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Maximum Bending Moment given Maximum Stress for Short Beams Formula

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Maximum Bending Moment occurs where shear force is zero. Check FAQs

M max = \frac{(σ max - (\frac{P}{A})) \cdot I}{y}

M_max - Maximum Bending Moment?σ_max - Maximum Stress?P - Axial Load?A - Cross Sectional Area?I - Area Moment of Inertia?y - Distance from Neutral Axis?

Maximum Bending Moment given Maximum Stress for Short Beams Example

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Here is how the Maximum Bending Moment given Maximum Stress for Short Beams equation looks like with Values.

Here is how the Maximum Bending Moment given Maximum Stress for Short Beams equation looks like with Units.

Here is how the Maximum Bending Moment given Maximum Stress for Short Beams equation looks like.

7.7 = \frac{(0.137 - (\frac{2000}{0.12})) \cdot 0.0016}{25}

7.7kN*m = \frac{(0.137MPa - (\frac{2000N}{0.12m²})) \cdot 0.0016m⁴}{25mm}

7.7 = \frac{(0.137 - (\frac{2000}{0.12})) \cdot 0.0016}{25}

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Maximum Bending Moment given Maximum Stress for Short Beams Solution

Follow our step by step solution on how to calculate Maximum Bending Moment given Maximum Stress for Short Beams?

FIRST Step Consider the formula

M max = \frac{(σ max - (\frac{P}{A})) \cdot I}{y}

Next Step Substitute values of Variables

∴

M max = \frac{(0.137MPa - (\frac{2000N}{0.12m²})) \cdot 0.0016m⁴}{25mm}

Next Step Convert Units

∴

M max = \frac{(136979Pa - (\frac{2000N}{0.12m²})) \cdot 0.0016m⁴}{0.025m}

Next Step Prepare to Evaluate

∴

M max = \frac{(136979 - (\frac{2000}{0.12})) \cdot 0.0016}{0.025}

Next Step Evaluate

∴

M max = 7699.98933333333N*m

Next Step Convert to Output's Unit

∴

M max = 7.69998933333333kN*m

LAST Step Rounding Answer

∴

M max = 7.7kN*m

Maximum Bending Moment given Maximum Stress for Short Beams Formula Elements

Variables

Maximum Bending Moment

Maximum Bending Moment occurs where shear force is zero.

Symbol: M_max

Measurement: Moment of ForceUnit: kN*m

Note: Value should be greater than 0.

Formulas to find Maximum Bending Moment

Maximum Stress

Maximum Stress is the maximum amount of stress the taken by the beam/column before it breaks.

Symbol: σ_max

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Maximum Stress

Axial Load

Axial Load is a force applied on a structure directly along an axis of the structure.

Symbol: P

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Axial Load

Cross Sectional Area

The Cross Sectional Area is the breadth times the depth of the beam structure.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Cross Sectional Area

Area Moment of Inertia

Area Moment of Inertia is a property of a two-dimensional plane shape where it shows how its points are dispersed in an arbitrary axis in the cross-sectional plane.

Symbol: I

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Area Moment of Inertia

Distance from Neutral Axis

Distance from Neutral Axis is measured between N.A. and the extreme point.

Symbol: y

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance from Neutral Axis

Other formulas in Combined Axial and Bending Loads category

Go Maximum Stress for Short Beams

σ max = (\frac{P}{A}) + (\frac{M max \cdot y}{I})

Go Axial Load given Maximum Stress for Short Beams

P = A \cdot (σ max - (\frac{M max \cdot y}{I}))

Go Cross-Sectional Area given Maximum Stress for Short Beams

A = \frac{P}{σ max - (\frac{M max \cdot y}{I})}

Go Neutral Axis to Outermost Fiber Distance given Maximum Stress for Short Beams

y = \frac{(σ max \cdot A \cdot I) - (P \cdot I)}{M max \cdot A}

How to Evaluate Maximum Bending Moment given Maximum Stress for Short Beams?

Maximum Bending Moment given Maximum Stress for Short Beams evaluator uses Maximum Bending Moment = ((Maximum Stress-(Axial Load/Cross Sectional Area))*Area Moment of Inertia)/Distance from Neutral Axis to evaluate the Maximum Bending Moment, The Maximum Bending Moment given Maximum Stress for Short Beams formula is defined as the bending of the beam or any structure upon the action of the arbitrary load. The maximum bending moment in the beam occurs at the point of maximum stress. Maximum Bending Moment is denoted by M_max symbol.

How to evaluate Maximum Bending Moment given Maximum Stress for Short Beams using this online evaluator? To use this online evaluator for Maximum Bending Moment given Maximum Stress for Short Beams, enter Maximum Stress (σ_max), Axial Load (P), Cross Sectional Area (A), Area Moment of Inertia (I) & Distance from Neutral Axis (y) and hit the calculate button.

FAQs on Maximum Bending Moment given Maximum Stress for Short Beams

What is the formula to find Maximum Bending Moment given Maximum Stress for Short Beams?

The formula of Maximum Bending Moment given Maximum Stress for Short Beams is expressed as Maximum Bending Moment = ((Maximum Stress-(Axial Load/Cross Sectional Area))*Area Moment of Inertia)/Distance from Neutral Axis. Here is an example- 0.0077 = ((136979-(2000/0.12))*0.0016)/0.025.

How to calculate Maximum Bending Moment given Maximum Stress for Short Beams?

With Maximum Stress (σ_max), Axial Load (P), Cross Sectional Area (A), Area Moment of Inertia (I) & Distance from Neutral Axis (y) we can find Maximum Bending Moment given Maximum Stress for Short Beams using the formula - Maximum Bending Moment = ((Maximum Stress-(Axial Load/Cross Sectional Area))*Area Moment of Inertia)/Distance from Neutral Axis.

Can the Maximum Bending Moment given Maximum Stress for Short Beams be negative?

No, the Maximum Bending Moment given Maximum Stress for Short Beams, measured in Moment of Force cannot be negative.

Which unit is used to measure Maximum Bending Moment given Maximum Stress for Short Beams?

Maximum Bending Moment given Maximum Stress for Short Beams 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 Maximum Bending Moment given Maximum Stress for Short Beams can be measured.

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Maximum Bending Moment given Maximum Stress for Short Beams Formula

Maximum Bending Moment given Maximum Stress for Short Beams Example

Maximum Bending Moment given Maximum Stress for Short Beams Solution

Maximum Bending Moment given Maximum Stress for Short Beams Formula Elements

Other formulas in Combined Axial and Bending Loads category

How to Evaluate Maximum Bending Moment given Maximum Stress for Short Beams?

FAQs on Maximum Bending Moment given Maximum Stress for Short Beams

Variable Name