Maximum Bending Stress for Circular Section given Moment of Load Calculator

✖Moment due to eccentric load is at any point of column section due to eccentric load.ⓘ Moment due to eccentric load [M]			+10% -10%
✖Diameter of Circular section is the diameter of the circular cross-section of the beam.ⓘ Diameter of Circular section [d_c]			+10% -10%
✖MOI of Area of Circular Section is the second moment of the area of the section about the neutral axis.ⓘ MOI of Area of Circular Section [I_circular]			+10% -10%

✖Maximum bending stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.ⓘ Maximum Bending Stress for Circular Section given Moment of Load [σb^max]

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Formula

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Maximum Bending Stress for Circular Section given Moment of Load

Formula

`"σb"^{"max"} = ("M"*"d"_{"c"})/(2*"I"_{"circular"})`

Example

`"1263.432MPa"=("8.1N*m"*"360mm")/(2*"1154mm⁴")`

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Maximum Bending Stress for Circular Section given Moment of Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum bending stress = (Moment due to eccentric load*Diameter of Circular section)/(2*MOI of Area of Circular Section)
σb^max = (M*d_c)/(2*I_circular)
This formula uses 4 Variables

Variables Used

Maximum bending stress - (Measured in Pascal) - Maximum bending stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.
Moment due to eccentric load - (Measured in Newton Meter) - Moment due to eccentric load is at any point of column section due to eccentric load.
Diameter of Circular section - (Measured in Meter) - Diameter of Circular section is the diameter of the circular cross-section of the beam.
MOI of Area of Circular Section - (Measured in Meter⁴) - MOI of Area of Circular Section is the second moment of the area of the section about the neutral axis.

STEP 1: Convert Input(s) to Base Unit

Moment due to eccentric load: 8.1 Newton Meter --> 8.1 Newton Meter No Conversion Required
Diameter of Circular section: 360 Millimeter --> 0.36 Meter (Check conversion here)
MOI of Area of Circular Section: 1154 Millimeter⁴ --> 1.154E-09 Meter⁴ (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σb^max = (M*d_c)/(2*I_circular) --> (8.1*0.36)/(2*1.154E-09)

Evaluating ... ...

σb^max = 1263431542.46101

STEP 3: Convert Result to Output's Unit

1263431542.46101 Pascal -->1263.43154246101 Megapascal (Check conversion here)

FINAL ANSWER

1263.43154246101 ≈ 1263.432 Megapascal <-- Maximum bending stress

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Direct And Bending Stress » Middle Quarter Rule For Circular Section » Maximum Bending Stress for Circular Section given Moment of Load

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National Institute Of Technology (NIT), Hamirpur

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< 18 Middle Quarter Rule For Circular Section Calculators

Eccentricity of Load given Minimum Bending Stress

Go Eccentricity of Loading = (((4*Eccentric load on column)/(pi*(Diameter^2)))-Minimum Bending Stress)*((pi*(Diameter^3))/(32*Eccentric load on column))

Minimum Bending Stress given Eccentric Load

Go Minimum Bending Stress = ((4*Eccentric load on column)/(pi*(Diameter^2)))*(1-((8*Eccentricity of Loading)/Diameter))

Eccentric Load given Minimum Bending Stress

Go Eccentric load on column = (Minimum Bending Stress*(pi*(Diameter^2)))*(1-((8*Eccentricity of Loading)/Diameter))/4

Eccentricity of Load given Maximum Bending Stress

Go Eccentricity of Loading = (Maximum Bending Moment*(pi*(Diameter^3)))/(32*Eccentric load on column)

Eccentric Load given maximum Bending Stress

Go Eccentric load on column = (Maximum Bending Moment*(pi*(Diameter^3)))/(32*Eccentricity of Loading)

Maximum Bending Stress given Eccentric Load

Go Maximum bending stress = (32*Eccentric load on column*Eccentricity of Loading)/(pi*(Diameter^3))

Maximum Bending Stress for Circular Section given Moment of Load

Go Maximum bending stress = (Moment due to eccentric load*Diameter of Circular section)/(2*MOI of Area of Circular Section)

Moment of Load given Maximum Bending Stress for Circular Section

Go Moment due to eccentric load = (Bending Stress in Column*(2*MOI of Area of Circular Section))/Diameter

