Maximum Shear Force in I Section Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
Fs = (𝜏max*I*b)/((B*(D^2-d^2))/8+(b*d^2)/8)
This formula uses 7 Variables
Variables Used
Shear Force on Beam - (Measured in Newton) - Shear Force on Beam is the force which causes shear deformation to occur in the shear plane.
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.
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
Maximum Shear Stress on Beam: 11 Megapascal --> 11000000 Pascal (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
Fs = (𝜏max*I*b)/((B*(D^2-d^2))/8+(b*d^2)/8) --> (11000000*0.00168*0.007)/((0.1*(9^2-0.45^2))/8+(0.007*0.45^2)/8)
Evaluating ... ...
Fs = 128.060704099995
STEP 3: Convert Result to Output's Unit
128.060704099995 Newton -->0.128060704099995 Kilonewton (Check conversion here)
FINAL ANSWER
0.128060704099995 0.128061 Kilonewton <-- Shear Force on Beam
(Calculation completed in 00.020 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 Force in I Section Formula

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)
Fs = (𝜏max*I*b)/((B*(D^2-d^2))/8+(b*d^2)/8)

What is shear force?

Shearing forces are unaligned forces pushing one part of a body in one specific direction, and another part of the body in the opposite direction.

How to Calculate Maximum Shear Force in I Section?

Maximum Shear Force in I Section calculator uses 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) to calculate the Shear Force on Beam, Maximum Shear Force in I Section is defined as a force applied perpendicular to a surface, in opposition to an offset force acting in the opposite direction. Shear Force on Beam is denoted by Fs symbol.

How to calculate Maximum Shear Force in I Section using this online calculator? To use this online calculator for Maximum Shear Force in I Section, enter Maximum Shear Stress on Beam (𝜏max), 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 Force in I Section calculation can be explained with given input values -> 0.000128 = (11000000*0.00168*0.007)/((0.1*(9^2-0.45^2))/8+(0.007*0.45^2)/8).

FAQ

What is Maximum Shear Force in I Section?
Maximum Shear Force in I Section is defined as a force applied perpendicular to a surface, in opposition to an offset force acting in the opposite direction and is represented as Fs = (𝜏max*I*b)/((B*(D^2-d^2))/8+(b*d^2)/8) or 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). Maximum Shear Stress on Beam that acts coplanar with a cross-section of material arises due to shear forces, 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 Force in I Section?
Maximum Shear Force in I Section is defined as a force applied perpendicular to a surface, in opposition to an offset force acting in the opposite direction is calculated using 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). To calculate Maximum Shear Force in I Section, you need Maximum Shear Stress on Beam (𝜏max), 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 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 & 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.
How many ways are there to calculate Shear Force on Beam?
In this formula, Shear Force on Beam uses 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 & Inner Depth of I Section. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • 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))
  • 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))
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