Equivalent Bending Moment for Solid Shaft Solution

STEP 0: Pre-Calculation Summary
Formula Used
Equivalent Bending Moment for Solid Shaft = (1/2)*(Maximum Bending Moment+sqrt(Maximum Bending Moment^2+Maximum Torque for Agitator^2))
Mesolidshaft = (1/2)*(Mm+sqrt(Mm^2+Tm^2))
This formula uses 1 Functions, 3 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Equivalent Bending Moment for Solid Shaft - (Measured in Newton Meter) - Equivalent Bending Moment for Solid Shaftt refers to a simplification method used in engineering to analyze the bending stresses experienced by a solid shaft under torsional loading conditions.
Maximum Bending Moment - (Measured in Newton Meter) - Maximum Bending Moment is the algebraic sum of the moments caused by the internal forces on the shaft and it causes the shaft to rotate.
Maximum Torque for Agitator - (Measured in Newton Meter) - Maximum Torque for Agitator refers to the highest amount of rotational force it can generate, typically measured in Newton-meters (Nm), to effectively mix or agitate a given substance or material.
STEP 1: Convert Input(s) to Base Unit
Maximum Bending Moment: 34000 Newton Millimeter --> 34 Newton Meter (Check conversion here)
Maximum Torque for Agitator: 4680 Newton Millimeter --> 4.68 Newton Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Mesolidshaft = (1/2)*(Mm+sqrt(Mm^2+Tm^2)) --> (1/2)*(34+sqrt(34^2+4.68^2))
Evaluating ... ...
Mesolidshaft = 34.1602913728177
STEP 3: Convert Result to Output's Unit
34.1602913728177 Newton Meter -->34160.2913728176 Newton Millimeter (Check conversion here)
FINAL ANSWER
34160.2913728176 34160.29 Newton Millimeter <-- Equivalent Bending Moment for Solid Shaft
(Calculation completed in 00.020 seconds)

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18 Design of Agitation System Components Calculators

Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment
Go Hollow Shaft Outer Diameter = ((Equivalent Twisting Moment)*(16/pi)*(1)/((Torsional Shear Stress in Shaft)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
Maximum Deflection due to Shaft with Uniform Weight
Go Deflection = (Uniformly Distributed Load per Unit Length*Length^(4))/((8*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4))
Maximum Torque for Hollow Shaft
Go Maximum Torque for Hollow Shaft = ((pi/16)*(Hollow Shaft Outer Diameter^3)*(Torsional Shear Stress in Shaft)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2))
Outside Diameter of Hollow Shaft based on Equivalent Bending Moment
Go Diameter of Hollow Shaft for Agitator = ((Equivalent Bending Moment)*(32/pi)*(1)/((Bending Stress)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
Maximum Deflection due to Each Load
Go Deflection due to each Load = (Concentrated Load*Length^(3))/((3*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4))
Equivalent Twisting Moment for Hollow Shaft
Go Equivalent Twisting Moment for Hollow Shaft = (pi/16)*(Bending Stress)*(Hollow Shaft Outer Diameter ^3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)
Equivalent Bending Moment for Hollow Shaft
Go Equivalent Bending Moment for Hollow Shaft = (pi/32)*(Bending Stress)*(Hollow Shaft Outer Diameter ^3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)
Diameter of Hollow Shaft Subjected to Maximum Bending Moment
Go Hollow Shaft Outer Diameter = (Maximum Bending Moment/((pi/32)*(Bending Stress)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2)))^(1/3)
Equivalent Bending Moment for Solid Shaft
Go Equivalent Bending Moment for Solid Shaft = (1/2)*(Maximum Bending Moment+sqrt(Maximum Bending Moment^2+Maximum Torque for Agitator^2))
Diameter of Solid Shaft Subjected to Maximum Bending Moment
Go Diameter of Solid Shaft for Agitator = ((Maximum Bending Moment for Solid Shaft)/((pi/32)*Bending Stress))^(1/3)
Maximum Torque for Solid Shaft
Go Maximum Torque for Solid Shaft = ((pi/16)*(Diameter of Shaft for Agitator^3)*(Torsional Shear Stress in Shaft))
Equivalent Twisting Moment for Solid Shaft
Go Equivalent Twisting Moment for Solid Shaft = (sqrt((Maximum Bending Moment^2)+(Maximum Torque for Agitator^2)))
Diameter of Solid Shaft based on Equivalent Twisting Moment
Go Diameter of Solid Shaft = (Equivalent Twisting Moment*16/pi*1/Torsional Shear Stress in Shaft)^(1/3)
Diameter of Solid Shaft based on Equivalent Bending Moment
Go Diameter of Solid Shaft for Agitator = (Equivalent Bending Moment*32/pi*1/Bending Stress)^(1/3)
Rated Motor Torque
Go Rated Motor Torque = ((Power*4500)/(2*pi*Speed of Agitator))
Force for Design of Shaft Based on Pure Bending
Go Force = Maximum Torque for Agitator/(0.75*Height of Manometer Liquid)
Maximum Bending Moment subject to Shaft
Go Maximum Bending Moment = Length of Shaft*Force
Critical Speed for Each Deflection
Go Critical Speed = 946/sqrt(Deflection)

