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Maximum Shear Stress in I Section Formula

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Maximum Shear Stress on Beam that acts coplanar with a cross-section of material arises due to shear forces. Check FAQs

𝜏 max = \frac{F s}{I \cdot b} \cdot (\frac{B \cdot (D^{2} - d^{2})}{8} + \frac{b \cdot d^{2}}{8})

𝜏_max - Maximum Shear Stress on Beam?F_s - Shear Force on Beam?I - Moment of Inertia of Area of Section?b - Thickness of Beam Web?B - Width of Beam Section?D - Outer Depth of I section?d - Inner Depth of I Section?

Maximum Shear Stress in I Section Example

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Here is how the Maximum Shear Stress in I Section equation looks like with Values.

Here is how the Maximum Shear Stress in I Section equation looks like with Units.

Here is how the Maximum Shear Stress in I Section equation looks like.

412.3045 = \frac{4.8}{0.0017 \cdot 7} \cdot (\frac{100 \cdot (9000^{2} - 450^{2})}{8} + \frac{7 \cdot 450^{2}}{8})

412.3045MPa = \frac{4.8kN}{0.0017m⁴ \cdot 7mm} \cdot (\frac{100mm \cdot ({9000mm}^{2} - {450mm}^{2})}{8} + \frac{7mm \cdot {450mm}^{2}}{8})

412.3045 = \frac{4.8}{0.0017 \cdot 7} \cdot (\frac{100 \cdot (9000^{2} - 450^{2})}{8} + \frac{7 \cdot 450^{2}}{8})

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Maximum Shear Stress in I Section Solution

Follow our step by step solution on how to calculate Maximum Shear Stress in I Section?

FIRST Step Consider the formula

𝜏 max = \frac{F s}{I \cdot b} \cdot (\frac{B \cdot (D^{2} - d^{2})}{8} + \frac{b \cdot d^{2}}{8})

Next Step Substitute values of Variables

∴

𝜏 max = \frac{4.8kN}{0.0017m⁴ \cdot 7mm} \cdot (\frac{100mm \cdot ({9000mm}^{2} - {450mm}^{2})}{8} + \frac{7mm \cdot {450mm}^{2}}{8})

Next Step Convert Units

∴

𝜏 max = \frac{4800N}{0.0017m⁴ \cdot 0.007m} \cdot (\frac{0.1m \cdot ({9m}^{2} - {0.45m}^{2})}{8} + \frac{0.007m \cdot {0.45m}^{2}}{8})

Next Step Prepare to Evaluate

∴

𝜏 max = \frac{4800}{0.0017 \cdot 0.007} \cdot (\frac{0.1 \cdot (9^{2} - {0.45}^{2})}{8} + \frac{0.007 \cdot {0.45}^{2}}{8})

Next Step Evaluate

∴

𝜏 max = 412304464.285714Pa

Next Step Convert to Output's Unit

∴

𝜏 max = 412.304464285714MPa

LAST Step Rounding Answer

∴

𝜏 max = 412.3045MPa

Maximum Shear Stress in I Section Formula Elements

Variables

Maximum Shear Stress on Beam

Maximum Shear Stress on Beam that acts coplanar with a cross-section of material arises due to shear forces.

Symbol: 𝜏_max

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Maximum Shear Stress on Beam

Shear Force on Beam

Shear Force on Beam is the force which causes shear deformation to occur in the shear plane.

Symbol: F_s

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 the second moment of the area of the section about the neutral axis.

Symbol: I

Measurement: Second Moment of AreaUnit: m⁴