Bending stress in fibre of curved beam given eccentricity Solution

STEP 0: Pre-Calculation Summary
Formula Used
Bending Stress = ((Bending moment in curved beam*Distance from Neutral Axis of Curved Beam)/(Cross sectional area of curved beam*(Eccentricity Between Centroidal and Neutral Axis)*(Radius of Neutral Axis-Distance from Neutral Axis of Curved Beam)))
σb = ((Mb*y)/(A*(e)*(RN-y)))
This formula uses 6 Variables
Variables Used
Bending Stress - (Measured in Pascal) - Bending stress or allowable bending stress is the amount of bending stress that can be generated in a material before its failure or fracture.
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.
Distance from Neutral Axis of Curved Beam - (Measured in Meter) - Distance from Neutral Axis of Curved Beam is defined as the distance from an axis in the cross-section of a curved beam along which there are no longitudinal stresses or strains.
Cross sectional area of curved beam - (Measured in Square Meter) - Cross sectional area of curved beam is the area of a two-dimensional section that is obtained when a beam 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 Neutral Axis - (Measured in Meter) - Radius of Neutral Axis is the radius of the axis of the curved beam passing through the points which have zero stress on them.
STEP 1: Convert Input(s) to Base Unit
Bending moment in curved beam: 985000 Newton Millimeter --> 985 Newton Meter (Check conversion here)
Distance from Neutral Axis of Curved Beam: 21 Millimeter --> 0.021 Meter (Check conversion here)
Cross sectional area of curved beam: 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 Neutral Axis: 78 Millimeter --> 0.078 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
σb = ((Mb*y)/(A*(e)*(RN-y))) --> ((985*0.021)/(0.00024*(0.0065)*(0.078-0.021)))
Evaluating ... ...
σb = 232624831.309042
STEP 3: Convert Result to Output's Unit
232624831.309042 Pascal -->232.624831309042 Newton per Square Millimeter (Check conversion here)
FINAL ANSWER
232.624831309042 Newton per Square Millimeter <-- Bending Stress
(Calculation completed in 00.047 seconds)

Credits

Created by Saurabh Patil
Shri Govindram Seksaria Institute of Technology and Science (SGSITS ), Indore
Saurabh Patil has created this Calculator and 700+ more calculators!
Verified by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
Anshika Arya has verified this Calculator and 2600+ more calculators!

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 of Curved Beam)/(Cross sectional area of curved beam*(Radius of Centroidal Axis-Radius of Neutral Axis)*(Radius of Neutral Axis-Distance from Neutral Axis of Curved Beam))) 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 of curved beam*(Radius of Centroidal Axis-Radius of Neutral Axis)*(Radius of Neutral Axis-Distance from Neutral Axis of Curved Beam)))/Distance from Neutral Axis of Curved Beam Go
Bending stress in fibre of curved beam given eccentricity
Bending Stress = ((Bending moment in curved beam*Distance from Neutral Axis of Curved Beam)/(Cross sectional area of curved beam*(Eccentricity Between Centroidal and Neutral Axis)*(Radius of Neutral Axis-Distance from Neutral Axis of Curved Beam))) Go
Bending stress in fiber of curved beam
Bending Stress = (Bending moment in curved beam*Distance from Neutral Axis of Curved Beam)/(Cross sectional area of curved beam*(Eccentricity Between Centroidal and Neutral Axis)*(Radius of Neutral Axis-Distance from Neutral Axis of Curved Beam)) Go
Bending moment at fibre of curved beam given bending stress and eccentricity
Bending moment in curved beam = (Bending Stress*(Cross sectional area of curved beam*(Radius of Centroidal Axis-Radius of Neutral Axis)*(Eccentricity Between Centroidal and Neutral Axis)))/Distance from Neutral Axis of Curved Beam Go
Distance of inner fiber from neutral axis of curved beam given bending stress at fibre
Distance of Inner Fibre from Neutral Axis = (Bending Stress at Inner Fibre*(Cross sectional area of curved beam)*Eccentricity Between Centroidal and Neutral Axis*(Radius of Inner Fibre))/(Bending moment in curved beam) 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 of curved beam)*Eccentricity Between Centroidal and Neutral Axis*(Radius of Inner Fibre)) Go
Bending moment in curved beam given bending stress at inner fibre
Bending moment in curved beam = (Bending Stress at Inner Fibre*(Cross sectional area of curved beam)*Eccentricity Between Centroidal and Neutral Axis*(Radius of Inner Fibre))/(Distance of Inner Fibre from Neutral Axis) 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 of curved beam
Eccentricity Between Centroidal and Neutral Axis = Radius of Centroidal Axis-Radius of Neutral Axis Go

Bending stress in fibre of curved beam given eccentricity Formula

Bending Stress = ((Bending moment in curved beam*Distance from Neutral Axis of Curved Beam)/(Cross sectional area of curved beam*(Eccentricity Between Centroidal and Neutral Axis)*(Radius of Neutral Axis-Distance from Neutral Axis of Curved Beam)))
σb = ((Mb*y)/(A*(e)*(RN-y)))

What is curved beam?

