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Beam Shear Stress Formula

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Beam Shear Stress is the stress that occurs within a beam due to forces acting parallel to its cross-section. Check FAQs

ζ b = \frac{ΣS \cdot Ay}{I \cdot t}

ζ_b - Beam Shear Stress?ΣS - Total Shear Force?Ay - First Moment of Area?I - Moment of Inertia?t - Thickness of Material?

Beam Shear Stress Example

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Here is how the Beam Shear Stress equation looks like with Values.

Here is how the Beam Shear Stress equation looks like with Units.

Here is how the Beam Shear Stress equation looks like.

27.4286 = \frac{320 \cdot 4500}{3.5 \cdot 0.015}

27.4286Pa = \frac{320N \cdot 4500mm³}{3.5kg·m² \cdot 0.015mm}

27.4286 = \frac{320 \cdot 4500}{3.5 \cdot 0.015}

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Beam Shear Stress Solution

Follow our step by step solution on how to calculate Beam Shear Stress?

FIRST Step Consider the formula

ζ b = \frac{ΣS \cdot Ay}{I \cdot t}

Next Step Substitute values of Variables

∴

ζ b = \frac{320N \cdot 4500mm³}{3.5kg·m² \cdot 0.015mm}

Next Step Convert Units

∴

ζ b = \frac{320N \cdot 4.5E-6m³}{3.5kg·m² \cdot 1.5E-5m}

Next Step Prepare to Evaluate

∴

ζ b = \frac{320 \cdot 4.5E-6}{3.5 \cdot 1.5E-5}

Next Step Evaluate

∴

ζ b = 27.4285714285714Pa

LAST Step Rounding Answer

∴

ζ b = 27.4286Pa

Beam Shear Stress Formula Elements

Variables

Beam Shear Stress

Beam Shear Stress is the stress that occurs within a beam due to forces acting parallel to its cross-section.

Symbol: ζ_b

Measurement: StressUnit: Pa

Note: Value should be greater than 0.

Formulas to find Beam Shear Stress

Total Shear Force

Total Shear Force is the total force acting on the slice under the consideration.

Symbol: ΣS

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Total Shear Force

First Moment of Area

The First Moment of Area of a shape, about a certain axis, equals the sum over all the infinitesimal parts of the shape of the area of that part times its distance from the axis [Σ(a × d)].

Symbol: Ay

Measurement: First Moment of AreaUnit: mm³

Note: Value should be greater than 0.

Formulas to find First Moment of Area

Moment of Inertia

Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.

Symbol: I

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of Inertia

Thickness of Material

The Thickness of Material is the distance through an object.

Symbol: t

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Thickness of Material

Other formulas in Stress category

Go Bending Stress

σ b = M b \cdot \frac{y}{I}

Go Bulk Stress

B stress = \frac{N.F}{A cs}

Go Direct Stress

σ = \frac{P axial}{A cs}

Go Maximum Shearing Stress

σ 1 = \frac{1.5 \cdot V}{A cs}

How to Evaluate Beam Shear Stress?

Beam Shear Stress evaluator uses Beam Shear Stress = (Total Shear Force*First Moment of Area)/(Moment of Inertia*Thickness of Material) to evaluate the Beam Shear Stress, The Beam shear stress Formula is defined as the shearing stress in beam is defined as the stress that occurs due to the internal shearing of the beam that results from shear force subjected to the beam. Beam Shear Stress is denoted by ζ_b symbol.

How to evaluate Beam Shear Stress using this online evaluator? To use this online evaluator for Beam Shear Stress, enter Total Shear Force (ΣS), First Moment of Area (Ay), Moment of Inertia (I) & Thickness of Material (t) and hit the calculate button.

FAQs on Beam Shear Stress

What is the formula to find Beam Shear Stress?

The formula of Beam Shear Stress is expressed as Beam Shear Stress = (Total Shear Force*First Moment of Area)/(Moment of Inertia*Thickness of Material). Here is an example- 27.42857 = (320*4.5E-06)/(3.5*1.5E-05).

How to calculate Beam Shear Stress?

With Total Shear Force (ΣS), First Moment of Area (Ay), Moment of Inertia (I) & Thickness of Material (t) we can find Beam Shear Stress using the formula - Beam Shear Stress = (Total Shear Force*First Moment of Area)/(Moment of Inertia*Thickness of Material).

Can the Beam Shear Stress be negative?

No, the Beam Shear Stress, measured in Stress cannot be negative.

Which unit is used to measure Beam Shear Stress?

Beam Shear Stress is usually measured using the Pascal[Pa] for Stress. Newton per Square Meter[Pa], Newton per Square Millimeter[Pa], Kilonewton per Square Meter[Pa] are the few other units in which Beam Shear Stress can be measured.

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Beam Shear Stress Formula

Beam Shear Stress Example

Beam Shear Stress Solution

Beam Shear Stress Formula Elements

Other formulas in Stress category

How to Evaluate Beam Shear Stress?

FAQs on Beam Shear Stress

Variable Name