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Maximum Longitudinal Shear Stress in Web for I beam Formula

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Maximum Longitudinal Shear Stress is the greatest extent a shear force can be concentrated in a small area. Check FAQs

τ maxlongitudinal = ((\frac{b f \cdot V}{8 \cdot b w \cdot I} \cdot (D^{2} - {d w}^{2}))) + (\frac{V \cdot {d w}^{2}}{8 \cdot I})

τ_{maxlongitudinal} - Maximum Longitudinal Shear Stress?b_f - Width of Flange?V - Shear Force?b_w - Width of Web?I - Area Moment of Inertia?D - Overall Depth of I Beam?d_w - Depth of Web?

Maximum Longitudinal Shear Stress in Web for I beam Example

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Here is how the Maximum Longitudinal Shear Stress in Web for I beam equation looks like with Values.

Here is how the Maximum Longitudinal Shear Stress in Web for I beam equation looks like with Units.

Here is how the Maximum Longitudinal Shear Stress in Web for I beam equation looks like.

344.3427 = ((\frac{250 \cdot 24.8}{8 \cdot 0.04 \cdot 3.6E+7} \cdot (800^{2} - 15^{2}))) + (\frac{24.8 \cdot 15^{2}}{8 \cdot 3.6E+7})

344.3427MPa = ((\frac{250mm \cdot 24.8kN}{8 \cdot 0.04m \cdot 3.6E+7mm⁴} \cdot ({800mm}^{2} - {15mm}^{2}))) + (\frac{24.8kN \cdot {15mm}^{2}}{8 \cdot 3.6E+7mm⁴})

344.3427 = ((\frac{250 \cdot 24.8}{8 \cdot 0.04 \cdot 3.6E+7} \cdot (800^{2} - 15^{2}))) + (\frac{24.8 \cdot 15^{2}}{8 \cdot 3.6E+7})

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Maximum Longitudinal Shear Stress in Web for I beam Solution

Follow our step by step solution on how to calculate Maximum Longitudinal Shear Stress in Web for I beam?

FIRST Step Consider the formula

τ maxlongitudinal = ((\frac{b f \cdot V}{8 \cdot b w \cdot I} \cdot (D^{2} - {d w}^{2}))) + (\frac{V \cdot {d w}^{2}}{8 \cdot I})

Next Step Substitute values of Variables

∴

τ maxlongitudinal = ((\frac{250mm \cdot 24.8kN}{8 \cdot 0.04m \cdot 3.6E+7mm⁴} \cdot ({800mm}^{2} - {15mm}^{2}))) + (\frac{24.8kN \cdot {15mm}^{2}}{8 \cdot 3.6E+7mm⁴})

Next Step Convert Units

∴

τ maxlongitudinal = ((\frac{0.25m \cdot 24800N}{8 \cdot 0.04m \cdot 3.6E-5m⁴} \cdot ({0.8m}^{2} - {0.015m}^{2}))) + (\frac{24800N \cdot {0.015m}^{2}}{8 \cdot 3.6E-5m⁴})

Next Step Prepare to Evaluate

∴

τ maxlongitudinal = ((\frac{0.25 \cdot 24800}{8 \cdot 0.04 \cdot 3.6E-5} \cdot ({0.8}^{2} - {0.015}^{2}))) + (\frac{24800 \cdot {0.015}^{2}}{8 \cdot 3.6E-5})

Next Step Evaluate

∴

τ maxlongitudinal = 344342725.694444Pa

Next Step Convert to Output's Unit

∴

τ maxlongitudinal = 344.342725694444MPa

LAST Step Rounding Answer

∴

τ maxlongitudinal = 344.3427MPa

Maximum Longitudinal Shear Stress in Web for I beam Formula Elements

Variables

Maximum Longitudinal Shear Stress

Maximum Longitudinal Shear Stress is the greatest extent a shear force can be concentrated in a small area.

Symbol: τ_{maxlongitudinal}

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Maximum Longitudinal Shear Stress

Width of Flange

Width of Flange is the dimension of the flange measured parallel to the neutral axis.

Symbol: b_f

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Width of Flange

Shear Force

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

Symbol: V

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Shear Force

Width of Web

Width of Web (bw) is the effective width of the member for flanged section.

Symbol: b_w

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Width of Web

Area Moment of Inertia

Area Moment of Inertia is a moment about the centroidal axis without considering mass.

