Radius of outer fibre 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 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%
✖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 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%

✖Radius of Outer Fibre is the radius of the outer fiber of a curved structural element.ⓘ Radius of outer fibre of curved beam given bending stress at fiber [R_o]

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Radius of outer fibre of curved beam given bending stress at fiber Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of 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*Bending Stress at Outer Fibre)
R_o = (M_b*h_o)/(A*e*σ_bo)
This formula uses 6 Variables

Variables Used

Radius of Outer Fibre - (Measured in Meter) - Radius of Outer Fibre is the radius of the outer 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 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.
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 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.

STEP 1: Convert Input(s) to Base Unit

Bending Moment in Curved Beam: 245000 Newton Millimeter --> 245 Newton Meter (Check conversion here)
Distance of Outer Fibre from Neutral Axis: 48 Millimeter --> 0.048 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 Outer Fibre: 85 Newton per Square Millimeter --> 85000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_o = (M_b*h_o)/(A*e*σ_bo) --> (245*0.048)/(0.00024*0.0065*85000000)

Evaluating ... ...

R_o = 0.0886877828054299

STEP 3: Convert Result to Output's Unit

0.0886877828054299 Meter -->88.6877828054299 Millimeter (Check conversion here)

FINAL ANSWER

88.6877828054299 ≈ 88.68778 Millimeter <-- Radius of Outer Fibre

(Calculation completed in 00.004 seconds)

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Shri Govindram Seksaria Institute of Technology and Science (SGSITS ), Indore

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< Radius of Fiber and Axis Calculators

Radius of centroidal axis of curved beam given bending stress

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

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

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

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

Radius of outer fibre of curved beam given bending stress at fiber Formula

Transgranular and Intergtanular fracture

Brittle fractures display either transgranular or intergranular fractures. This depends upon whether the grain boundaries are stronger or weaker than the grains:
Transgranular fracture - The fracture travels through the grain of the material. Cracks choose the path of least resistance.
Intergranular fracture - The crack travels along the grain boundaries, and not through the actual grains. This usually occurs when the phase in the grain boundary is weak and brittle.

How to Calculate Radius of outer fibre of curved beam given bending stress at fiber?

Radius of outer fibre of curved beam given bending stress at fiber calculator uses Radius of 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*Bending Stress at Outer Fibre) to calculate the Radius of Outer Fibre, Radius of outer fibre of curved beam given bending stress at fiber is the radius of the outermost fiber of a curved beam and is the radius of curvature of the outer surface of the beam. Radius of Outer Fibre is denoted by R_o symbol.

How to calculate Radius of outer fibre of curved beam given bending stress at fiber using this online calculator? To use this online calculator for Radius of outer fibre of curved beam given bending stress at fiber, enter Bending Moment in Curved Beam (M_b), Distance of Outer Fibre from Neutral Axis (h_o), Cross Sectional Area of Curved Beam (A), Eccentricity Between Centroidal and Neutral Axis (e) & Bending Stress at Outer Fibre (σ_bo) and hit the calculate button. Here is how the Radius of outer fibre of curved beam given bending stress at fiber calculation can be explained with given input values -> 88687.78 = (245*0.048)/(0.00024*0.0065*85000000).

FAQ

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

Radius of outer fibre of curved beam given bending stress at fiber is the radius of the outermost fiber of a curved beam and is the radius of curvature of the outer surface of the beam and is represented as R_o = (M_b*h_o)/(A*e*σ_bo) or Radius of 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*Bending Stress at Outer 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 Outer 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 Outer Fibre is the amount of bending moment at the outer fiber of a curved structural element.

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

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

In this formula, Radius of Outer Fibre uses Bending Moment in Curved Beam, Distance of Outer Fibre from Neutral Axis, Cross Sectional Area of Curved Beam, Eccentricity Between Centroidal and Neutral Axis & Bending Stress at Outer Fibre. We can use 2 other way(s) to calculate the same, which is/are as follows -

Radius of Outer Fibre = Radius of Inner Fibre*e^(Distance from Neutral Axis of Curved Beam/Radius of Neutral Axis)
Radius of Outer Fibre = (sqrt(4*Radius of Neutral Axis)-sqrt(Radius of Inner Fibre))^2

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