Diameter of Circular Section given Maximum Bending Stress

Go Diameter = (Bending Stress in Column*(2*MOI of Area of Circular Section))/Moment due to eccentric load

Moment of Inertia of Circular Section given Maximum Bending Stress for Circular Section

Go MOI of Area of Circular Section = (Moment due to eccentric load*Diameter)/(2*Maximum bending stress)

Diameter of Circular Section given Direct Stress

Go Diameter = sqrt((4*Eccentric load on column)/(pi*Direct Stress))

Direct stress for circular section

Go Direct Stress = (4*Eccentric load on column)/(pi*(Diameter^2))

Eccentric load for given direct stress for circular section

Go Eccentric load on column = (Direct Stress*pi*(Diameter^2))/4

Minimum Bending Stress given Direct and Bending Stress

Go Minimum Bending Stress = Direct Stress-Bending Stress in Column

Condition for Maximum Bending Stress given Diameter

Go Diameter = 2*Distance from Neutral Layer

Condition for maximum bending stress

Go Distance from Neutral Layer = Diameter/2

Diameter of circular section if maximum value of eccentricity is known(for no tensile stress case)

Go Diameter = 8*Eccentricity of Loading

Maximum value of eccentricity for no tensile stress

Go Eccentricity of Loading = Diameter/8

Maximum Bending Stress for Circular Section given Moment of Load Formula

Maximum bending stress = (Moment due to eccentric load*Diameter of Circular section)/(2*MOI of Area of Circular Section)
σb^max = (M*d_c)/(2*I_circular)

What is shear stress and strain?

Shear strain is the deformation of an object or medium under shear stress. The shear modulus is the elastic modulus in this case. Shear stress is caused by forces acting along the object's two parallel surfaces.

How to Calculate Maximum Bending Stress for Circular Section given Moment of Load?

Maximum Bending Stress for Circular Section given Moment of Load calculator uses Maximum bending stress = (Moment due to eccentric load*Diameter of Circular section)/(2*MOI of Area of Circular Section) to calculate the Maximum bending stress, The Maximum bending stress for circular section given moment of load formula is defined as a more specific type of normal stress. Maximum bending stress is denoted by σb^max symbol.

How to calculate Maximum Bending Stress for Circular Section given Moment of Load using this online calculator? To use this online calculator for Maximum Bending Stress for Circular Section given Moment of Load, enter Moment due to eccentric load (M), Diameter of Circular section (d_c) & MOI of Area of Circular Section (I_circular) and hit the calculate button. Here is how the Maximum Bending Stress for Circular Section given Moment of Load calculation can be explained with given input values -> 0.001263 = (8.1*0.36)/(2*1.154E-09).

FAQ

What is Maximum Bending Stress for Circular Section given Moment of Load?

The Maximum bending stress for circular section given moment of load formula is defined as a more specific type of normal stress and is represented as σb^max = (M*d_c)/(2*I_circular) or Maximum bending stress = (Moment due to eccentric load*Diameter of Circular section)/(2*MOI of Area of Circular Section). Moment due to eccentric load is at any point of column section due to eccentric load, Diameter of Circular section is the diameter of the circular cross-section of the beam & MOI of Area of Circular Section is the second moment of the area of the section about the neutral axis.

How to calculate Maximum Bending Stress for Circular Section given Moment of Load?

The Maximum bending stress for circular section given moment of load formula is defined as a more specific type of normal stress is calculated using Maximum bending stress = (Moment due to eccentric load*Diameter of Circular section)/(2*MOI of Area of Circular Section). To calculate Maximum Bending Stress for Circular Section given Moment of Load, you need Moment due to eccentric load (M), Diameter of Circular section (d_c) & MOI of Area of Circular Section (I_circular). With our tool, you need to enter the respective value for Moment due to eccentric load, Diameter of Circular section & MOI of Area of Circular Section 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 Maximum bending stress?

In this formula, Maximum bending stress uses Moment due to eccentric load, Diameter of Circular section & MOI of Area of Circular Section. We can use 1 other way(s) to calculate the same, which is/are as follows -

Maximum bending stress = (32*Eccentric load on column*Eccentricity of Loading)/(pi*(Diameter^3))

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