Minimum Bending Stress given Eccentric Load Solution

STEP 0: Pre-Calculation Summary
Formula Used
Minimum Bending Stress = ((4*Eccentric load on column)/(pi*(Diameter^2)))*(1-((8*Eccentricity of Loading)/Diameter))
σbmin = ((4*P)/(pi*(d^2)))*(1-((8*eload)/d))
This formula uses 1 Constants, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Minimum Bending Stress - (Measured in Pascal) - Minimum Bending Stress is the minimum stress caused by the bending moments.
Eccentric load on column - (Measured in Newton) - Eccentric load on column is the load that causes direct stress as well as bending stress.
Diameter - (Measured in Meter) - Diameter is a straight line passing from side to side through the center of a body or figure, especially a circle or sphere.
Eccentricity of Loading - (Measured in Meter) - Eccentricity of Loading is the distance between the actual line of action of loads and the line of action that would produce a uniform stress over the cross section of the specimen.
STEP 1: Convert Input(s) to Base Unit
Eccentric load on column: 7 Kilonewton --> 7000 Newton (Check conversion here)
Diameter: 142 Millimeter --> 0.142 Meter (Check conversion here)
Eccentricity of Loading: 2.3 Millimeter --> 0.0023 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
σbmin = ((4*P)/(pi*(d^2)))*(1-((8*eload)/d)) --> ((4*7000)/(pi*(0.142^2)))*(1-((8*0.0023)/0.142))
Evaluating ... ...
σbmin = 384734.91108993
STEP 3: Convert Result to Output's Unit
384734.91108993 Pascal -->0.38473491108993 Megapascal (Check conversion here)
FINAL ANSWER
0.38473491108993 0.384735 Megapascal <-- Minimum Bending Stress
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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National Institute of Technology (NIT), Srinagar
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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

Minimum Bending Stress given Eccentric Load Formula

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

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 Minimum Bending Stress given Eccentric Load?

Minimum Bending Stress given Eccentric Load calculator uses Minimum Bending Stress = ((4*Eccentric load on column)/(pi*(Diameter^2)))*(1-((8*Eccentricity of Loading)/Diameter)) to calculate the Minimum Bending Stress, The Minimum bending stress given eccentric load formula is defined as a more specific type of normal stress. Minimum Bending Stress is denoted by σbmin symbol.

How to calculate Minimum Bending Stress given Eccentric Load using this online calculator? To use this online calculator for Minimum Bending Stress given Eccentric Load, enter Eccentric load on column (P), Diameter (d) & Eccentricity of Loading (eload) and hit the calculate button. Here is how the Minimum Bending Stress given Eccentric Load calculation can be explained with given input values -> -4.5E-6 = ((4*7000)/(pi*(0.142^2)))*(1-((8*0.0023)/0.142)).

FAQ

What is Minimum Bending Stress given Eccentric Load?
The Minimum bending stress given eccentric load formula is defined as a more specific type of normal stress and is represented as σbmin = ((4*P)/(pi*(d^2)))*(1-((8*eload)/d)) or Minimum Bending Stress = ((4*Eccentric load on column)/(pi*(Diameter^2)))*(1-((8*Eccentricity of Loading)/Diameter)). Eccentric load on column is the load that causes direct stress as well as bending stress, Diameter is a straight line passing from side to side through the center of a body or figure, especially a circle or sphere & Eccentricity of Loading is the distance between the actual line of action of loads and the line of action that would produce a uniform stress over the cross section of the specimen.
How to calculate Minimum Bending Stress given Eccentric Load?
The Minimum bending stress given eccentric load formula is defined as a more specific type of normal stress is calculated using Minimum Bending Stress = ((4*Eccentric load on column)/(pi*(Diameter^2)))*(1-((8*Eccentricity of Loading)/Diameter)). To calculate Minimum Bending Stress given Eccentric Load, you need Eccentric load on column (P), Diameter (d) & Eccentricity of Loading (eload). With our tool, you need to enter the respective value for Eccentric load on column, Diameter & Eccentricity of Loading 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 Minimum Bending Stress?
In this formula, Minimum Bending Stress uses Eccentric load on column, Diameter & Eccentricity of Loading. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Minimum Bending Stress = Direct Stress-Bending Stress in Column
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