Bending Moment given Maximum Shear Stress Solution

STEP 0: Pre-Calculation Summary
Formula Used
Bending Moment in Shaft for MSST = sqrt((Maximum Shear Stress in Shaft from MSST/(16/(pi*Diameter of Shaft from MSST^3)))^2-Torsional Moment in Shaft for MSST^2)
Mb MSST = sqrt((𝜏max MSST/(16/(pi*dMSST^3)))^2-Mtt^2)
This formula uses 1 Constants, 1 Functions, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
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
Bending Moment in Shaft for MSST - (Measured in Newton Meter) - Bending Moment in Shaft for MSST is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to bend.
Maximum Shear Stress in Shaft from MSST - (Measured in Pascal) - Maximum Shear Stress in Shaft from MSST is maximum shear stress in a shaft calculated using Maximum Shear Stress Theory.
Diameter of Shaft from MSST - (Measured in Meter) - Diameter of Shaft from MSST is the diameter of the shaft according to the Maximum Shear Stress Theory.
Torsional Moment in Shaft for MSST - (Measured in Newton Meter) - Torsional Moment in Shaft for MSST is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to twist.
STEP 1: Convert Input(s) to Base Unit
Maximum Shear Stress in Shaft from MSST: 58.9 Newton per Square Millimeter --> 58900000 Pascal (Check conversion here)
Diameter of Shaft from MSST: 45 Millimeter --> 0.045 Meter (Check conversion here)
Torsional Moment in Shaft for MSST: 387000 Newton Millimeter --> 387 Newton Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Mb MSST = sqrt((𝜏max MSST/(16/(pi*dMSST^3)))^2-Mtt^2) --> sqrt((58900000/(16/(pi*0.045^3)))^2-387^2)
Evaluating ... ...
Mb MSST = 980.230025906046
STEP 3: Convert Result to Output's Unit
980.230025906046 Newton Meter -->980230.025906046 Newton Millimeter (Check conversion here)
FINAL ANSWER
980230.025906046 980230 Newton Millimeter <-- Bending Moment in Shaft for MSST
(Calculation completed in 00.004 seconds)

Credits

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Osmania University (OU), Hyderabad
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14 Maximum Shear Stress and Principal Stress Theory Calculators

Diameter of Shaft given Permissible Value of Maximum Principle Stress
Go Diameter of Shaft from MPST = (16/(pi*Maximum Principle Stress in Shaft)*(Bending Moment in Shaft+sqrt(Bending Moment in Shaft^2+Torsional Moment in Shaft^2)))^(1/3)
Permissible Value of Maximum Principle Stress
Go Maximum Principle Stress in Shaft = 16/(pi*Diameter of Shaft from MPST^3)*(Bending Moment in Shaft+sqrt(Bending Moment in Shaft^2+Torsional Moment in Shaft^2))
Diameter of Shaft given Principle Shear Stress Maximum Shear Stress Theory
Go Diameter of Shaft from MSST = (16/(pi*Maximum Shear Stress in Shaft from MSST)*sqrt(Bending Moment in Shaft for MSST^2+Torsional Moment in Shaft for MSST^2))^(1/3)
Bending Moment given Maximum Shear Stress
Go Bending Moment in Shaft for MSST = sqrt((Maximum Shear Stress in Shaft from MSST/(16/(pi*Diameter of Shaft from MSST^3)))^2-Torsional Moment in Shaft for MSST^2)
Torsional Moment given Maximum Shear Stress
Go Torsional Moment in Shaft for MSST = sqrt((pi*Diameter of Shaft from MSST^3*Maximum Shear Stress in Shaft from MSST/16)^2-Bending Moment in Shaft for MSST^2)
Maximum Shear Stress in Shafts
Go Maximum Shear Stress in Shaft from MSST = 16/(pi*Diameter of Shaft from MSST^3)*sqrt(Bending Moment in Shaft for MSST^2+Torsional Moment in Shaft for MSST^2)
Torsional Moment given Equivalent Bending Moment
Go Torsional Moment in Shaft for MSST = sqrt((Equivalent Bending Moment from MSST-Bending Moment in Shaft for MSST)^2-Bending Moment in Shaft for MSST^2)
Equivalent Bending Moment given Torsional Moment
Go Equivalent Bending Moment from MSST = Bending Moment in Shaft for MSST+sqrt(Bending Moment in Shaft for MSST^2+Torsional Moment in Shaft for MSST^2)
Factor of Safety given Permissible Value of Maximum Shear Stress
Go Factor of Safety of Shaft = 0.5*Yield Strength in Shaft from MSST/Maximum Shear Stress in Shaft from MSST
Yield Strength in Shear Maximum Shear Stress Theory
Go Shear Yield Strength in Shaft from MSST = 0.5*Factor of Safety of Shaft*Maximum Principle Stress in Shaft
Permissible Value of Maximum Shear Stress
Go Maximum Shear Stress in Shaft from MSST = 0.5*Yield Strength in Shaft from MSST/Factor of Safety of Shaft
Yield Stress in Shear given Permissible Value of Maximum Principle Stress
Go Yield Strength in Shaft from MPST = Maximum Principle Stress in Shaft*Factor of Safety of Shaft
Permissible Value of Maximum Principle Stress using Factor of Safety
Go Maximum Principle Stress in Shaft = Yield Strength in Shaft from MPST/Factor of Safety of Shaft
Factor of Safety given Permissible Value of Maximum Principle Stress
Go Factor of Safety of Shaft = Yield Strength in Shaft from MPST/Maximum Principle Stress in Shaft

