Bending moment in curved beam given bending stress at outer fibre Calculator

✖Bending Stress at Outer Fibre is the amount of bending moment at the outer fiber of a curved structural element.ⓘ Bending Stress at Outer Fibre [σ_bo]			+10% -10%
✖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.ⓘ Cross sectional area of curved beam [A]			+10% -10%
✖Eccentricity Between Centroidal and Neutral Axis is the distance between the centroidal and the neutral axis of a curved structural element.ⓘ Eccentricity Between Centroidal and Neutral Axis [e]			+10% -10%
✖Radius of Outer Fibre is the radius of the outer fiber of a curved structural element.ⓘ Radius of Outer Fibre [R_o]			+10% -10%
✖Distance of Outer Fibre from Neutral Axis is the point where the fibers of a material undergoing bending are stretched maximum.ⓘ Distance of Outer Fibre from Neutral Axis [h_o]			+10% -10%

✖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 moment in curved beam given bending stress at outer fibre [M_b]

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Formula

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Bending moment in curved beam given bending stress at outer fibre

Formula

`"M"_{"b"} = (("σ"_{"b"}"o")*("A")*"e"*("R"_{"o"}))/("h"_{"o"})`

Example

`"994500N*mm"=("85N/mm²"*("240mm²")*"6.5mm"*("90mm"))/("12mm")`

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

STEP 0: Pre-Calculation Summary

Formula Used

Bending moment in curved beam = (Bending Stress at Outer Fibre*(Cross sectional area of curved beam)*Eccentricity Between Centroidal and Neutral Axis*(Radius of Outer Fibre))/(Distance of Outer Fibre from Neutral Axis)
M_b = (σ_bo*(A)*e*(R_o))/(h_o)
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 Outer Fibre - (Measured in Pascal) - Bending Stress at Outer Fibre is the amount of bending moment at the outer fiber of a curved structural element.
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 Outer Fibre - (Measured in Meter) - Radius of Outer Fibre is the radius of the outer fiber of a curved structural element.
Distance of Outer Fibre from Neutral Axis - (Measured in Meter) - Distance of Outer Fibre from Neutral Axis is the point where the fibers of a material undergoing bending are stretched maximum.

STEP 1: Convert Input(s) to Base Unit

Bending Stress at Outer Fibre: 85 Newton per Square Millimeter --> 85000000 Pascal (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 Outer Fibre: 90 Millimeter --> 0.09 Meter (Check conversion here)
Distance of Outer Fibre from Neutral Axis: 12 Millimeter --> 0.012 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_b = (σ_bo*(A)*e*(R_o))/(h_o) --> (85000000*(0.00024)*0.0065*(0.09))/(0.012)

Evaluating ... ...

M_b = 994.5

STEP 3: Convert Result to Output's Unit

994.5 Newton Meter -->994500 Newton Millimeter (Check conversion here)

FINAL ANSWER

994500 Newton Millimeter <-- Bending moment in curved beam

(Calculation completed in 00.007 seconds)

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< 20 Design of Curved Beams Calculators

Bending stress in fibre of curved beam given radius of centroidal axis

Go 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)))

Bending moment at fibre of curved beam given bending stress and radius of centroidal axis

Go 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

Bending stress in fibre of curved beam given eccentricity

Go 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 in fiber of curved beam

Go 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 at fibre of curved beam given bending stress and eccentricity

Go 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

Eccentricity between centroidal and neutral axis of curved beam given bending stress at inner fibre

Go Eccentricity Between Centroidal and Neutral Axis = (Bending moment in curved beam*Distance of Inner Fibre from Neutral Axis)/((Cross sectional area of curved beam)*Bending Stress at Inner Fibre*(Radius of Inner Fibre))

Eccentricity between centroidal and neutral axis of curved beam given bending stress at outer fibre

Go Eccentricity Between Centroidal and Neutral Axis = (Bending moment in curved beam*Distance of Outer Fibre from Neutral Axis)/((Cross sectional area of curved beam)*Bending Stress at Outer Fibre*(Radius of Outer Fibre))

Distance of inner fiber from neutral axis of curved beam given bending stress at fibre

Go 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)

Distance of outer fibre from neutral axis of curved beam given bending stress at fibre

Go Distance of Outer Fibre from Neutral Axis = (Bending Stress at Outer Fibre*(Cross sectional area of curved beam)*Eccentricity Between Centroidal and Neutral Axis*(Radius of Outer Fibre))/(Bending moment in curved beam)

Area of cross section of curved beam given bending stress at inner fiber

Go Cross sectional area of curved beam = (Bending moment in curved beam*Distance of Inner Fibre from Neutral Axis)/((Eccentricity Between Centroidal and Neutral Axis)*Bending Stress at Inner Fibre*(Radius of Inner Fibre))

Area of cross section of curved beam given bending stress at outer fiber

Go Cross sectional area of curved beam = (Bending moment in curved beam*Distance of Outer Fibre from Neutral Axis)/((Eccentricity Between Centroidal and Neutral Axis)*Bending Stress at Outer Fibre*(Radius of Outer Fibre))

