Radius of Curvature given Radial Stress in Member Calculator

✖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.ⓘ Bending Moment for Radial Stress [M'_b]			+10% -10%
✖The radial stress induced by a bending moment in a member of constant cross-section.ⓘ Radial Stress [σ_r]			+10% -10%
✖Width of Cross Section defines the geometric measurement or extent of the member from side to side.ⓘ Width of Cross Section [w]			+10% -10%
✖Depth of Cross Section (Height), in (mm) defines the geometrical measure from head to foot or from base to top of the section considered.ⓘ Depth of Cross Section [d]			+10% -10%

✖Radius of Curvature at Centerline of Member in mm is the radius of the circle that touches the curve at a given point.ⓘ Radius of Curvature given Radial Stress in Member [R]

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Radius of Curvature given Radial Stress in Member Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Curvature at Centerline of Member = (3*Bending Moment for Radial Stress)/(2*Radial Stress*Width of Cross Section*Depth of Cross Section)
R = (3*M'_b)/(2*σ_r*w*d)
This formula uses 5 Variables

Variables Used

Radius of Curvature at Centerline of Member - (Measured in Meter) - Radius of Curvature at Centerline of Member in mm is the radius of the circle that touches the curve at a given point.
Bending Moment for Radial Stress - (Measured in Newton Meter) - 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.
Radial Stress - (Measured in Pascal) - The radial stress induced by a bending moment in a member of constant cross-section.
Width of Cross Section - (Measured in Meter) - Width of Cross Section defines the geometric measurement or extent of the member from side to side.
Depth of Cross Section - (Measured in Meter) - Depth of Cross Section (Height), in (mm) defines the geometrical measure from head to foot or from base to top of the section considered.

STEP 1: Convert Input(s) to Base Unit

Bending Moment for Radial Stress: 800 Newton Meter --> 800 Newton Meter No Conversion Required
Radial Stress: 1.30719 Megapascal --> 1307190 Pascal (Check conversion here)
Width of Cross Section: 51 Millimeter --> 0.051 Meter (Check conversion here)
Depth of Cross Section: 200 Millimeter --> 0.2 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R = (3*M'_b)/(2*σ_r*w*d) --> (3*800)/(2*1307190*0.051*0.2)

Evaluating ... ...

R = 0.089999968500011

STEP 3: Convert Result to Output's Unit

0.089999968500011 Meter -->89.999968500011 Millimeter (Check conversion here)

FINAL ANSWER

89.999968500011 ≈ 89.99997 Millimeter <-- Radius of Curvature at Centerline of Member

(Calculation completed in 00.020 seconds)

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< Radial Stresses and Curvature Factor Calculators

Radius of Curvature given Radial Stress in Member

LaTeX Go Radius of Curvature at Centerline of Member = (3*Bending Moment for Radial Stress)/(2*Radial Stress*Width of Cross Section*Depth of Cross Section)

Cross Section Width given Radial Stress in Member

LaTeX Go Width of Cross Section = (3*Bending Moment for Radial Stress)/(2*Radial Stress*Radius of Curvature at Centerline of Member*Depth of Cross Section)

Radial Stress Induced by Bending Moment in Member

LaTeX Go Radial Stress = 3*Bending Moment for Radial Stress/(2*Radius of Curvature at Centerline of Member*Width of Cross Section*Depth of Cross Section)

Bending Moment given Radial Stress in Member

LaTeX Go Bending Moment for Radial Stress = (2*Radial Stress*Radius of Curvature at Centerline of Member*Width of Cross Section*Depth of Cross Section)/3

Radius of Curvature given Radial Stress in Member Formula

LaTeX Go

Radius of Curvature at Centerline of Member = (3*Bending Moment for Radial Stress)/(2*Radial Stress*Width of Cross Section*Depth of Cross Section)
R = (3*M'_b)/(2*σ_r*w*d)

What is Bending Moment?

Bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.

What is Radial Stress?

Radial stress is stress towards or away from the central axis of a component. Radial stresses in curved beams are generally computed using only the bending moment.

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

Radius of Curvature given Radial Stress in Member calculator 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 calculate 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 calculate Radius of Curvature given Radial Stress in Member using this online calculator? To use this online calculator 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. Here is how the Radius of Curvature given Radial Stress in Member calculation can be explained with given input values -> 89999.97 = (3*800)/(2*1307190*0.051*0.2).

FAQ

What is Radius of Curvature given Radial Stress in 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 and is represented as R = (3*M'_b)/(2*σ_r*w*d) or Radius of Curvature at Centerline of Member = (3*Bending Moment for Radial Stress)/(2*Radial Stress*Width of Cross Section*Depth of Cross Section). 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, The radial stress induced by a bending moment in a member of constant cross-section, Width of Cross Section defines the geometric measurement or extent of the member from side to side & Depth of Cross Section (Height), in (mm) defines the geometrical measure from head to foot or from base to top of the section considered.

How to calculate Radius of Curvature given Radial Stress in 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 is calculated using 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 calculate Radius of Curvature given Radial Stress in Member, you need Bending Moment for Radial Stress (M'_b), Radial Stress (σ_r), Width of Cross Section (w) & Depth of Cross Section (d). With our tool, you need to enter the respective value for Bending Moment for Radial Stress, Radial Stress, Width of Cross Section & Depth of Cross Section and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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