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Radius of Curvature given Radial Stress in Member Formula

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

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

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

Radius of Curvature given Radial Stress in Member Example

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Here is how the Radius of Curvature given Radial Stress in Member equation looks like with Values.

Here is how the Radius of Curvature given Radial Stress in Member equation looks like with Units.

Here is how the Radius of Curvature given Radial Stress in Member equation looks like.

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

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

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

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Radius of Curvature given Radial Stress in Member Solution

Follow our step by step solution on how to calculate Radius of Curvature given Radial Stress in Member?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

R = \frac{3 \cdot 800N*m}{2 \cdot 1.3E+6Pa \cdot 0.051m \cdot 0.2m}

Next Step Prepare to Evaluate

∴

R = \frac{3 \cdot 800}{2 \cdot 1.3E+6 \cdot 0.051 \cdot 0.2}

Next Step Evaluate

∴

R = 0.089999968500011m

Next Step Convert to Output's Unit

∴

R = 89.999968500011mm

LAST Step Rounding Answer

∴

R = 90mm

Radius of Curvature given Radial Stress in Member Formula Elements

Variables

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

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

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

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 Radial Stress Induced by Bending Moment in Member

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

Go Bending Moment given Radial Stress in Member

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

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 Radius of Curvature given Radial Stress in Member?

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

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

FAQs on Radius of Curvature given Radial Stress in Member

What is the formula to find Radius of Curvature given Radial Stress in Member?

The formula of Radius of Curvature given Radial Stress in Member is expressed as Radius of Curvature at Centerline of Member = (3*Bending Moment for Radial Stress)/(2*Radial Stress*Width of Cross Section*Depth of Cross Section). Here is an example- 89999.97 = (3*800)/(2*1307190*0.051*0.2).

How to calculate Radius of Curvature given Radial Stress in Member?

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

Can the Radius of Curvature given Radial Stress in Member be negative?

No, the Radius of Curvature given Radial Stress in Member, measured in Length cannot be negative.

Which unit is used to measure Radius of Curvature given Radial Stress in Member?

Radius of Curvature given Radial Stress in Member is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Radius of Curvature given Radial Stress in Member can be measured.

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Radius of Curvature given Radial Stress in Member Formula

Radius of Curvature given Radial Stress in Member Example

Radius of Curvature given Radial Stress in Member Solution

Radius of Curvature given Radial Stress in Member Formula Elements

Other formulas in Radial Stresses and Curvature Factor category

How to Evaluate Radius of Curvature given Radial Stress in Member?

FAQs on Radius of Curvature given Radial Stress in Member

Variable Name