A curved beam is defined as a beam in which the neutral axis in the unloaded condition is curved instead of straight. The following assumptions are made in the stress analysis of curved beam:
(i) Plane sections perpendicular to the axis of the beam remain plane after bending.
(ii) The moduli of elasticity in tension and compression are equal.
(iii) The material is homogeneous and obeys Hooke’s law.

How to Calculate Bending stress in fibre of curved beam given eccentricity?

Bending stress in fibre of curved beam given eccentricity calculator uses Bending Stress = ((Bending moment in curved beam*Distance from Neutral Axis of Curved Beam)/(Cross sectional area of curved beam*(Eccentricity Between Centroidal and Neutral Axis)*(Radius of Neutral Axis-Distance from Neutral Axis of Curved Beam))) to calculate the Bending Stress, Bending stress in fibre of curved beam given eccentricity is the amount of bending stress induced into the fiber of a curved beam and usually, this fiber is in tension or compression. Bending Stress is denoted by σb symbol.

How to calculate Bending stress in fibre of curved beam given eccentricity using this online calculator? To use this online calculator for Bending stress in fibre of curved beam given eccentricity, enter Bending moment in curved beam (Mb), Distance from Neutral Axis of Curved Beam (y), Cross sectional area of curved beam (A), Eccentricity Between Centroidal and Neutral Axis (e) & Radius of Neutral Axis (RN) and hit the calculate button. Here is how the Bending stress in fibre of curved beam given eccentricity calculation can be explained with given input values -> 232.6248 = ((985*0.021)/(0.00024*(0.0065)*(0.078-0.021))).

FAQ

What is Bending stress in fibre of curved beam given eccentricity?
Bending stress in fibre of curved beam given eccentricity is the amount of bending stress induced into the fiber of a curved beam and usually, this fiber is in tension or compression and is represented as σb = ((Mb*y)/(A*(e)*(RN-y))) or Bending Stress = ((Bending moment in curved beam*Distance from Neutral Axis of Curved Beam)/(Cross sectional area of curved beam*(Eccentricity Between Centroidal and Neutral Axis)*(Radius of Neutral Axis-Distance from Neutral Axis of Curved Beam))). 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, Distance from Neutral Axis of Curved Beam is defined as the distance from an axis in the cross-section of a curved beam along which there are no longitudinal stresses or strains, Cross sectional area of curved beam is the area of a two-dimensional section that is obtained when a beam 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 Neutral Axis is the radius of the axis of the curved beam passing through the points which have zero stress on them.
How to calculate Bending stress in fibre of curved beam given eccentricity?
Bending stress in fibre of curved beam given eccentricity is the amount of bending stress induced into the fiber of a curved beam and usually, this fiber is in tension or compression is calculated using Bending Stress = ((Bending moment in curved beam*Distance from Neutral Axis of Curved Beam)/(Cross sectional area of curved beam*(Eccentricity Between Centroidal and Neutral Axis)*(Radius of Neutral Axis-Distance from Neutral Axis of Curved Beam))). To calculate Bending stress in fibre of curved beam given eccentricity, you need Bending moment in curved beam (Mb), Distance from Neutral Axis of Curved Beam (y), Cross sectional area of curved beam (A), Eccentricity Between Centroidal and Neutral Axis (e) & Radius of Neutral Axis (RN). With our tool, you need to enter the respective value for Bending moment in curved beam, Distance from Neutral Axis of Curved Beam, Cross sectional area of curved beam, Eccentricity Between Centroidal and Neutral Axis & Radius of 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 Stress?
In this formula, Bending Stress uses Bending moment in curved beam, Distance from Neutral Axis of Curved Beam, Cross sectional area of curved beam, Eccentricity Between Centroidal and Neutral Axis & Radius of Neutral Axis. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Bending Stress = (Bending moment in curved beam*Distance from Neutral Axis of Curved Beam)/(Cross sectional area of curved beam*(Eccentricity Between Centroidal and Neutral Axis)*(Radius of Neutral Axis-Distance from Neutral Axis of Curved Beam))
  • Bending Stress = ((Bending moment in curved beam*Distance from Neutral Axis of Curved Beam)/(Cross sectional area of curved beam*(Radius of Centroidal Axis-Radius of Neutral Axis)*(Radius of Neutral Axis-Distance from Neutral Axis of Curved Beam)))
Share Image
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!