Bending moment in curved beam given bending stress at inner fibre Solution

STEP 0: Pre-Calculation Summary
Formula Used
Bending moment in curved beam = (Bending Stress at Inner Fibre*(Cross Sectional Area)*Eccentricity Between Centroidal and Neutral Axis*(Radius of Inner Fibre))/(Distance of Inner Fibre from Neutral Axis)
Mb = (b)i*(A)*e*(Ri))/(hi)
This formula uses 6 Variables
Variables Used
Bending moment in curved beam - (Measured in Newton Meter) - Bending moment in curved beam 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 Stress at Inner Fibre - (Measured in Pascal) - Bending Stress at Inner Fibre is the amount of bending moment at the inner fibre of a curved structural element.
Cross Sectional Area - (Measured in Square Meter) - Cross sectional area is the area of a two-dimensional shape that is obtained when a three-dimensional shape is sliced perpendicular to some specified axis at a point.
Eccentricity Between Centroidal and Neutral Axis - (Measured in Meter) - Eccentricity Between Centroidal and Neutral Axis is the distance between the centroidal and the neutral axis of a curved structural element.
Radius of Inner Fibre - (Measured in Meter) - Radius of Inner Fibre is the radius of the inner fibre of a curved structural elementt.
Distance of Inner Fibre from Neutral Axis - (Measured in Meter) - Distance of Inner Fibre from Neutral Axis is the point where the fibers of a material undergoing bending is stretched maximum.
STEP 1: Convert Input(s) to Base Unit
Bending Stress at Inner Fibre: 80 Newton per Square Millimeter --> 80000000 Pascal (Check conversion here)
Cross Sectional Area: 240 Square Millimeter --> 0.00024 Square Meter (Check conversion here)
Eccentricity Between Centroidal and Neutral Axis: 6.5 Millimeter --> 0.0065 Meter (Check conversion here)
Radius of Inner Fibre: 70 Millimeter --> 0.07 Meter (Check conversion here)
Distance of Inner Fibre from Neutral Axis: 10 Millimeter --> 0.01 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Mb = ((σb)i*(A)*e*(Ri))/(hi) --> (80000000*(0.00024)*0.0065*(0.07))/(0.01)
Evaluating ... ...
Mb = 873.6
STEP 3: Convert Result to Output's Unit
873.6 Newton Meter -->873600 Newton Millimeter (Check conversion here)
FINAL ANSWER
873600 Newton Millimeter <-- Bending moment in curved beam
(Calculation completed in 00.047 seconds)

Credits

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Shri Govindram Seksaria Institute of Technology and Science (SGSITS ), Indore
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10+ Design of curved beams Calculators

Bending stress in fibre of curved beam given radius of centroidal axis
Bending Stress = ((Bending moment in curved beam*Distance from Neutral Axis)/(Cross Sectional Area*(Radius of Centroidal Axis-Radius of Neutral Axis)*(Radius of Neutral Axis-Distance from Neutral Axis))) Go
Bending moment at fibre of curved beam given bending stress and radius of centroidal axis
Bending moment in curved beam = (Bending Stress*(Cross Sectional Area*(Radius of Centroidal Axis-Radius of Neutral Axis)*(Radius of Neutral Axis-Distance from Neutral Axis)))/Distance from Neutral Axis Go
Bending stress in fibre of curved beam given eccentricity
Bending Stress = ((Bending moment in curved beam*Distance from Neutral Axis)/(Cross Sectional Area*(Eccentricity Between Centroidal and Neutral Axis)*(Radius of Neutral Axis-Distance from Neutral Axis))) Go
Bending stress at fiber
Bending Stress = (Bending moment in curved beam*Distance from Neutral Axis)/(Cross Sectional Area*(Eccentricity Between Centroidal and Neutral Axis)*(Radius of Neutral Axis-Distance from Neutral Axis)) Go
Bending moment at fibre of curved beam given bending stress and eccentricity
Bending moment in curved beam = (Bending Stress*(Cross Sectional Area*(Radius of Centroidal Axis-Radius of Neutral Axis)*(Eccentricity Between Centroidal and Neutral Axis)))/Distance from Neutral Axis Go
Bending stress at inner fibre of curved beam given bending moment
Bending Stress at Inner Fibre = (Bending moment in curved beam*Distance of Inner Fibre from Neutral Axis)/((Cross Sectional Area)*Eccentricity Between Centroidal and Neutral Axis*(Radius of Inner Fibre)) Go
Bending stress at inner fiber
Bending Stress = (Bending moment in curved beam*Distance of Inner Fibre from Neutral Axis)/(Cross Sectional Area*Eccentricity Between Centroidal and Neutral Axis*Radius of Inner Fibre) Go
Bending stress at outer fiber
Bending Stress = (Bending moment in curved beam*Distance of Outer Fibre from Neutral Axis)/(Cross Sectional Area*Eccentricity Between Centroidal and Neutral Axis*Radius of Outer Fibre) Go
Eccentricity between centroidal and neutral axis of curved beam given radius of both axis
Eccentricity Between Centroidal and Neutral Axis = Radius of Centroidal Axis-Radius of Neutral Axis Go
Eccentricity between central and neutral axis
Eccentricity Between Centroidal and Neutral Axis = Radius of Centroidal Axis-Radius of Neutral Axis Go

Bending moment in curved beam given bending stress at inner fibre Formula

Bending moment in curved beam = (Bending Stress at Inner Fibre*(Cross Sectional Area)*Eccentricity Between Centroidal and Neutral Axis*(Radius of Inner Fibre))/(Distance of Inner Fibre from Neutral Axis)
Mb = (b)i*(A)*e*(Ri))/(hi)

What is fracture point?