Symbol: I

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find Area Moment of Inertia

Overall Depth of I Beam

Overall Depth of I Beam is the total height or depth of the I-section from the top fiber of the top flange to the bottom fiber of the bottom flange.

Symbol: D

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Overall Depth of I Beam

Depth of Web

Depth of Web is the dimension of the web measured perpendicular to the neutral axis.

Symbol: d_w

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth of Web

Other formulas in I Beam category

Go Longitudinal Shear Stress in Flange at Lower Depth of I beam

τ = (\frac{V}{8 \cdot I}) \cdot (D^{2} - {d w}^{2})

Go Transverse Shear given Longitudinal Shear Stress in Flange for I beam

V = \frac{8 \cdot I \cdot τ}{D^{2} - {d w}^{2}}

How to Evaluate Maximum Longitudinal Shear Stress in Web for I beam?

Maximum Longitudinal Shear Stress in Web for I beam evaluator uses Maximum Longitudinal Shear Stress = (((Width of Flange*Shear Force)/(8*Width of Web*Area Moment of Inertia)*(Overall Depth of I Beam^2-Depth of Web^2)))+((Shear Force*Depth of Web^2)/(8*Area Moment of Inertia)) to evaluate the Maximum Longitudinal Shear Stress, The Maximum Longitudinal Shear Stress in Web for I beam formula is defined as maximum of all the calculated longitudinal shear stresses experienced by the beam. Maximum Longitudinal Shear Stress is denoted by τ_{maxlongitudinal} symbol.

How to evaluate Maximum Longitudinal Shear Stress in Web for I beam using this online evaluator? To use this online evaluator for Maximum Longitudinal Shear Stress in Web for I beam, enter Width of Flange (b_f), Shear Force (V), Width of Web (b_w), Area Moment of Inertia (I), Overall Depth of I Beam (D) & Depth of Web (d_w) and hit the calculate button.

FAQs on Maximum Longitudinal Shear Stress in Web for I beam

What is the formula to find Maximum Longitudinal Shear Stress in Web for I beam?

The formula of Maximum Longitudinal Shear Stress in Web for I beam is expressed as Maximum Longitudinal Shear Stress = (((Width of Flange*Shear Force)/(8*Width of Web*Area Moment of Inertia)*(Overall Depth of I Beam^2-Depth of Web^2)))+((Shear Force*Depth of Web^2)/(8*Area Moment of Inertia)). Here is an example- 0.000344 = (((0.25*24800)/(8*0.04*3.6E-05)*(0.8^2-0.015^2)))+((24800*0.015^2)/(8*3.6E-05)).

How to calculate Maximum Longitudinal Shear Stress in Web for I beam?

With Width of Flange (b_f), Shear Force (V), Width of Web (b_w), Area Moment of Inertia (I), Overall Depth of I Beam (D) & Depth of Web (d_w) we can find Maximum Longitudinal Shear Stress in Web for I beam using the formula - Maximum Longitudinal Shear Stress = (((Width of Flange*Shear Force)/(8*Width of Web*Area Moment of Inertia)*(Overall Depth of I Beam^2-Depth of Web^2)))+((Shear Force*Depth of Web^2)/(8*Area Moment of Inertia)).

Can the Maximum Longitudinal Shear Stress in Web for I beam be negative?

Yes, the Maximum Longitudinal Shear Stress in Web for I beam, measured in Stress can be negative.

Which unit is used to measure Maximum Longitudinal Shear Stress in Web for I beam?

Maximum Longitudinal Shear Stress in Web for I beam is usually measured using the Megapascal[MPa] for Stress. Pascal[MPa], Newton per Square Meter[MPa], Newton per Square Millimeter[MPa] are the few other units in which Maximum Longitudinal Shear Stress in Web for I beam can be measured.

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Maximum Longitudinal Shear Stress in Web for I beam Formula

Maximum Longitudinal Shear Stress in Web for I beam Example

Maximum Longitudinal Shear Stress in Web for I beam Solution

Maximum Longitudinal Shear Stress in Web for I beam Formula Elements

Other formulas in I Beam category

How to Evaluate Maximum Longitudinal Shear Stress in Web for I beam?

FAQs on Maximum Longitudinal Shear Stress in Web for I beam

Variable Name