FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Shear Stress for Rectangular Section Formula

GoShear Stress Variation across Neutral Axis for Rectangular Section Formula

Fx Copy

LaTeX Copy

Shear stress in beam is the internal stress that arises from the application of shear force and acts parallel to the cross-section of the beam. Check FAQs

𝜏 = \frac{V}{2 \cdot I} \cdot (\frac{d^{2}}{4} - σ^{2})

𝜏 - Shear Stress in Beam?V - Shear Force on Beam?I - Moment of Inertia of Area of Section?d - Depth of Rectangular Section?σ - Distance from Neutral Axis?

Shear Stress for Rectangular Section Example

With values

With units

Only example

Here is how the Shear Stress for Rectangular Section equation looks like with Values.

Here is how the Shear Stress for Rectangular Section equation looks like with Units.

Here is how the Shear Stress for Rectangular Section equation looks like.

0.029 = \frac{4.8}{2 \cdot 0.0017} \cdot (\frac{285^{2}}{4} - 5^{2})

0.029MPa = \frac{4.8kN}{2 \cdot 0.0017m⁴} \cdot (\frac{{285mm}^{2}}{4} - {5mm}^{2})

0.029 = \frac{4.8}{2 \cdot 0.0017} \cdot (\frac{285^{2}}{4} - 5^{2})

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Physics » Category

Mechanical » Category

Strength of Materials » fx Shear Stress for Rectangular Section

Shear Stress for Rectangular Section Solution

Follow our step by step solution on how to calculate Shear Stress for Rectangular Section?

FIRST Step Consider the formula

𝜏 = \frac{V}{2 \cdot I} \cdot (\frac{d^{2}}{4} - σ^{2})

Next Step Substitute values of Variables

∴

𝜏 = \frac{4.8kN}{2 \cdot 0.0017m⁴} \cdot (\frac{{285mm}^{2}}{4} - {5mm}^{2})

Next Step Convert Units

∴

𝜏 = \frac{4800N}{2 \cdot 0.0017m⁴} \cdot (\frac{{0.285m}^{2}}{4} - {0.005m}^{2})

Next Step Prepare to Evaluate

∴

𝜏 = \frac{4800}{2 \cdot 0.0017} \cdot (\frac{{0.285}^{2}}{4} - {0.005}^{2})

Next Step Evaluate

∴

𝜏 = 28973.2142857143Pa

Next Step Convert to Output's Unit

∴

𝜏 = 0.0289732142857143MPa

LAST Step Rounding Answer

∴

𝜏 = 0.029MPa

Shear Stress for Rectangular Section Formula Elements

Variables

Shear Stress in Beam

Shear stress in beam is the internal stress that arises from the application of shear force and acts parallel to the cross-section of the beam.

Symbol: 𝜏

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear Stress in Beam

Shear Force on Beam

Shear Force on Beam refers to the internal force that acts parallel to the cross-section of the beam is the result of external loads, reactions at supports, and the beam’s own weight.

Symbol: V

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Shear Force on Beam

Moment of Inertia of Area of Section

Moment of inertia of area of section is a geometric property that measures how a cross-section’s area is distributed relative to an axis for predicting a beam’s resistance to bending and deflection.

Symbol: I

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Moment of Inertia of Area of Section

Depth of Rectangular Section

Depth of rectangular section is the vertical dimension of the cross-section of the beam helps in calculating various stresses and ensuring the structural integrity of the beam.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth of Rectangular Section

Distance from Neutral Axis

Distance from neutral axis in a beam is the perpendicular distance from the neutral axis to a specific point within the beam’s cross-section. It is an imaginary line where the bending stress is zero.

Symbol: σ

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Distance from Neutral Axis

Other Formulas to find Shear Stress in Beam

Go Shear Stress Variation across Neutral Axis for Rectangular Section

𝜏 = \frac{3}{2} \cdot \frac{V}{b \cdot d}

Other formulas in Shear Stress in Rectangular Section category

Go Distance of C.G of Area (above Considered Level) from Neutral Axis for Rectangular Section

ȳ = \frac{1}{2} \cdot (σ + \frac{d}{2})

Go Distance of Considered Level from Neutral Axis for Rectangular Section

σ = 2 \cdot (ȳ - \frac{d}{4})

Go Shear Force for Rectangular Section

V = \frac{2 \cdot I \cdot 𝜏}{\frac{d^{2}}{4} - σ^{2}}

Go Moment of Inertia of Rectangular Section about Neutral Axis

I = \frac{V}{2 \cdot 𝜏} \cdot (\frac{d^{2}}{4} - σ^{2})

How to Evaluate Shear Stress for Rectangular Section?

Shear Stress for Rectangular Section evaluator 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 evaluate the Shear Stress in Beam, Shear Stress for Rectangular Section formula is defined as a measure of the internal resisting forces that occur within a rectangular beam when an external force is applied, causing deformation and stress distribution across the beam's cross-section. Shear Stress in Beam is denoted by 𝜏 symbol.

How to evaluate Shear Stress for Rectangular Section using this online evaluator? To use this online evaluator for Shear Stress for Rectangular Section, enter Shear Force on Beam (V), Moment of Inertia of Area of Section (I), Depth of Rectangular Section (d) & Distance from Neutral Axis (σ) and hit the calculate button.

FAQs on Shear Stress for Rectangular Section

What is the formula to find Shear Stress for Rectangular Section?

The formula of Shear Stress for Rectangular Section is expressed as 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). Here is an example- 2.9E-8 = 4800/(2*0.00168)*(0.285^2/4-0.005^2).

How to calculate Shear Stress for Rectangular Section?

With Shear Force on Beam (V), Moment of Inertia of Area of Section (I), Depth of Rectangular Section (d) & Distance from Neutral Axis (σ) we can find Shear Stress for Rectangular Section using the 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).

What are the other ways to Calculate Shear Stress in Beam?

Here are the different ways to Calculate Shear Stress in Beam-

Shear Stress in Beam=3/2*Shear Force on Beam/(Beam Width at Considered Level*Depth of Rectangular Section)

Can the Shear Stress for Rectangular Section be negative?

No, the Shear Stress for Rectangular Section, measured in Pressure cannot be negative.

Which unit is used to measure Shear Stress for Rectangular Section?

Shear Stress for Rectangular Section is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Shear Stress for Rectangular Section can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

Shear Stress for Rectangular Section Formula

​GoShear Stress Variation across Neutral Axis for Rectangular Section Formula

Shear Stress for Rectangular Section Example

Shear Stress for Rectangular Section Solution

Shear Stress for Rectangular Section Formula Elements

Other Formulas to find Shear Stress in Beam

Other formulas in Shear Stress in Rectangular Section category

How to Evaluate Shear Stress for Rectangular Section?

FAQs on Shear Stress for Rectangular Section

Variable Name

GoShear Stress Variation across Neutral Axis for Rectangular Section Formula