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Vishwakarma University (VU), Pune
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## Bending stress in shaft Solution

STEP 0: Pre-Calculation Summary
Formula Used
bending_stress = (32*Bending moment)/(pi*(Diameter of shaft^3))
𝛔b = (32*Mb)/(pi*(d^3))
This formula uses 1 Constants, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Bending moment - The 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. (Measured in Newton Meter)
Diameter of shaft - The Diameter of shaft is defined as the diameter of the hole in the iron laminations that contains the shaft. (Measured in Centimeter)
STEP 1: Convert Input(s) to Base Unit
Bending moment: 50 Newton Meter --> 50 Newton Meter No Conversion Required
Diameter of shaft: 10 Centimeter --> 0.1 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
𝛔b = (32*Mb)/(pi*(d^3)) --> (32*50)/(pi*(0.1^3))
Evaluating ... ...
𝛔b = 509295.817894065
STEP 3: Convert Result to Output's Unit
509295.817894065 Pascal -->509295.817894065 Newton per Square Meter (Check conversion here)
509295.817894065 Newton per Square Meter <-- Bending Stress
(Calculation completed in 00.000 seconds)

## < 10+ Machine Design Calculators

Shear stress on circular fillet weld subjected to Torsion
shear_stress = 2*Torque acting on rod/(pi*Throat thickness*Nominal Diameter^2) Go
Shear strength in parallel fillet weld
shear_strength_in_parallel_fillet_weld = Tensile force on plates/(0.707*Leg of the weld*Length of weld) Go
Permissible tensile strength for double transverse fillet joint
permissible_tensile_strength = Tensile force on plates/(1.414*Length of weld*Leg of the weld) Go
Strength of Butt Joint
tensile_strength = Tensile force on plates/(Throat thickness*Length of weld) Go
Shear Stress for long fillet weld subjected to torsion
shear_stress = 3*Torque acting on rod/(Throat thickness*(Length of weld^2)) Go
Power Transmitted
shaft_power = (2*pi*Speed of Rotation*Torque) Go
Shear strength for double parallel fillet weld
permissible_shear_stress = 1.414*Leg of the weld/Tensile force on plates Go
Strain Energy Density
strain_energy_density = 0.5*Principle Stress*Principle Strain Go
Factor of Safety given Ultimate and Working Stress
factorofsafety = Fracture Stress/Working Stress Go
Thickness Of Cotter Joint
thickness_of_cotter = 0.31*Diameter of rod Go

### Bending stress in shaft Formula

bending_stress = (32*Bending moment)/(pi*(Diameter of shaft^3))
𝛔b = (32*Mb)/(pi*(d^3))

## What is bending stress in shaft?

It is nominal stress when the shaft is subjected to a load which cause bending and become fatigued. These are mostly occur when shafts are subjected to tensile load.

## How to Calculate Bending stress in shaft?

Bending stress in shaft calculator uses bending_stress = (32*Bending moment)/(pi*(Diameter of shaft^3)) to calculate the Bending Stress, The bending stress in shaft is the normal stress that shaft encounters when it is subjected to a large load at a particular point that causes the object to bend and become fatigued. Bending Stress is denoted by 𝛔b symbol.

How to calculate Bending stress in shaft using this online calculator? To use this online calculator for Bending stress in shaft, enter Bending moment (Mb) & Diameter of shaft (d) and hit the calculate button. Here is how the Bending stress in shaft calculation can be explained with given input values -> 509295.8 = (32*50)/(pi*(0.1^3)).

### FAQ

What is Bending stress in shaft?
The bending stress in shaft is the normal stress that shaft encounters when it is subjected to a large load at a particular point that causes the object to bend and become fatigued and is represented as 𝛔b = (32*Mb)/(pi*(d^3)) or bending_stress = (32*Bending moment)/(pi*(Diameter of shaft^3)). The 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 Diameter of shaft is defined as the diameter of the hole in the iron laminations that contains the shaft.
How to calculate Bending stress in shaft?
The bending stress in shaft is the normal stress that shaft encounters when it is subjected to a large load at a particular point that causes the object to bend and become fatigued is calculated using bending_stress = (32*Bending moment)/(pi*(Diameter of shaft^3)). To calculate Bending stress in shaft, you need Bending moment (Mb) & Diameter of shaft (d). With our tool, you need to enter the respective value for Bending moment & Diameter of shaft 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 Bending Stress?
In this formula, Bending Stress uses Bending moment & Diameter of shaft. We can use 10 other way(s) to calculate the same, which is/are as follows -
• tensile_strength = Tensile force on plates/(Throat thickness*Length of weld)
• strain_energy_density = 0.5*Principle Stress*Principle Strain
• permissible_tensile_strength = Tensile force on plates/(1.414*Length of weld*Leg of the weld)
• shear_strength_in_parallel_fillet_weld = Tensile force on plates/(0.707*Leg of the weld*Length of weld)
• shear_stress = 3*Torque acting on rod/(Throat thickness*(Length of weld^2))
• shear_stress = 2*Torque acting on rod/(pi*Throat thickness*Nominal Diameter^2)
• factorofsafety = Fracture Stress/Working Stress
• permissible_shear_stress = 1.414*Leg of the weld/Tensile force on plates
• shaft_power = (2*pi*Speed of Rotation*Torque)
• thickness_of_cotter = 0.31*Diameter of rod
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