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Bending Moment of Simply Supported Beam Carrying UDL Formula

GoMaximum Bending Moment of Simply Supported Beams with Point Load at Centre Formula

GoMaximum Bending Moment of Simply Supported Beam with Uniformly Distributed Load Formula

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Bending Moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. Check FAQs

M = (\frac{w \cdot L \cdot x}{2}) - (w \cdot \frac{x^{2}}{2})

M - Bending Moment?w - Load per Unit Length?L - Length of Beam?x - Distance x from Support?

Bending Moment of Simply Supported Beam Carrying UDL Example

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Here is how the Bending Moment of Simply Supported Beam Carrying UDL equation looks like with Values.

Here is how the Bending Moment of Simply Supported Beam Carrying UDL equation looks like with Units.

Here is how the Bending Moment of Simply Supported Beam Carrying UDL equation looks like.

57.0037 = (\frac{67.46 \cdot 2600 \cdot 1300}{2}) - (67.46 \cdot \frac{1300^{2}}{2})

57.0037kN*m = (\frac{67.46kN/m \cdot 2600mm \cdot 1300mm}{2}) - (67.46kN/m \cdot \frac{{1300mm}^{2}}{2})

57.0037 = (\frac{67.46 \cdot 2600 \cdot 1300}{2}) - (67.46 \cdot \frac{1300^{2}}{2})

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Bending Moment of Simply Supported Beam Carrying UDL Solution

Follow our step by step solution on how to calculate Bending Moment of Simply Supported Beam Carrying UDL?

FIRST Step Consider the formula

M = (\frac{w \cdot L \cdot x}{2}) - (w \cdot \frac{x^{2}}{2})

Next Step Substitute values of Variables

∴

M = (\frac{67.46kN/m \cdot 2600mm \cdot 1300mm}{2}) - (67.46kN/m \cdot \frac{{1300mm}^{2}}{2})

Next Step Convert Units

∴

M = (\frac{67460N/m \cdot 2.6m \cdot 1.3m}{2}) - (67460N/m \cdot \frac{{1.3m}^{2}}{2})

Next Step Prepare to Evaluate

∴

M = (\frac{67460 \cdot 2.6 \cdot 1.3}{2}) - (67460 \cdot \frac{{1.3}^{2}}{2})

Next Step Evaluate

∴

M = 57003.7N*m

LAST Step Convert to Output's Unit

∴

M = 57.0037kN*m

Bending Moment of Simply Supported Beam Carrying UDL Formula Elements

Variables

Bending Moment

Bending Moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.

Symbol: M

Measurement: Moment of ForceUnit: kN*m

Note: Value can be positive or negative.

Formulas to find Bending Moment

Load per Unit Length

Load per Unit Length is the load distributed per unit meter.

Symbol: w

Measurement: Surface TensionUnit: kN/m

Note: Value can be positive or negative.

Formulas to find Load per Unit Length

Length of Beam

Length of Beam is defined as the distance between the supports.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Beam

Distance x from Support

Distance x from Support is the length of a beam from the support to any point on the beam.

Symbol: x

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance x from Support

Other Formulas to find Bending Moment

Go Maximum Bending Moment of Simply Supported Beams with Point Load at Centre

M = \frac{P \cdot L}{4}

Go Maximum Bending Moment of Simply Supported Beam with Uniformly Distributed Load

M = \frac{w \cdot L^{2}}{8}

Go Maximum Bending Moment of Simply Supported Beams with Uniformly Varying Load

M = \frac{q \cdot L^{2}}{9 \cdot \sqrt{3}}

Go Maximum Bending Moment of Cantilever Beam Subjected to Point Load at Free End

M = P \cdot L

Other formulas in Beam Moments category

Go Moment on Fixed End of Fixed Beam having Point Load at Center

FEM = \frac{P \cdot L}{8}

Go Moment on Fixed End of Fixed Beam having UDL over Entire Length

FEM = \frac{w \cdot (L^{2})}{12}

Go Fixed End Moment at Left Support with Point Load at Certain Distance from Left Support

FEM = (\frac{P \cdot (b^{2}) \cdot a}{L^{2}})

Go Fixed End Moment at Left Support Carrying Right Angled Triangular Load at Right Angled End A

FEM = \frac{q \cdot (L^{2})}{20}

How to Evaluate Bending Moment of Simply Supported Beam Carrying UDL?

Bending Moment of Simply Supported Beam Carrying UDL evaluator uses Bending Moment = ((Load per Unit Length*Length of Beam*Distance x from Support)/2)-(Load per Unit Length*(Distance x from Support^2)/2) to evaluate the Bending Moment, The Bending Moment of Simply Supported Beam Carrying UDL formula is defined as the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. Bending Moment is denoted by M symbol.

How to evaluate Bending Moment of Simply Supported Beam Carrying UDL using this online evaluator? To use this online evaluator for Bending Moment of Simply Supported Beam Carrying UDL, enter Load per Unit Length (w), Length of Beam (L) & Distance x from Support (x) and hit the calculate button.

FAQs on Bending Moment of Simply Supported Beam Carrying UDL

What is the formula to find Bending Moment of Simply Supported Beam Carrying UDL?

The formula of Bending Moment of Simply Supported Beam Carrying UDL is expressed as Bending Moment = ((Load per Unit Length*Length of Beam*Distance x from Support)/2)-(Load per Unit Length*(Distance x from Support^2)/2). Here is an example- 0.057004 = ((67460*2.6*1.3)/2)-(67460*(1.3^2)/2).

How to calculate Bending Moment of Simply Supported Beam Carrying UDL?

With Load per Unit Length (w), Length of Beam (L) & Distance x from Support (x) we can find Bending Moment of Simply Supported Beam Carrying UDL using the formula - Bending Moment = ((Load per Unit Length*Length of Beam*Distance x from Support)/2)-(Load per Unit Length*(Distance x from Support^2)/2).

What are the other ways to Calculate Bending Moment?

Here are the different ways to Calculate Bending Moment-

Bending Moment=(Point Load*Length of Beam)/4
Bending Moment=(Load per Unit Length*Length of Beam^2)/8
Bending Moment=(Uniformly Varying Load*Length of Beam^2)/(9*sqrt(3))

Can the Bending Moment of Simply Supported Beam Carrying UDL be negative?

Yes, the Bending Moment of Simply Supported Beam Carrying UDL, measured in Moment of Force can be negative.

Which unit is used to measure Bending Moment of Simply Supported Beam Carrying UDL?

Bending Moment of Simply Supported Beam Carrying UDL is usually measured using the Kilonewton Meter[kN*m] for Moment of Force. Newton Meter[kN*m], Millinewton Meter[kN*m], Micronewton Meter[kN*m] are the few other units in which Bending Moment of Simply Supported Beam Carrying UDL can be measured.

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