Shear Stress for Rectangular Section Solution

STEP 0: Pre-Calculation Summary
Formula Used
Shear Stress in Beam = Shear Force on Beam/(2*Moment of Inertia of Area of Section)*(Depth of Rectangular Section^2/4-Distance from Neutral Axis^2)
𝜏beam = Fs/(2*I)*(drec^2/4-y^2)
This formula uses 5 Variables
Variables Used
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.
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.
Depth of Rectangular Section - (Measured in Meter) - Depth of Rectangular Section is the distance from the top or surface to the bottom of the section.
Distance from Neutral Axis - (Measured in Meter) - Distance from Neutral Axis is the distance of the considered layer from the neutral layer.
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
Depth of Rectangular Section: 285 Millimeter --> 0.285 Meter (Check conversion here)
Distance from Neutral Axis: 5 Millimeter --> 0.005 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
𝜏beam = Fs/(2*I)*(drec^2/4-y^2) --> 4800/(2*0.00168)*(0.285^2/4-0.005^2)
Evaluating ... ...
𝜏beam = 28973.2142857143
STEP 3: Convert Result to Output's Unit
28973.2142857143 Pascal -->0.0289732142857143 Megapascal (Check conversion here)
FINAL ANSWER
0.0289732142857143 0.028973 Megapascal <-- Shear Stress in Beam
(Calculation completed in 00.020 seconds)

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National Institute Of Technology (NIT), Hamirpur
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Indian Institute of Information Technology (IIIT), Guwahati
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10+ Shear Stress in Rectangular Section Calculators

Moment of Inertia of Rectangular Section about Neutral Axis
Go Moment of Inertia of Area of Section = Shear Force on Beam/(2*Shear Stress in Beam)*(Depth of Rectangular Section^2/4-Distance from Neutral Axis^2)
Shear Stress for Rectangular Section
Go Shear Stress in Beam = Shear Force on Beam/(2*Moment of Inertia of Area of Section)*(Depth of Rectangular Section^2/4-Distance from Neutral Axis^2)
Shear Force for Rectangular Section
Go Shear Force on Beam = (2*Moment of Inertia of Area of Section*Shear Stress in Beam)/(Depth of Rectangular Section^2/4-Distance from Neutral Axis^2)
Average Shear Stress for Rectangular Section
Go Average Shear Stress on Beam = Shear Force on Beam/(Beam Width at Considered Level*Depth of Rectangular Section)
Shear Stress Variation across Neutral Axis for Rectangular Section
Go Shear Stress in Beam = 3/2*Shear Force on Beam/(Beam Width at Considered Level*Depth of Rectangular Section)
Shear Force Variation across Neutral Axis for Rectangular Section
Go Shear Force on Beam = 2/3*Shear Stress in Beam*Beam Width at Considered Level*Depth of Rectangular Section
Distance of C.G of Area (above Considered Level) from Neutral Axis for Rectangular Section
Go Distance of CG of Area from NA = 1/2*(Distance from Neutral Axis+Depth of Rectangular Section/2)
Distance of Considered Level from Neutral Axis for Rectangular Section
Go Distance from Neutral Axis = 2*(Distance of CG of Area from NA-Depth of Rectangular Section/4)
Average Shear Stress given Maximum Shear Stress for Rectangular Section
Go Average Shear Stress on Beam = 2/3*Maximum Shear Stress on Beam
Maximum Shear Stress for Rectangular Section
Go Maximum Shear Stress on Beam = 3/2*Average Shear Stress on Beam

Shear Stress for Rectangular Section Formula

Shear Stress in Beam = Shear Force on Beam/(2*Moment of Inertia of Area of Section)*(Depth of Rectangular Section^2/4-Distance from Neutral Axis^2)
𝜏beam = Fs/(2*I)*(drec^2/4-y^2)

In which section maximum shear stress position is not at the neutral axis of section?

Nevertheless, the maximum shear stress does not always occur at the neutral axis. For instance, in the case of a cross section having nonparallel sides, such as a triangular section, the maximum value of Q/b (and thus τxy) occurs at mid height, h/2, while the neutral axis is located at a distance h/3 from the base.

How to Calculate Shear Stress for Rectangular Section?

Shear Stress for Rectangular Section calculator uses Shear Stress in Beam = Shear Force on Beam/(2*Moment of Inertia of Area of Section)*(Depth of Rectangular Section^2/4-Distance from Neutral Axis^2) to calculate the Shear Stress in Beam, The Shear stress for rectangular section formula is defined as force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. Shear Stress in Beam is denoted by 𝜏beam symbol.

How to calculate Shear Stress for Rectangular Section using this online calculator? To use this online calculator for Shear Stress for Rectangular Section, enter Shear Force on Beam (Fs), Moment of Inertia of Area of Section (I), Depth of Rectangular Section (drec) & Distance from Neutral Axis (y) and hit the calculate button. Here is how the Shear Stress for Rectangular Section calculation can be explained with given input values -> 2.9E-8 = 4800/(2*0.00168)*(0.285^2/4-0.005^2).

FAQ

What is Shear Stress for Rectangular Section?
The Shear stress for rectangular section formula is defined as force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress and is represented as 𝜏beam = Fs/(2*I)*(drec^2/4-y^2) or Shear Stress in Beam = Shear Force on Beam/(2*Moment of Inertia of Area of Section)*(Depth of Rectangular Section^2/4-Distance from Neutral Axis^2). 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, Depth of Rectangular Section is the distance from the top or surface to the bottom of the section & Distance from Neutral Axis is the distance of the considered layer from the neutral layer.
How to calculate Shear Stress for Rectangular Section?
The Shear stress for rectangular section formula is defined as force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress is calculated using Shear Stress in Beam = Shear Force on Beam/(2*Moment of Inertia of Area of Section)*(Depth of Rectangular Section^2/4-Distance from Neutral Axis^2). To calculate Shear Stress for Rectangular Section, you need Shear Force on Beam (Fs), Moment of Inertia of Area of Section (I), Depth of Rectangular Section (drec) & Distance from Neutral Axis (y). With our tool, you need to enter the respective value for Shear Force on Beam, Moment of Inertia of Area of Section, Depth of Rectangular Section & Distance from Neutral Axis 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 Stress in Beam?
In this formula, Shear Stress in Beam uses Shear Force on Beam, Moment of Inertia of Area of Section, Depth of Rectangular Section & Distance from Neutral Axis. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Shear Stress in Beam = 3/2*Shear Force on Beam/(Beam Width at Considered Level*Depth of Rectangular Section)
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