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Shear Force for Rectangular Section Formula

GoShear Force Variation across Neutral Axis for Rectangular Section Formula

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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. Check FAQs

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

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

Shear Force for Rectangular Section Example

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

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

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

994.0216 = \frac{2 \cdot 0.0017 \cdot 6}{\frac{285^{2}}{4} - 5^{2}}

994.0216kN = \frac{2 \cdot 0.0017m⁴ \cdot 6MPa}{\frac{{285mm}^{2}}{4} - {5mm}^{2}}

994.0216 = \frac{2 \cdot 0.0017 \cdot 6}{\frac{285^{2}}{4} - 5^{2}}

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Shear Force for Rectangular Section Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V = \frac{2 \cdot 0.0017m⁴ \cdot 6MPa}{\frac{{285mm}^{2}}{4} - {5mm}^{2}}

Next Step Convert Units

∴

V = \frac{2 \cdot 0.0017m⁴ \cdot 6E+6Pa}{\frac{{0.285m}^{2}}{4} - {0.005m}^{2}}

Next Step Prepare to Evaluate

∴

V = \frac{2 \cdot 0.0017 \cdot 6E+6}{\frac{{0.285}^{2}}{4} - {0.005}^{2}}

Next Step Evaluate

∴

V = 994021.57164869N

Next Step Convert to Output's Unit

∴

V = 994.02157164869kN

LAST Step Rounding Answer

∴

V = 994.0216kN

Shear Force for Rectangular Section Formula Elements

Variables

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

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

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 Force on Beam

Go Shear Force Variation across Neutral Axis for Rectangular Section

V = \frac{2}{3} \cdot 𝜏 \cdot 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 Stress for Rectangular Section

𝜏 = \frac{V}{2 \cdot I} \cdot (\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 Force for Rectangular Section?

Shear Force for Rectangular Section evaluator uses 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) to evaluate the Shear Force on Beam, Shear Force for Rectangular Section formula is defined as a measure of the internal forces that occur in a rectangular section of a beam, resulting from the external loads applied, which can cause the beam to deform or even fail. Shear Force on Beam is denoted by V symbol.

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

FAQs on Shear Force for Rectangular Section

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

The formula of Shear Force for Rectangular Section is expressed as 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). Here is an example- 0.994022 = (2*0.00168*6000000)/(0.285^2/4-0.005^2).

How to calculate Shear Force for Rectangular Section?

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

What are the other ways to Calculate Shear Force on Beam?

Here are the different ways to Calculate Shear Force on Beam-

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

Can the Shear Force for Rectangular Section be negative?

Yes, the Shear Force for Rectangular Section, measured in Force can be negative.

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

Shear Force for Rectangular Section is usually measured using the Kilonewton[kN] for Force. Newton[kN], Exanewton[kN], Meganewton[kN] are the few other units in which Shear Force for Rectangular Section can be measured.

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Shear Force for Rectangular Section Formula

​GoShear Force Variation across Neutral Axis for Rectangular Section Formula

Shear Force for Rectangular Section Example

Shear Force for Rectangular Section Solution

Shear Force for Rectangular Section Formula Elements

Other Formulas to find Shear Force on Beam

Other formulas in Shear Stress in Rectangular Section category

How to Evaluate Shear Force for Rectangular Section?

FAQs on Shear Force for Rectangular Section

Variable Name

GoShear Force Variation across Neutral Axis for Rectangular Section Formula