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Depth of Beam for Uniform Strength in Bending Stress Formula

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Depth of Beam is the vertical measurement between its upper and lower surfaces, perpendicular to its length and width. Check FAQs

d Beam = \sqrt{\frac{3 \cdot w \cdot L}{f \cdot 2 \cdot b Beam}}

d_Beam - Depth of Beam?w - Load on Beam?L - Length of Beam?f - Allowable Bending Stress?b_Beam - Width of Beam?

Depth of Beam for Uniform Strength in Bending Stress Example

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Here is how the Depth of Beam for Uniform Strength in Bending Stress equation looks like with Values.

Here is how the Depth of Beam for Uniform Strength in Bending Stress equation looks like with Units.

Here is how the Depth of Beam for Uniform Strength in Bending Stress equation looks like.

100.0801 = \sqrt{\frac{3 \cdot 50 \cdot 5000}{120 \cdot 2 \cdot 312}}

100.0801mm = \sqrt{\frac{3 \cdot 50kN \cdot 5000mm}{120MPa \cdot 2 \cdot 312mm}}

100.0801 = \sqrt{\frac{3 \cdot 50 \cdot 5000}{120 \cdot 2 \cdot 312}}

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Depth of Beam for Uniform Strength in Bending Stress Solution

Follow our step by step solution on how to calculate Depth of Beam for Uniform Strength in Bending Stress?

FIRST Step Consider the formula

d Beam = \sqrt{\frac{3 \cdot w \cdot L}{f \cdot 2 \cdot b Beam}}

Next Step Substitute values of Variables

∴

d Beam = \sqrt{\frac{3 \cdot 50kN \cdot 5000mm}{120MPa \cdot 2 \cdot 312mm}}

Next Step Convert Units

∴

d Beam = \sqrt{\frac{3 \cdot 50000N \cdot 5m}{1.2E+8Pa \cdot 2 \cdot 0.312m}}

Next Step Prepare to Evaluate

∴

d Beam = \sqrt{\frac{3 \cdot 50000 \cdot 5}{1.2E+8 \cdot 2 \cdot 0.312}}

Next Step Evaluate

∴

d Beam = 0.100080096128179m

Next Step Convert to Output's Unit

∴

d Beam = 100.080096128179mm

LAST Step Rounding Answer

∴

d Beam = 100.0801mm

Depth of Beam for Uniform Strength in Bending Stress Formula Elements

Variables

Functions

Depth of Beam

Depth of Beam is the vertical measurement between its upper and lower surfaces, perpendicular to its length and width.

Symbol: d_Beam

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth of Beam

Load on Beam

Load on Beam is the external force or weight applied to the beam, potentially causing deformation or stress.

Symbol: w

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Load on Beam

Length of Beam

Length of Beam is the dimension that measures the span or extent along the longitudinal axis, from one end to another.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Beam

Allowable Bending Stress

Allowable Bending Stress is the maximum stress a material can endure without exceeding its elastic limit under bending deformation.

Symbol: f

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Allowable Bending Stress

Width of Beam

Width of Beam is the horizontal dimension between its opposite surfaces or edges, perpendicular to its depth and length.

Symbol: b_Beam

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Width of Beam

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Section Modulus for Various Shapes category

Go Section Modulus of Rectangular Shape

Z = \frac{b \cdot d^{2}}{6}

Go Breadth of Rectangular Shape given Section Modulus

b = \frac{6 \cdot Z}{d^{2}}

Go Depth of Rectangular Shape given Section Modulus

d = \sqrt{\frac{6 \cdot Z}{b}}

Go Section Modulus of Hollow Rectangular Shape

Z = \frac{(B o \cdot {D o}^{3}) - (B i \cdot {D i}^{3})}{6 \cdot D o}

How to Evaluate Depth of Beam for Uniform Strength in Bending Stress?

Depth of Beam for Uniform Strength in Bending Stress evaluator uses Depth of Beam = sqrt((3*Load on Beam*Length of Beam)/(Allowable Bending Stress*2*Width of Beam)) to evaluate the Depth of Beam, The Depth of Beam for Uniform Strength in Bending Stress formula is defined as the vertical dimension that ensures consistent stress distribution. Depth of Beam is denoted by d_Beam symbol.

How to evaluate Depth of Beam for Uniform Strength in Bending Stress using this online evaluator? To use this online evaluator for Depth of Beam for Uniform Strength in Bending Stress, enter Load on Beam (w), Length of Beam (L), Allowable Bending Stress (f) & Width of Beam (b_Beam) and hit the calculate button.

FAQs on Depth of Beam for Uniform Strength in Bending Stress

What is the formula to find Depth of Beam for Uniform Strength in Bending Stress?

The formula of Depth of Beam for Uniform Strength in Bending Stress is expressed as Depth of Beam = sqrt((3*Load on Beam*Length of Beam)/(Allowable Bending Stress*2*Width of Beam)). Here is an example- 100080.1 = sqrt((3*50000*5)/(120000000*2*0.312)).

How to calculate Depth of Beam for Uniform Strength in Bending Stress?

With Load on Beam (w), Length of Beam (L), Allowable Bending Stress (f) & Width of Beam (b_Beam) we can find Depth of Beam for Uniform Strength in Bending Stress using the formula - Depth of Beam = sqrt((3*Load on Beam*Length of Beam)/(Allowable Bending Stress*2*Width of Beam)). This formula also uses Square Root (sqrt) function(s).

Can the Depth of Beam for Uniform Strength in Bending Stress be negative?

No, the Depth of Beam for Uniform Strength in Bending Stress, measured in Length cannot be negative.

Which unit is used to measure Depth of Beam for Uniform Strength in Bending Stress?

Depth of Beam for Uniform Strength in Bending Stress is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Depth of Beam for Uniform Strength in Bending Stress can be measured.

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Depth of Beam for Uniform Strength in Bending Stress Formula

Depth of Beam for Uniform Strength in Bending Stress Example

Depth of Beam for Uniform Strength in Bending Stress Solution

Depth of Beam for Uniform Strength in Bending Stress Formula Elements

Other formulas in Section Modulus for Various Shapes category

How to Evaluate Depth of Beam for Uniform Strength in Bending Stress?

FAQs on Depth of Beam for Uniform Strength in Bending Stress

Variable Name