8 Shaft Subjected to Combined Twisting Moment and Bending Moment Calculators

Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment
Go Hollow Shaft Outer Diameter = ((Equivalent Twisting Moment)*(16/pi)*(1)/((Torsional Shear Stress in Shaft)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
Outside Diameter of Hollow Shaft based on Equivalent Bending Moment
Go Diameter of Hollow Shaft for Agitator = ((Equivalent Bending Moment)*(32/pi)*(1)/((Bending Stress)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)
Equivalent Twisting Moment for Hollow Shaft
Go Equivalent Twisting Moment for Hollow Shaft = (pi/16)*(Bending Stress)*(Hollow Shaft Outer Diameter ^3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)
Equivalent Bending Moment for Hollow Shaft
Go Equivalent Bending Moment for Hollow Shaft = (pi/32)*(Bending Stress)*(Hollow Shaft Outer Diameter ^3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)
Equivalent Bending Moment for Solid Shaft
Go Equivalent Bending Moment for Solid Shaft = (1/2)*(Maximum Bending Moment+sqrt(Maximum Bending Moment^2+Maximum Torque for Agitator^2))
Equivalent Twisting Moment for Solid Shaft
Go Equivalent Twisting Moment for Solid Shaft = (sqrt((Maximum Bending Moment^2)+(Maximum Torque for Agitator^2)))
Diameter of Solid Shaft based on Equivalent Twisting Moment
Go Diameter of Solid Shaft = (Equivalent Twisting Moment*16/pi*1/Torsional Shear Stress in Shaft)^(1/3)
Diameter of Solid Shaft based on Equivalent Bending Moment
Go Diameter of Solid Shaft for Agitator = (Equivalent Bending Moment*32/pi*1/Bending Stress)^(1/3)

Equivalent Bending Moment for Solid Shaft Formula

Equivalent Bending Moment for Solid Shaft = (1/2)*(Maximum Bending Moment+sqrt(Maximum Bending Moment^2+Maximum Torque for Agitator^2))
Mesolidshaft = (1/2)*(Mm+sqrt(Mm^2+Tm^2))

What is Maximum Shear Stress Theory for Brittle Materials?

Maximum shear stress theory states that yielding will occur when a particular point undergoes a maximum shear stress that is equal to half of the uniaxial yield strength.

How to Calculate Equivalent Bending Moment for Solid Shaft?

Equivalent Bending Moment for Solid Shaft calculator uses Equivalent Bending Moment for Solid Shaft = (1/2)*(Maximum Bending Moment+sqrt(Maximum Bending Moment^2+Maximum Torque for Agitator^2)) to calculate the Equivalent Bending Moment for Solid Shaft, The Equivalent Bending Moment for Solid Shaft formula is defined as that alone produces maximum normal stress equal to the maximum normal stress produce due to combined bending and torsion. Equivalent Bending Moment for Solid Shaft is denoted by Mesolidshaft symbol.

How to calculate Equivalent Bending Moment for Solid Shaft using this online calculator? To use this online calculator for Equivalent Bending Moment for Solid Shaft, enter Maximum Bending Moment (Mm) & Maximum Torque for Agitator (Tm) and hit the calculate button. Here is how the Equivalent Bending Moment for Solid Shaft calculation can be explained with given input values -> 3.4E+7 = (1/2)*(34+sqrt(34^2+4.68^2)).

FAQ

What is Equivalent Bending Moment for Solid Shaft?
The Equivalent Bending Moment for Solid Shaft formula is defined as that alone produces maximum normal stress equal to the maximum normal stress produce due to combined bending and torsion and is represented as Mesolidshaft = (1/2)*(Mm+sqrt(Mm^2+Tm^2)) or Equivalent Bending Moment for Solid Shaft = (1/2)*(Maximum Bending Moment+sqrt(Maximum Bending Moment^2+Maximum Torque for Agitator^2)). Maximum Bending Moment is the algebraic sum of the moments caused by the internal forces on the shaft and it causes the shaft to rotate & Maximum Torque for Agitator refers to the highest amount of rotational force it can generate, typically measured in Newton-meters (Nm), to effectively mix or agitate a given substance or material.
How to calculate Equivalent Bending Moment for Solid Shaft?
The Equivalent Bending Moment for Solid Shaft formula is defined as that alone produces maximum normal stress equal to the maximum normal stress produce due to combined bending and torsion is calculated using Equivalent Bending Moment for Solid Shaft = (1/2)*(Maximum Bending Moment+sqrt(Maximum Bending Moment^2+Maximum Torque for Agitator^2)). To calculate Equivalent Bending Moment for Solid Shaft, you need Maximum Bending Moment (Mm) & Maximum Torque for Agitator (Tm). With our tool, you need to enter the respective value for Maximum Bending Moment & Maximum Torque for Agitator and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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