Bending stress at inner fibre of curved beam given bending moment

Go 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))

Bending moment in curved beam given bending stress at inner fibre

Go 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)

Bending stress at outer fibre of curved beam given bending moment

Go Bending Stress at Outer Fibre = (Bending moment in curved beam*Distance of Outer Fibre from Neutral Axis)/((Cross sectional area of curved beam)*Eccentricity Between Centroidal and Neutral Axis*(Radius of Outer Fibre))

Bending moment in curved beam given bending stress at outer fibre

Go Bending moment in curved beam = (Bending Stress at Outer Fibre*(Cross sectional area of curved beam)*Eccentricity Between Centroidal and Neutral Axis*(Radius of Outer Fibre))/(Distance of Outer Fibre from Neutral Axis)

Distance of fibre from neutral axis of rectangular curved beam given inner and outer fiber radius

Go Distance from Neutral Axis of Curved Beam = (Radius of Inner Fibre)*ln(Radius of Outer Fibre/Radius of Inner Fibre)

Eccentricity between centroidal and neutral axis of curved beam given radius of both axis

Go Eccentricity Between Centroidal and Neutral Axis = Radius of Centroidal Axis-Radius of Neutral Axis

Eccentricity between central and neutral axis of curved beam

Go Eccentricity Between Centroidal and Neutral Axis = Radius of Centroidal Axis-Radius of Neutral Axis

Distance of fibre from neutral axis of rectangular curved beam given radius of centroidal axis

Go Distance from Neutral Axis of Curved Beam = 2*(Radius of Centroidal Axis-Radius of Inner Fibre)

Diameter of circular curved beam given radius of centroidal axis

Go Diameter of circular curved beam = 2*(Radius of Centroidal Axis-Radius of Inner Fibre)

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

What is meant by stress strain diagram?

A stress-strain diagram or stress-strain curve is used to illustrate the relationship between a material's stress and strain. A stress-strain curve can be constructed from data obtained in any mechanical test where the load is applied to a material and continuous measurements of stress and strain are made simultaneously.

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

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

How to calculate Bending moment in curved beam given bending stress at outer fibre using this online calculator? To use this online calculator for Bending moment in curved beam given bending stress at outer fibre, enter Bending Stress at Outer Fibre (σ_bo), Cross sectional area of curved beam (A), Eccentricity Between Centroidal and Neutral Axis (e), Radius of Outer Fibre (R_o) & Distance of Outer Fibre from Neutral Axis (h_o) and hit the calculate button. Here is how the Bending moment in curved beam given bending stress at outer fibre calculation can be explained with given input values -> 9.9E+8 = (85000000*(0.00024)*0.0065*(0.09))/(0.012).

FAQ

What is Bending moment in curved beam given bending stress at outer fibre?

Bending moment in curved beam given bending stress at outer fibre is the amount of bending moment at the outermost fibre of the curved beam and arises due to the force responsible for the curvature of the beam and is represented as M_b = (σ_bo*(A)*e*(R_o))/(h_o) or Bending moment in curved beam = (Bending Stress at Outer Fibre*(Cross sectional area of curved beam)*Eccentricity Between Centroidal and Neutral Axis*(Radius of Outer Fibre))/(Distance of Outer Fibre from Neutral Axis). Bending Stress at Outer Fibre is the amount of bending moment at the outer fiber of a curved structural element, 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 Outer Fibre is the radius of the outer fiber of a curved structural element & Distance of Outer Fibre from Neutral Axis is the point where the fibers of a material undergoing bending are stretched maximum.

How to calculate Bending moment in curved beam given bending stress at outer fibre?

Bending moment in curved beam given bending stress at outer fibre is the amount of bending moment at the outermost fibre of 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 Outer Fibre*(Cross sectional area of curved beam)*Eccentricity Between Centroidal and Neutral Axis*(Radius of Outer Fibre))/(Distance of Outer Fibre from Neutral Axis). To calculate Bending moment in curved beam given bending stress at outer fibre, you need Bending Stress at Outer Fibre (σ_bo), Cross sectional area of curved beam (A), Eccentricity Between Centroidal and Neutral Axis (e), Radius of Outer Fibre (R_o) & Distance of Outer Fibre from Neutral Axis (h_o). With our tool, you need to enter the respective value for Bending Stress at Outer Fibre, Cross sectional area of curved beam, Eccentricity Between Centroidal and Neutral Axis, Radius of Outer Fibre & Distance of Outer 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 Outer Fibre, Cross sectional area of curved beam, Eccentricity Between Centroidal and Neutral Axis, Radius of Outer Fibre & Distance of Outer 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 of curved beam*(Radius of Centroidal Axis-Radius of Neutral Axis)*(Eccentricity Between Centroidal and Neutral Axis)))/Distance from Neutral Axis of Curved Beam
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
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)

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