Bending Moment given Maximum Shear Stress Calculator

✖Maximum Shear Stress in Shaft from MSST is the maximum shear stress developed in a shaft due to twisting or torsional loading, affecting its structural integrity.ⓘ Maximum Shear Stress in Shaft from MSST [𝜏_{max MSST}]			+10% -10%
✖Diameter of Shaft from MSST is the diameter of a shaft calculated based on maximum shear stress theory to determine the shaft's strength and stability.ⓘ Diameter of Shaft from MSST [d_MSST]			+10% -10%
✖Torsional Moment in Shaft for MSST is the maximum twisting moment that a shaft can withstand without failing, considering maximum shear stress and principal stress theory.ⓘ Torsional Moment in Shaft for MSST [Mt_t]			+10% -10%

✖Bending Moment in Shaft for MSST is the maximum twisting force that causes shear stress in a shaft, affecting its structural integrity and stability.ⓘ Bending Moment given Maximum Shear Stress [M_{b MSST}]

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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)
M_{b MSST} = sqrt((𝜏_{max MSST}/(16/(pi*d_MSST^3)))^2-Mt_t^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 maximum twisting force that causes shear stress in a shaft, affecting its structural integrity and stability.
Maximum Shear Stress in Shaft from MSST - (Measured in Pascal) - Maximum Shear Stress in Shaft from MSST is the maximum shear stress developed in a shaft due to twisting or torsional loading, affecting its structural integrity.
Diameter of Shaft from MSST - (Measured in Meter) - Diameter of Shaft from MSST is the diameter of a shaft calculated based on maximum shear stress theory to determine the shaft's strength and stability.
Torsional Moment in Shaft for MSST - (Measured in Newton Meter) - Torsional Moment in Shaft for MSST is the maximum twisting moment that a shaft can withstand without failing, considering maximum shear stress and principal stress theory.

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: 387582.1 Newton Millimeter --> 387.5821 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_{b MSST} = sqrt((𝜏_{max MSST}/(16/(pi*d_MSST^3)))^2-Mt_t^2) --> sqrt((58900000/(16/(pi*0.045^3)))^2-387.5821^2)

Evaluating ... ...

M_{b MSST} = 980.000009922121

STEP 3: Convert Result to Output's Unit

980.000009922121 Newton Meter -->980000.009922121 Newton Millimeter (Check conversion here)

FINAL ANSWER

980000.009922121 ≈ 980000 Newton Millimeter <-- Bending Moment in Shaft for MSST

(Calculation completed in 00.004 seconds)

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Osmania University (OU), Hyderabad

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< Maximum Shear Stress and Principal Stress Theory Calculators

Diameter of Shaft given Permissible Value of Maximum Principle Stress

LaTeX 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

LaTeX 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))

Permissible Value of Maximum Principle Stress using Factor of Safety

LaTeX 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

LaTeX Go Factor of Safety of Shaft = Yield Strength in Shaft from MPST/Maximum Principle Stress in Shaft

Bending Moment given Maximum Shear Stress Formula

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Define Bending Moment?

A bending moment is the internal force that causes a beam or structural element to bend when subjected to external loads. It occurs when forces are applied perpendicular to the length of the element, causing it to bend or curve. The bending moment is calculated based on the magnitude of the force and its distance from a specific point, typically measured along the beam. It plays a crucial role in structural engineering, helping to determine the strength and stability of beams and other load-bearing elements.

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, Bending Moment given Maximum Shear Stress formula is defined as a measure of the maximum stress that an object can withstand without deforming plastically, calculated based on the maximum shear stress and principal stress theory, providing a critical value for structural integrity and material failure analysis in mechanical engineering. Bending Moment in Shaft for MSST is denoted by M_{b 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 (𝜏_{max MSST}), Diameter of Shaft from MSST (d_MSST) & Torsional Moment in Shaft for MSST (Mt_t) 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)))^2-387.5821^2).

FAQ

What is Bending Moment given Maximum Shear Stress?

Bending Moment given Maximum Shear Stress formula is defined as a measure of the maximum stress that an object can withstand without deforming plastically, calculated based on the maximum shear stress and principal stress theory, providing a critical value for structural integrity and material failure analysis in mechanical engineering and is represented as M_{b MSST} = sqrt((𝜏_{max MSST}/(16/(pi*d_MSST^3)))^2-Mt_t^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 the maximum shear stress developed in a shaft due to twisting or torsional loading, affecting its structural integrity, Diameter of Shaft from MSST is the diameter of a shaft calculated based on maximum shear stress theory to determine the shaft's strength and stability & Torsional Moment in Shaft for MSST is the maximum twisting moment that a shaft can withstand without failing, considering maximum shear stress and principal stress theory.

How to calculate Bending Moment given Maximum Shear Stress?

Bending Moment given Maximum Shear Stress formula is defined as a measure of the maximum stress that an object can withstand without deforming plastically, calculated based on the maximum shear stress and principal stress theory, providing a critical value for structural integrity and material failure analysis in mechanical engineering 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 (𝜏_{max MSST}), Diameter of Shaft from MSST (d_MSST) & Torsional Moment in Shaft for MSST (Mt_t). 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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