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))
Ro = (Mb*ho)/((A)*e*(σbo))
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: 985000 Newton Millimeter --> 985 Newton Meter (Check conversion here)
Distance of Outer Fibre from Neutral Axis: 12 Millimeter --> 0.012 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
Ro = (Mb*ho)/((A)*e*(σbo)) --> (985*0.012)/((0.00024)*0.0065*(85000000))
Evaluating ... ...
Ro = 0.0891402714932127
STEP 3: Convert Result to Output's Unit
0.0891402714932127 Meter -->89.1402714932127 Millimeter (Check conversion here)
FINAL ANSWER
89.1402714932127 89.14027 Millimeter <-- Radius of Outer Fibre
(Calculation completed in 00.020 seconds)

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16 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 inner fiber of curved beam given bending stress at fiber
Go 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))
Radius of outer fibre of curved beam given bending stress at fiber
Go 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))
Radius of neutral axis of curved beam of rectangular section given radius of inner and outer fiber
Go Radius of Neutral Axis = Distance from Neutral Axis of Curved Beam/ln(Radius of Outer Fibre/Radius of Inner Fibre)
Radius of neutral axis of curved beam of circular section given radius of inner and outer fibre
Go Radius of Neutral Axis = (((sqrt(Radius of Outer Fibre))+(sqrt(Radius of Inner Fibre)))^2)/4
Radius of inner fiber of rectangular curved beam given radius of neutral axis and outer fiber
Go Radius of Inner Fibre = (Radius of Outer Fibre)/(e^(Distance from Neutral Axis of Curved Beam/Radius of Neutral Axis))
Radius of outer fiber of rectangular curved beam given radius of neutral axis and inner fiber
Go Radius of Outer Fibre = (Radius of Inner Fibre)*(e^(Distance from Neutral Axis of Curved Beam/Radius of Neutral Axis))
Radius of inner fiber of circular curved beam given radius of neutral axis and outer fiber
Go Radius of Inner Fibre = (sqrt(4*Radius of Neutral Axis)-sqrt(Radius of Outer Fibre))^2
Radius of outer fiber of circular curved beam given radius of neutral axis and inner fiber
Go Radius of Outer Fibre = (sqrt(4*Radius of Neutral Axis)-sqrt(Radius of Inner Fibre))^2
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 centroidal axis of curved beam of rectangular section given radius of inner fiber
Go Radius of Centroidal Axis = (Radius of Inner Fibre)+(Distance from Neutral Axis of Curved Beam/2)
Radius of inner fibre of curved beam of rectangular section given radius of centroidal axis
Go Radius of Inner Fibre = (Radius of Centroidal Axis)-(Distance from Neutral Axis of Curved Beam/2)
Radius of centroidal axis of curved beam of circular section given radius of inner fiber
Go Radius of Centroidal Axis = (Radius of Inner Fibre)+(Diameter of circular curved beam/2)
Radius of inner fiber of curved beam of circular section given radius of centroidal axis
Go Radius of Inner Fibre = (Radius of Centroidal Axis)-(Diameter of circular curved beam/2)

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

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))
Ro = (Mb*ho)/((A)*e*(σbo))

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 Ro 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 (Mb), Distance of Outer Fibre from Neutral Axis (ho), Cross sectional area of curved beam (A), Eccentricity Between Centroidal and Neutral Axis (e) & Bending Stress at Outer Fibre 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 -> 89140.27 = (985*0.012)/((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 Ro = (Mb*ho)/((A)*e*(σbo)) 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 (Mb), Distance of Outer Fibre from Neutral Axis (ho), Cross sectional area of curved beam (A), Eccentricity Between Centroidal and Neutral Axis (e) & Bending Stress at Outer Fibre 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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