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Cross Section Depth given Radial Stress in Member Formula

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

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

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

Cross Section Depth given Radial Stress in Member Example

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Here is how the Cross Section Depth given Radial Stress in Member equation looks like with Values.

Here is how the Cross Section Depth given Radial Stress in Member equation looks like with Units.

Here is how the Cross Section Depth given Radial Stress in Member equation looks like.

199.9999 = \frac{3 \cdot 800}{2 \cdot 1.3072 \cdot 90 \cdot 51}

199.9999mm = \frac{3 \cdot 800N*m}{2 \cdot 1.3072MPa \cdot 90mm \cdot 51mm}

199.9999 = \frac{3 \cdot 800}{2 \cdot 1.3072 \cdot 90 \cdot 51}

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Cross Section Depth given Radial Stress in Member Solution

Follow our step by step solution on how to calculate Cross Section Depth given Radial Stress in Member?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

d = \frac{3 \cdot 800N*m}{2 \cdot 1.3E+6Pa \cdot 0.09m \cdot 0.051m}

Next Step Prepare to Evaluate

∴

d = \frac{3 \cdot 800}{2 \cdot 1.3E+6 \cdot 0.09 \cdot 0.051}

Next Step Evaluate

∴

d = 0.199999930000025m

Next Step Convert to Output's Unit

∴

d = 199.999930000025mm

LAST Step Rounding Answer

∴

d = 199.9999mm

Cross Section Depth given Radial Stress in Member Formula Elements

Variables

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

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

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

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 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}

How to Evaluate Cross Section Depth given Radial Stress in Member?

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

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

FAQs on Cross Section Depth given Radial Stress in Member

What is the formula to find Cross Section Depth given Radial Stress in Member?

The formula of Cross Section Depth given Radial Stress in Member is expressed as Depth of Cross Section = (3*Bending Moment for Radial Stress)/(2*Radial Stress*Radius of Curvature at Centerline of Member*Width of Cross Section). Here is an example- 199999.9 = (3*800)/(2*1307190*0.09*0.051).

How to calculate Cross Section Depth given Radial Stress in Member?

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

Can the Cross Section Depth given Radial Stress in Member be negative?

No, the Cross Section Depth given Radial Stress in Member, measured in Length cannot be negative.

Which unit is used to measure Cross Section Depth given Radial Stress in Member?

Cross Section Depth 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 Cross Section Depth given Radial Stress in Member can be measured.

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Cross Section Depth given Radial Stress in Member Formula

Cross Section Depth given Radial Stress in Member Example

Cross Section Depth given Radial Stress in Member Solution

Cross Section Depth given Radial Stress in Member Formula Elements

Other formulas in Radial Stresses and Curvature Factor category

How to Evaluate Cross Section Depth given Radial Stress in Member?

FAQs on Cross Section Depth given Radial Stress in Member

Variable Name