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Elasto Plastic Bending Moment of Rectangular Beam Formula

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Elasto Plastic Bending Moment is the maximum moment a beam can withstand before it deforms plastically due to bending stress, affecting its structural integrity. Check FAQs

M ep = \frac{σ 0 \cdot b \cdot (3 \cdot d^{2} - 4 \cdot η^{2})}{12}

M_ep - Elasto Plastic Bending Moment?σ₀ - Yield Stress?b - Breadth of Rectangular Beam?d - Depth of Rectangular Beam?η - Depth of Outermost Shell Yields?

Elasto Plastic Bending Moment of Rectangular Beam Example

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Here is how the Elasto Plastic Bending Moment of Rectangular Beam equation looks like with Values.

Here is how the Elasto Plastic Bending Moment of Rectangular Beam equation looks like with Units.

Here is how the Elasto Plastic Bending Moment of Rectangular Beam equation looks like.

1.8E+6 = \frac{230 \cdot 80 \cdot (3 \cdot 20^{2} - 4 \cdot {1.1}^{2})}{12}

1.8E+6N*mm = \frac{230N/mm² \cdot 80mm \cdot (3 \cdot {20mm}^{2} - 4 \cdot {1.1mm}^{2})}{12}

1.8E+6 = \frac{230 \cdot 80 \cdot (3 \cdot 20^{2} - 4 \cdot {1.1}^{2})}{12}

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Elasto Plastic Bending Moment of Rectangular Beam Solution

Follow our step by step solution on how to calculate Elasto Plastic Bending Moment of Rectangular Beam?

FIRST Step Consider the formula

M ep = \frac{σ 0 \cdot b \cdot (3 \cdot d^{2} - 4 \cdot η^{2})}{12}

Next Step Substitute values of Variables

∴

M ep = \frac{230N/mm² \cdot 80mm \cdot (3 \cdot {20mm}^{2} - 4 \cdot {1.1mm}^{2})}{12}

Next Step Convert Units

∴

M ep = \frac{2.3E+8Pa \cdot 0.08m \cdot (3 \cdot {0.02m}^{2} - 4 \cdot {0.0011m}^{2})}{12}

Next Step Prepare to Evaluate

∴

M ep = \frac{2.3E+8 \cdot 0.08 \cdot (3 \cdot {0.02}^{2} - 4 \cdot {0.0011}^{2})}{12}

Next Step Evaluate

∴

M ep = 1832.57866666667N*m

Next Step Convert to Output's Unit

∴

M ep = 1832578.66666667N*mm

LAST Step Rounding Answer

∴

M ep = 1.8E+6N*mm

Elasto Plastic Bending Moment of Rectangular Beam Formula Elements

Variables

Elasto Plastic Bending Moment

Elasto Plastic Bending Moment is the maximum moment a beam can withstand before it deforms plastically due to bending stress, affecting its structural integrity.

Symbol: M_ep

Measurement: Moment of ForceUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Elasto Plastic Bending Moment

Yield Stress

Yield Stress is the stress at which a material begins to deform plastically, typically measured in bending beams under external loads.

Symbol: σ₀

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Yield Stress

Breadth of Rectangular Beam

Breadth of Rectangular Beam is the horizontal distance of a rectangular beam's cross-section, perpendicular to its length, in bending beam applications.

Symbol: b

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Breadth of Rectangular Beam

Depth of Rectangular Beam

Depth of Rectangular Beam is the vertical distance from the neutral axis to the bottom of the beam, used to calculate bending stresses and moments.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth of Rectangular Beam

Depth of Outermost Shell Yields

Depth of Outermost Shell Yields is the maximum distance from the neutral axis to the outermost fiber of a beam under bending stress.

Symbol: η

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth of Outermost Shell Yields

Other formulas in Plastic Bending of Beams category

Go Incipient Bending Moment of Rectangular Beam

M i = \frac{b \cdot d^{2} \cdot σ 0}{6}

Go Fully Plastic Bending Moment

M f = \frac{b \cdot d^{2} \cdot σ 0}{4}

How to Evaluate Elasto Plastic Bending Moment of Rectangular Beam?

Elasto Plastic Bending Moment of Rectangular Beam evaluator uses Elasto Plastic Bending Moment = (Yield Stress*Breadth of Rectangular Beam*(3*Depth of Rectangular Beam^2-4*Depth of Outermost Shell Yields^2))/12 to evaluate the Elasto Plastic Bending Moment, Elasto Plastic Bending Moment of Rectangular Beam formula is defined as a measure of the maximum bending moment that a rectangular beam can withstand before it starts to deform plastically, considering the yield strength, beam dimensions, and the extent of plastic deformation. Elasto Plastic Bending Moment is denoted by M_ep symbol.

How to evaluate Elasto Plastic Bending Moment of Rectangular Beam using this online evaluator? To use this online evaluator for Elasto Plastic Bending Moment of Rectangular Beam, enter Yield Stress (σ₀), Breadth of Rectangular Beam (b), Depth of Rectangular Beam (d) & Depth of Outermost Shell Yields (η) and hit the calculate button.

FAQs on Elasto Plastic Bending Moment of Rectangular Beam

What is the formula to find Elasto Plastic Bending Moment of Rectangular Beam?

The formula of Elasto Plastic Bending Moment of Rectangular Beam is expressed as Elasto Plastic Bending Moment = (Yield Stress*Breadth of Rectangular Beam*(3*Depth of Rectangular Beam^2-4*Depth of Outermost Shell Yields^2))/12. Here is an example- 1.8E+9 = (230000000*0.08*(3*0.02^2-4*0.0011^2))/12.

How to calculate Elasto Plastic Bending Moment of Rectangular Beam?

With Yield Stress (σ₀), Breadth of Rectangular Beam (b), Depth of Rectangular Beam (d) & Depth of Outermost Shell Yields (η) we can find Elasto Plastic Bending Moment of Rectangular Beam using the formula - Elasto Plastic Bending Moment = (Yield Stress*Breadth of Rectangular Beam*(3*Depth of Rectangular Beam^2-4*Depth of Outermost Shell Yields^2))/12.

Can the Elasto Plastic Bending Moment of Rectangular Beam be negative?

No, the Elasto Plastic Bending Moment of Rectangular Beam, measured in Moment of Force cannot be negative.

Which unit is used to measure Elasto Plastic Bending Moment of Rectangular Beam?

Elasto Plastic Bending Moment of Rectangular Beam is usually measured using the Newton Millimeter[N*mm] for Moment of Force. Newton Meter[N*mm], Kilonewton Meter[N*mm], Millinewton Meter[N*mm] are the few other units in which Elasto Plastic Bending Moment of Rectangular Beam can be measured.

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Elasto Plastic Bending Moment of Rectangular Beam Formula

Elasto Plastic Bending Moment of Rectangular Beam Example

Elasto Plastic Bending Moment of Rectangular Beam Solution

Elasto Plastic Bending Moment of Rectangular Beam Formula Elements

Other formulas in Plastic Bending of Beams category

How to Evaluate Elasto Plastic Bending Moment of Rectangular Beam?

FAQs on Elasto Plastic Bending Moment of Rectangular Beam

Variable Name