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Radial Stress Induced by Bending Moment in Member Formula

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The radial stress induced by a bending moment in a member of constant cross-section. Check FAQs

σ r = 3 \cdot \frac{M' b}{2 \cdot R \cdot w \cdot d}

σ_r - Radial Stress?M'_b - Bending Moment for Radial Stress?R - Radius of Curvature at Centerline of Member?w - Width of Cross Section?d - Depth of Cross Section?

Radial Stress Induced by Bending Moment in Member Example

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Here is how the Radial Stress Induced by Bending Moment in Member equation looks like with Values.

Here is how the Radial Stress Induced by Bending Moment in Member equation looks like with Units.

Here is how the Radial Stress Induced by Bending Moment in Member equation looks like.

1.3072 = 3 \cdot \frac{800}{2 \cdot 90 \cdot 51 \cdot 200}

1.3072MPa = 3 \cdot \frac{800N*m}{2 \cdot 90mm \cdot 51mm \cdot 200mm}

1.3072 = 3 \cdot \frac{800}{2 \cdot 90 \cdot 51 \cdot 200}

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Radial Stress Induced by Bending Moment in Member Solution

Follow our step by step solution on how to calculate Radial Stress Induced by Bending Moment in Member?

FIRST Step Consider the formula

σ r = 3 \cdot \frac{M' b}{2 \cdot R \cdot w \cdot d}

Next Step Substitute values of Variables

∴

σ r = 3 \cdot \frac{800N*m}{2 \cdot 90mm \cdot 51mm \cdot 200mm}

Next Step Convert Units

∴

σ r = 3 \cdot \frac{800N*m}{2 \cdot 0.09m \cdot 0.051m \cdot 0.2m}

Next Step Prepare to Evaluate

∴

σ r = 3 \cdot \frac{800}{2 \cdot 0.09 \cdot 0.051 \cdot 0.2}

Next Step Evaluate

∴

σ r = 1307189.54248366Pa

Next Step Convert to Output's Unit

∴

σ r = 1.30718954248366MPa

LAST Step Rounding Answer

∴

σ r = 1.3072MPa

Radial Stress Induced by Bending Moment in Member Formula Elements

Variables

Radial Stress

The radial stress induced by a bending moment in a member of constant cross-section.

Symbol: σ_r

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Radial Stress

Bending Moment for Radial Stress

Bending Moment for Radial Stress 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'_b

Measurement: Moment of ForceUnit: N*m

Note: Value should be greater than 0.

Formulas to find Bending Moment for Radial Stress

Radius of Curvature at Centerline of Member

Radius of Curvature at Centerline of Member in mm is the radius of the circle that touches the curve at a given point.

Symbol: R

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Curvature at Centerline of Member

Width of Cross Section

Width of Cross Section defines the geometric measurement or extent of the member from side to side.

Symbol: w

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Width of Cross Section

Depth of Cross Section

Depth of Cross Section (Height), in (mm) defines the geometrical measure from head to foot or from base to top of the section considered.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth of Cross Section

Other formulas in Radial Stresses and Curvature Factor category

Go Bending Moment given Radial Stress in Member

M' b = \frac{2 \cdot σ r \cdot R \cdot w \cdot d}{3}

Go Radius of Curvature given Radial Stress in Member

R = \frac{3 \cdot M' b}{2 \cdot σ r \cdot w \cdot d}

Go Cross Section Width given Radial Stress in Member

w = \frac{3 \cdot M' b}{2 \cdot σ r \cdot R \cdot d}

Go Cross Section Depth given Radial Stress in Member

d = \frac{3 \cdot M' b}{2 \cdot σ r \cdot R \cdot w}

How to Evaluate Radial Stress Induced by Bending Moment in Member?

Radial Stress Induced by Bending Moment in Member evaluator uses Radial Stress = 3*Bending Moment for Radial Stress/(2*Radius of Curvature at Centerline of Member*Width of Cross Section*Depth of Cross Section) to evaluate the Radial Stress, The Radial Stress Induced by Bending Moment in Member formula is defined as influenced by the parameters bending moment, the radius of curvature at the centerline of the member, the width of the cross-section, and the depth of the cross-section. Radial Stress is denoted by σ_r symbol.

How to evaluate Radial Stress Induced by Bending Moment in Member using this online evaluator? To use this online evaluator for Radial Stress Induced by Bending Moment in Member, enter Bending Moment for Radial Stress (M'_b), Radius of Curvature at Centerline of Member (R), Width of Cross Section (w) & Depth of Cross Section (d) and hit the calculate button.

FAQs on Radial Stress Induced by Bending Moment in Member

What is the formula to find Radial Stress Induced by Bending Moment in Member?

The formula of Radial Stress Induced by Bending Moment in Member is expressed as Radial Stress = 3*Bending Moment for Radial Stress/(2*Radius of Curvature at Centerline of Member*Width of Cross Section*Depth of Cross Section). Here is an example- 1.3E-6 = 3*800/(2*0.09*0.051*0.2).

How to calculate Radial Stress Induced by Bending Moment in Member?

With Bending Moment for Radial Stress (M'_b), Radius of Curvature at Centerline of Member (R), Width of Cross Section (w) & Depth of Cross Section (d) we can find Radial Stress Induced by Bending Moment in Member using the formula - Radial Stress = 3*Bending Moment for Radial Stress/(2*Radius of Curvature at Centerline of Member*Width of Cross Section*Depth of Cross Section).

Can the Radial Stress Induced by Bending Moment in Member be negative?

No, the Radial Stress Induced by Bending Moment in Member, measured in Stress cannot be negative.

Which unit is used to measure Radial Stress Induced by Bending Moment in Member?

Radial Stress Induced by Bending Moment in Member 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 Radial Stress Induced by Bending Moment in Member can be measured.

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Radial Stress Induced by Bending Moment in Member Formula

Radial Stress Induced by Bending Moment in Member Example

Radial Stress Induced by Bending Moment in Member Solution

Radial Stress Induced by Bending Moment in Member Formula Elements

Other formulas in Radial Stresses and Curvature Factor category

How to Evaluate Radial Stress Induced by Bending Moment in Member?

FAQs on Radial Stress Induced by Bending Moment in Member

Variable Name