Radius of inner fiber of curved beam given bending stress at fiber Calculator

✖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 [M_b]			+10% -10%
✖Distance of Inner Fibre from Neutral Axis is the point where the fibers of a material undergoing bending are stretched maximum.ⓘ Distance of Inner Fibre from Neutral Axis [h_i]			+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%
✖Bending Stress at Inner Fibre is the amount of bending moment at the inner fiber of a curved structural element.ⓘ Bending Stress at Inner Fibre [σ_bi]			+10% -10%

✖Radius of Inner Fibre is the radius of the inner fiber of a curved structural element.ⓘ Radius of inner fiber of curved beam given bending stress at fiber [R_i]

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Radius of inner fiber of curved beam given bending stress at fiber Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of 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*Bending Stress at Inner Fibre)
R_i = (M_b*h_i)/(A*e*σ_bi)
This formula uses 6 Variables

Variables Used

Radius of Inner Fibre - (Measured in Meter) - Radius of Inner Fibre is the radius of the inner fiber of a curved structural element.
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 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 are stretched maximum.
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.
Bending Stress at Inner Fibre - (Measured in Pascal) - Bending Stress at Inner Fibre is the amount of bending moment at the inner fiber of a curved structural element.

STEP 1: Convert Input(s) to Base Unit

Bending Moment in Curved Beam: 245000 Newton Millimeter --> 245 Newton Meter (Check conversion here)
Distance of Inner Fibre from Neutral Axis: 37.5 Millimeter --> 0.0375 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)
Bending Stress at Inner Fibre: 78.5 Newton per Square Millimeter --> 78500000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_i = (M_b*h_i)/(A*e*σ_bi) --> (245*0.0375)/(0.00024*0.0065*78500000)

Evaluating ... ...

R_i = 0.0750244977951984

STEP 3: Convert Result to Output's Unit

0.0750244977951984 Meter -->75.0244977951984 Millimeter (Check conversion here)

FINAL ANSWER

75.0244977951984 ≈ 75.0245 Millimeter <-- Radius of Inner Fibre

(Calculation completed in 00.020 seconds)

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< Radius of Fiber and Axis Calculators

Radius of centroidal axis of curved beam given bending stress

LaTeX Go Radius of Centroidal Axis = ((Bending Moment in Curved Beam*Distance from Neutral Axis of Curved Beam)/(Cross Sectional Area of Curved Beam*Bending Stress*(Radius of Neutral Axis-Distance from Neutral Axis of Curved Beam)))+Radius of Neutral Axis

Radius of neutral axis of curved beam given bending stress

LaTeX Go Radius of Neutral Axis = ((Bending Moment in Curved Beam*Distance from Neutral Axis of Curved Beam)/(Cross Sectional Area of Curved Beam*Bending Stress*Eccentricity Between Centroidal and Neutral Axis))+Distance from Neutral Axis of Curved Beam

Radius of centroidal axis of curved beam given eccentricity between axis

LaTeX Go Radius of Centroidal Axis = Radius of Neutral Axis+Eccentricity Between Centroidal and Neutral Axis

Radius of neutral axis of curved beam given eccentricity between axis

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

Radius of inner fiber of curved beam given bending stress at fiber Formula

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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 Radius of inner fiber of curved beam given bending stress at fiber?

Radius of inner fiber of curved beam given bending stress at fiber calculator uses Radius of 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*Bending Stress at Inner Fibre) to calculate the Radius of Inner Fibre, Radius of inner fiber of curved beam given bending stress at fiber is the radius of the innermost fiber of a curved beam and is the radius of curvature of the inner surface of the beam. Radius of Inner Fibre is denoted by R_i symbol.

How to calculate Radius of inner fiber of curved beam given bending stress at fiber using this online calculator? To use this online calculator for Radius of inner fiber of curved beam given bending stress at fiber, enter Bending Moment in Curved Beam (M_b), Distance of Inner Fibre from Neutral Axis (h_i), Cross Sectional Area of Curved Beam (A), Eccentricity Between Centroidal and Neutral Axis (e) & Bending Stress at Inner Fibre (σ_bi) and hit the calculate button. Here is how the Radius of inner fiber of curved beam given bending stress at fiber calculation can be explained with given input values -> 75024.5 = (245*0.0375)/(0.00024*0.0065*78500000).

FAQ

What is Radius of inner fiber of curved beam given bending stress at fiber?

Radius of inner fiber of curved beam given bending stress at fiber is the radius of the innermost fiber of a curved beam and is the radius of curvature of the inner surface of the beam and is represented as R_i = (M_b*h_i)/(A*e*σ_bi) or Radius of 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*Bending Stress at Inner Fibre). 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 of Inner Fibre from Neutral Axis is the point where the fibers of a material undergoing bending are stretched maximum, 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 & Bending Stress at Inner Fibre is the amount of bending moment at the inner fiber of a curved structural element.

How to calculate Radius of inner fiber of curved beam given bending stress at fiber?

Radius of inner fiber of curved beam given bending stress at fiber is the radius of the innermost fiber of a curved beam and is the radius of curvature of the inner surface of the beam is calculated using Radius of 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*Bending Stress at Inner Fibre). To calculate Radius of inner fiber of curved beam given bending stress at fiber, you need Bending Moment in Curved Beam (M_b), Distance of Inner Fibre from Neutral Axis (h_i), Cross Sectional Area of Curved Beam (A), Eccentricity Between Centroidal and Neutral Axis (e) & Bending Stress at Inner Fibre (σ_bi). With our tool, you need to enter the respective value for Bending Moment in Curved Beam, Distance of Inner Fibre from Neutral Axis, Cross Sectional Area of Curved Beam, Eccentricity Between Centroidal and Neutral Axis & Bending Stress at Inner Fibre 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 Radius of Inner Fibre?

In this formula, Radius of Inner Fibre uses Bending Moment in Curved Beam, Distance of Inner Fibre from Neutral Axis, Cross Sectional Area of Curved Beam, Eccentricity Between Centroidal and Neutral Axis & Bending Stress at Inner Fibre. We can use 3 other way(s) to calculate the same, which is/are as follows -

Radius of Inner Fibre = Radius of Centroidal Axis-Distance from Neutral Axis of Curved Beam/2
Radius of Inner Fibre = (Radius of Outer Fibre)/(e^(Distance from Neutral Axis of Curved Beam/Radius of Neutral Axis))
Radius of Inner Fibre = Radius of Centroidal Axis-Diameter of Circular Curved Beam/2

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