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

STEP 0: Pre-Calculation Summary
Formula Used
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))
A = (Mb*ho)/((e)*σbo*(Ro))
This formula uses 6 Variables
Variables Used
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.
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.
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.
Radius of Outer Fibre - (Measured in Meter) - Radius of Outer Fibre is the radius of 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)
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)
Radius of Outer Fibre: 90 Millimeter --> 0.09 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
A = (Mb*ho)/((e)*σbo*(Ro)) --> (985*0.012)/((0.0065)*85000000*(0.09))
Evaluating ... ...
A = 0.000237707390648567
STEP 3: Convert Result to Output's Unit
0.000237707390648567 Square Meter -->237.707390648567 Square Millimeter (Check conversion here)
FINAL ANSWER
237.707390648567 237.7074 Square Millimeter <-- Cross sectional area of curved beam
(Calculation completed in 00.020 seconds)

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

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

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))
A = (Mb*ho)/((e)*σbo*(Ro))

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

Area of cross section of curved beam given bending stress at outer fiber calculator uses 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)) to calculate the Cross sectional area of curved beam, The Area of cross section of curved beam given bending stress at outer fiber is the cross-sectional area of the transverse section of a curved beam. Cross sectional area of curved beam is denoted by A symbol.

How to calculate Area of cross section of curved beam given bending stress at outer fiber using this online calculator? To use this online calculator for Area of cross section of curved beam given bending stress at outer fiber, enter Bending moment in curved beam (Mb), Distance of Outer Fibre from Neutral Axis (ho), Eccentricity Between Centroidal and Neutral Axis (e), Bending Stress at Outer Fibre bo) & Radius of Outer Fibre (Ro) and hit the calculate button. Here is how the Area of cross section of curved beam given bending stress at outer fiber calculation can be explained with given input values -> 2.4E+8 = (985*0.012)/((0.0065)*85000000*(0.09)).

FAQ

What is Area of cross section of curved beam given bending stress at outer fiber?
The Area of cross section of curved beam given bending stress at outer fiber is the cross-sectional area of the transverse section of a curved beam and is represented as A = (Mb*ho)/((e)*σbo*(Ro)) or 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 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, 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 & Radius of Outer Fibre is the radius of the outer fiber of a curved structural element.
How to calculate Area of cross section of curved beam given bending stress at outer fiber?
The Area of cross section of curved beam given bending stress at outer fiber is the cross-sectional area of the transverse section of a curved beam is calculated using 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)). To calculate Area of cross section of curved beam given bending stress at outer fiber, you need Bending moment in curved beam (Mb), Distance of Outer Fibre from Neutral Axis (ho), Eccentricity Between Centroidal and Neutral Axis (e), Bending Stress at Outer Fibre bo) & Radius of Outer Fibre (Ro). With our tool, you need to enter the respective value for 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 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 Cross sectional area of curved beam?
In this formula, Cross sectional area of curved beam uses 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. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • 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))
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