Radial Stress Induced by Bending Moment in Member Solution

STEP 0: Pre-Calculation Summary
Formula Used
Radial Stress = 3*Bending Moment for Radial Stress/(2*Radius of Curvature at Centerline of Member*Width of Cross Section*Depth of Cross Section)
σr = 3*M'b/(2*R*w*d)
This formula uses 5 Variables
Variables Used
Radial Stress - (Measured in Pascal) - The radial stress induced by a bending moment in a member of constant cross-section.
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.
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
Bending Moment for Radial Stress: 800 Newton Meter --> 800 Newton Meter No Conversion Required
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
σr = 3*M'b/(2*R*w*d) --> 3*800/(2*0.09*0.051*0.2)
Evaluating ... ...
σr = 1307189.54248366
STEP 3: Convert Result to Output's Unit
1307189.54248366 Pascal -->1.30718954248366 Megapascal (Check conversion here)
FINAL ANSWER
1.30718954248366 1.30719 Megapascal <-- Radial Stress
(Calculation completed in 00.020 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)

Radial Stress Induced by Bending Moment in Member 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)
σr = 3*M'b/(2*R*w*d)

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.

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. The most common or simplest structural element subjected to bending moments is the beam.

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

Radial Stress Induced by Bending Moment in Member calculator 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 calculate 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 σr symbol.

How to calculate Radial Stress Induced by Bending Moment in Member using this online calculator? To use this online calculator 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. Here is how the Radial Stress Induced by Bending Moment in Member calculation can be explained with given input values -> 1.3E-6 = 3*800/(2*0.09*0.051*0.2).

FAQ

What is Radial Stress Induced by Bending Moment in Member?
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 and is represented as σr = 3*M'b/(2*R*w*d) or 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 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, 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 Radial Stress Induced by Bending Moment in Member?
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 is calculated using 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 calculate Radial Stress Induced by Bending Moment in Member, you need 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). With our tool, you need to enter the respective value for Bending Moment 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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