Bending Moment given Radial Stress in Member Calculator

✖The radial stress induced by a bending moment in a member of constant cross-section.ⓘ Radial Stress [σ_r]			+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 at Centerline of Member [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%

✖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 given Radial Stress in Member [M'_b]

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Formula

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Bending Moment given Radial Stress in Member

Formula

`"M'"_{"b"} = (2*"σ"_{"r"}*"R"*"w"*"d")/3`

Example

`"800.0003N*m"=(2*"1.30719MPa"*"90mm"*"51mm"*"200mm")/3`

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Bending Moment given Radial Stress in Member Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
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

Radial Stress: 1.30719 Megapascal --> 1307190 Pascal (Check conversion here)
Radius of Curvature at Centerline of Member: 90 Millimeter --> 0.09 Meter (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

M'_b = (2*σ_r*R*w*d)/3 --> (2*1307190*0.09*0.051*0.2)/3

Evaluating ... ...

M'_b = 800.00028

STEP 3: Convert Result to Output's Unit

800.00028 Newton Meter --> No Conversion Required

FINAL ANSWER

800.00028 ≈ 800.0003 Newton Meter <-- Bending Moment for Radial Stress

(Calculation completed in 00.004 seconds)

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< 7 Radial Stresses and Curvature Factor Calculators

Radius of Curvature given Radial Stress in Member

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

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)

Cross Section Depth given Radial Stress in Member

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

Radial Stress Induced by Bending Moment in Member

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

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

Curvature Factor for Adjustment in Design Value for Curved Portions of Wood

Go Curvature Factor = 1-(2000*(Lamination Thickness/Radius of Curvature at Centerline of Member)^2)

Size Factor for Adjustment in Design Value for Bending

Go Size Factor = (12/Depth of Cross Section)^(1/9)

Bending Moment given Radial Stress in Member Formula

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

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 Bending Moment given Radial Stress in Member?

Bending Moment given Radial Stress in Member calculator uses Bending Moment for Radial Stress = (2*Radial Stress*Radius of Curvature at Centerline of Member*Width of Cross Section*Depth of Cross Section)/3 to calculate the Bending Moment for Radial Stress, The Bending Moment given Radial Stress in Member formula is defined by the parameters such as radius of curvature at the centerline of the member, the width and depth of the cross-section. Bending Moment for Radial Stress is denoted by M'_b symbol.

How to calculate Bending Moment given Radial Stress in Member using this online calculator? To use this online calculator for Bending Moment given Radial Stress in Member, enter Radial Stress (σ_r), Radius of Curvature at Centerline of Member (R), Width of Cross Section (w) & Depth of Cross Section (d) and hit the calculate button. Here is how the Bending Moment given Radial Stress in Member calculation can be explained with given input values -> 800.0003 = (2*1307190*0.09*0.051*0.2)/3.

FAQ

What is Bending Moment given Radial Stress in Member?

The Bending Moment given Radial Stress in Member formula is defined by the parameters such as radius of curvature at the centerline of the member, the width and depth of the cross-section and is represented as M'_b = (2*σ_r*R*w*d)/3 or Bending Moment for Radial Stress = (2*Radial Stress*Radius of Curvature at Centerline of Member*Width of Cross Section*Depth of Cross Section)/3. The radial stress induced by a bending moment in a member of constant cross-section, Radius of Curvature at Centerline of Member in mm is the radius of the circle that touches the curve at a given point, 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 Bending Moment given Radial Stress in Member?

The Bending Moment given Radial Stress in Member formula is defined by the parameters such as radius of curvature at the centerline of the member, the width and depth of the cross-section is calculated using Bending Moment for Radial Stress = (2*Radial Stress*Radius of Curvature at Centerline of Member*Width of Cross Section*Depth of Cross Section)/3. To calculate Bending Moment given Radial Stress in Member, you need Radial Stress (σ_r), Radius of Curvature at Centerline of Member (R), Width of Cross Section (w) & Depth of Cross Section (d). With our tool, you need to enter the respective value for Radial Stress, Radius of Curvature at Centerline of Member, 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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