The Fracture Point can be defined as the breaking limit of material beyond which if further stress is applied it will rupture and break apart. It is basically a material strength gauging parameter.

How to Calculate Bending moment in curved beam given bending stress at inner fibre?

Bending moment in curved beam given bending stress at inner fibre calculator uses Bending moment in curved beam = (Bending Stress at Inner Fibre*(Cross Sectional Area)*Eccentricity Between Centroidal and Neutral Axis*(Radius of Inner Fibre))/(Distance of Inner Fibre from Neutral Axis) to calculate the Bending moment in curved beam, Bending moment in curved beam given bending stress at inner fibre is the amount of bending moment at the curved beam and arises due to the force responsible for the curvature of the beam. Bending moment in curved beam is denoted by Mb symbol.

How to calculate Bending moment in curved beam given bending stress at inner fibre using this online calculator? To use this online calculator for Bending moment in curved beam given bending stress at inner fibre, enter Bending Stress at Inner Fibre ((σb)i), Cross Sectional Area (A), Eccentricity Between Centroidal and Neutral Axis (e), Radius of Inner Fibre (Ri) & Distance of Inner Fibre from Neutral Axis (hi) and hit the calculate button. Here is how the Bending moment in curved beam given bending stress at inner fibre calculation can be explained with given input values -> 72800 = (30000000*(0.00024)*0.0065*(0.07))/(0.045).

FAQ

What is Bending moment in curved beam given bending stress at inner fibre?
Bending moment in curved beam given bending stress at inner fibre is the amount of bending moment at the curved beam and arises due to the force responsible for the curvature of the beam and is represented as Mb = (b)i*(A)*e*(Ri))/(hi) or Bending moment in curved beam = (Bending Stress at Inner Fibre*(Cross Sectional Area)*Eccentricity Between Centroidal and Neutral Axis*(Radius of Inner Fibre))/(Distance of Inner Fibre from Neutral Axis). Bending Stress at Inner Fibre is the amount of bending moment at the inner fibre of a curved structural element, Cross sectional area is the area of a two-dimensional shape that is obtained when a three-dimensional shape is sliced perpendicular to some specified axis at a point, Eccentricity Between Centroidal and Neutral Axis is the distance between the centroidal and the neutral axis of a curved structural element, Radius of Inner Fibre is the radius of the inner fibre of a curved structural elementt & Distance of Inner Fibre from Neutral Axis is the point where the fibers of a material undergoing bending is stretched maximum.
How to calculate Bending moment in curved beam given bending stress at inner fibre?
Bending moment in curved beam given bending stress at inner fibre is the amount of bending moment at the curved beam and arises due to the force responsible for the curvature of the beam is calculated using Bending moment in curved beam = (Bending Stress at Inner Fibre*(Cross Sectional Area)*Eccentricity Between Centroidal and Neutral Axis*(Radius of Inner Fibre))/(Distance of Inner Fibre from Neutral Axis). To calculate Bending moment in curved beam given bending stress at inner fibre, you need Bending Stress at Inner Fibre ((σb)i), Cross Sectional Area (A), Eccentricity Between Centroidal and Neutral Axis (e), Radius of Inner Fibre (Ri) & Distance of Inner Fibre from Neutral Axis (hi). With our tool, you need to enter the respective value for Bending Stress at Inner Fibre, Cross Sectional Area, Eccentricity Between Centroidal and Neutral Axis, Radius of Inner Fibre & Distance of Inner Fibre from Neutral Axis and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Bending moment in curved beam?
In this formula, Bending moment in curved beam uses Bending Stress at Inner Fibre, Cross Sectional Area, Eccentricity Between Centroidal and Neutral Axis, Radius of Inner Fibre & Distance of Inner Fibre from Neutral Axis. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Bending moment in curved beam = (Bending Stress*(Cross Sectional Area*(Radius of Centroidal Axis-Radius of Neutral Axis)*(Eccentricity Between Centroidal and Neutral Axis)))/Distance from Neutral Axis
  • Bending moment in curved beam = (Bending Stress*(Cross Sectional Area*(Radius of Centroidal Axis-Radius of Neutral Axis)*(Radius of Neutral Axis-Distance from Neutral Axis)))/Distance from Neutral Axis
  • Bending moment in curved beam = (Bending Stress at Outer Fibre*(Cross Sectional Area)*Eccentricity Between Centroidal and Neutral Axis*(Radius of Outer Fibre))/(Distance of Outer Fibre from Neutral Axis)
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