Web = (Shear Force on Beam*Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/(8*Moment of Inertia of Area of Section*Shear Stress in Beam)
Width of Section given Shear Stress at Junction of Top of Web
Go Width of Beam Section = (Shear Stress in Beam*8*Moment of Inertia of Area of Section*Thickness of Beam Web)/(Shear Force on Beam*(Outer Depth of I section^2-Inner Depth of I Section^2))
Shear Stress at Junction of Top of Web
Go Shear Stress in Beam = (Shear Force on Beam*Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/(8*Moment of Inertia of Area of Section*Thickness of Beam Web)
Shear Force at Junction of Top of Web
Go Shear Force on Beam = (8*Moment of Inertia of Area of Section*Thickness of Beam Web*Shear Stress in Beam)/(Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))
Thickness of Web
Go Thickness of Beam Web = (2*Moment of Inertia of Area of Section)/((Inner Depth of I Section^2)/4-Distance from Neutral Axis^2)
Moment of Shaded Area of Web about Neutral Axis
Go Moment of Inertia of Area of Section = Thickness of Beam Web/2*(Inner Depth of I Section^2/4-Distance from Neutral Axis^2)
Width of Section given Moment of Flange Area about Neutral Axis
Go Width of Beam Section = (8*Moment of Inertia of Area of Section)/(Outer Depth of I section^2-Inner Depth of I Section^2)
Moment of Flange Area about Neutral Axis
Go Moment of Inertia of Area of Section = (Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/8
Distance of Considered Level from Neutral Axis at Junction of Top of Web
Go Distance from Neutral Axis = Inner Depth of I Section/2

Maximum Shear Stress in I Section Formula

Maximum Shear Stress on Beam = Shear Force on Beam/(Moment of Inertia of Area of Section*Thickness of Beam Web)*((Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/8+(Thickness of Beam Web*Inner Depth of I Section^2)/8)
𝜏max = Fs/(I*b)*((B*(D^2-d^2))/8+(b*d^2)/8)

Why shear stress is maximum at neutral axis?

The maximum shear stress is located at the neutral axis. As the point moves further from the neutral axis, the value of the shear stress is reduced until it reaches zero at both extremes. On the other hand, if the member is subjected to an axial load, shear stress varies with rotating the element.

How to Calculate Maximum Shear Stress in I Section?

Maximum Shear Stress in I Section calculator uses Maximum Shear Stress on Beam = Shear Force on Beam/(Moment of Inertia of Area of Section*Thickness of Beam Web)*((Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/8+(Thickness of Beam Web*Inner Depth of I Section^2)/8) to calculate the Maximum Shear Stress on Beam, The Maximum Shear Stress in I Section formula is defined as a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. Maximum Shear Stress on Beam is denoted by 𝜏max symbol.

How to calculate Maximum Shear Stress in I Section using this online calculator? To use this online calculator for Maximum Shear Stress in I Section, enter Shear Force on Beam (Fs), Moment of Inertia of Area of Section (I), Thickness of Beam Web (b), Width of Beam Section (B), Outer Depth of I section (D) & Inner Depth of I Section (d) and hit the calculate button. Here is how the Maximum Shear Stress in I Section calculation can be explained with given input values -> 0.000412 = 4800/(0.00168*0.007)*((0.1*(9^2-0.45^2))/8+(0.007*0.45^2)/8).

FAQ

What is Maximum Shear Stress in I Section?
The Maximum Shear Stress in I Section formula is defined as a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress and is represented as 𝜏max = Fs/(I*b)*((B*(D^2-d^2))/8+(b*d^2)/8) or Maximum Shear Stress on Beam = Shear Force on Beam/(Moment of Inertia of Area of Section*Thickness of Beam Web)*((Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/8+(Thickness of Beam Web*Inner Depth of I Section^2)/8). Shear Force on Beam is the force which causes shear deformation to occur in the shear plane, Moment of Inertia of Area of Section is the second moment of the area of the section about the neutral axis, Thickness of Beam Web is the thickness of the vertical piece that connects the two flanges, Width of Beam Section is the width of the rectangular cross-section of the beam parallel to the axis in consideration, The Outer Depth of I section is a measure of distance, the distance between the outer bars of the I-section & Inner Depth of I Section is a measure of distance, the distance between the inner bars of the I-section.
How to calculate Maximum Shear Stress in I Section?
The Maximum Shear Stress in I Section formula is defined as a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress is calculated using Maximum Shear Stress on Beam = Shear Force on Beam/(Moment of Inertia of Area of Section*Thickness of Beam Web)*((Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/8+(Thickness of Beam Web*Inner Depth of I Section^2)/8). To calculate Maximum Shear Stress in I Section, you need Shear Force on Beam (Fs), Moment of Inertia of Area of Section (I), Thickness of Beam Web (b), Width of Beam Section (B), Outer Depth of I section (D) & Inner Depth of I Section (d). With our tool, you need to enter the respective value for Shear Force on Beam, Moment of Inertia of Area of Section, Thickness of Beam Web, Width of Beam Section, Outer Depth of I section & Inner Depth of I Section 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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