Bending Moment given Maximum Shear Stress Formula

Bending Moment in Shaft for MSST = sqrt((Maximum Shear Stress in Shaft from MSST/(16/(pi*Diameter of Shaft from MSST^3)))^2-Torsional Moment in Shaft for MSST^2)
Mb MSST = sqrt((𝜏max MSST/(16/(pi*dMSST^3)))^2-Mtt^2)

Define Bending Moment

In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. The most common or simplest structural element subjected to bending moments is the beam.

How to Calculate Bending Moment given Maximum Shear Stress?

Bending Moment given Maximum Shear Stress calculator uses Bending Moment in Shaft for MSST = sqrt((Maximum Shear Stress in Shaft from MSST/(16/(pi*Diameter of Shaft from MSST^3)))^2-Torsional Moment in Shaft for MSST^2) to calculate the Bending Moment in Shaft for MSST, The Bending Moment given Maximum Shear Stress formula is defined as the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. Bending Moment in Shaft for MSST is denoted by Mb MSST symbol.

How to calculate Bending Moment given Maximum Shear Stress using this online calculator? To use this online calculator for Bending Moment given Maximum Shear Stress, enter Maximum Shear Stress in Shaft from MSST (𝜏max MSST), Diameter of Shaft from MSST (dMSST) & Torsional Moment in Shaft for MSST (Mtt) and hit the calculate button. Here is how the Bending Moment given Maximum Shear Stress calculation can be explained with given input values -> 9.8E+8 = sqrt((58900000/(16/(pi*0.045^3)))^2-387^2).

FAQ

What is Bending Moment given Maximum Shear Stress?
The Bending Moment given Maximum Shear Stress formula is defined as the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend and is represented as Mb MSST = sqrt((𝜏max MSST/(16/(pi*dMSST^3)))^2-Mtt^2) or Bending Moment in Shaft for MSST = sqrt((Maximum Shear Stress in Shaft from MSST/(16/(pi*Diameter of Shaft from MSST^3)))^2-Torsional Moment in Shaft for MSST^2). Maximum Shear Stress in Shaft from MSST is maximum shear stress in a shaft calculated using Maximum Shear Stress Theory, Diameter of Shaft from MSST is the diameter of the shaft according to the Maximum Shear Stress Theory & Torsional Moment in Shaft for MSST is the reaction induced in a structural shaft element when an external force or moment is applied to the element, causing the element to twist.
How to calculate Bending Moment given Maximum Shear Stress?
The Bending Moment given Maximum Shear Stress formula is defined as the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend is calculated using Bending Moment in Shaft for MSST = sqrt((Maximum Shear Stress in Shaft from MSST/(16/(pi*Diameter of Shaft from MSST^3)))^2-Torsional Moment in Shaft for MSST^2). To calculate Bending Moment given Maximum Shear Stress, you need Maximum Shear Stress in Shaft from MSST (𝜏max MSST), Diameter of Shaft from MSST (dMSST) & Torsional Moment in Shaft for MSST (Mtt). With our tool, you need to enter the respective value for Maximum Shear Stress in Shaft from MSST, Diameter of Shaft from MSST & Torsional Moment in Shaft for MSST 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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