Maximum Shear Stress in I Section Calculator

✖Shear Force on Beam is the force which causes shear deformation to occur in the shear plane.ⓘ Shear Force on Beam [F_s]			+10% -10%
✖Moment of Inertia of Area of Section is the second moment of the area of the section about the neutral axis.ⓘ Moment of Inertia of Area of Section [I]			+10% -10%
✖Thickness of Beam Web is the thickness of the vertical piece that connects the two flanges.ⓘ Thickness of Beam Web [b]			+10% -10%
✖Width of Beam Section is the width of the rectangular cross-section of the beam parallel to the axis in consideration.ⓘ Width of Beam Section [B]			+10% -10%
✖The Outer Depth of I section is a measure of distance, the distance between the outer bars of the I-section.ⓘ Outer Depth of I section [D]			+10% -10%
✖Inner Depth of I Section is a measure of distance, the distance between the inner bars of the I-section.ⓘ Inner Depth of I Section [d]			+10% -10%

✖Maximum Shear Stress on Beam that acts coplanar with a cross-section of material arises due to shear forces.ⓘ Maximum Shear Stress in I Section [𝜏_max]

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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)
𝜏_max = F_s/(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

𝜏_max = F_s/(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 ... ...

𝜏_max = 412304464.285714

STEP 3: Convert Result to Output's Unit

412304464.285714 Pascal -->412.304464285714 Megapascal (Check conversion here)

FINAL ANSWER

412.304464285714 ≈ 412.3045 Megapascal <-- Maximum Shear Stress on Beam

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< Shear Stress Distribution in Web Calculators

Moment of Inertia of Section given Shear Stress at Junction of Top of Web

LaTeX 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

LaTeX 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

LaTeX 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 Force at Junction of Top of Web

LaTeX 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))

Maximum Shear Stress in I Section Formula

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What is Shear Stress?

Shear stress is a type of stress that acts parallel or tangential to the surface of a material, as opposed to normal stress, which acts perpendicular to the surface. It occurs when a force is applied that tends to cause different parts of a material to slide or move parallel to each other in opposite directions.

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 measure of the maximum stress that occurs at the cross-section of an I-shaped beam when it is subjected to shear force, providing a critical value for structural engineers to ensure the beam's integrity and safety. Maximum Shear Stress on Beam is denoted by 𝜏_max 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 (F_s), 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 measure of the maximum stress that occurs at the cross-section of an I-shaped beam when it is subjected to shear force, providing a critical value for structural engineers to ensure the beam's integrity and safety and is represented as 𝜏_max = F_s/(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 measure of the maximum stress that occurs at the cross-section of an I-shaped beam when it is subjected to shear force, providing a critical value for structural engineers to ensure the beam's integrity and safety 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 (F_s), 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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