Nominal Bending Stress in Round Shaft with Shoulder Fillet Solution

STEP 0: Pre-Calculation Summary
Formula Used
Nominal Stress = (32*Bending Moment on Round Shaft)/(pi*Smaller Diameter of Shaft with Fillet^3)
σo = (32*Mb)/(pi*dsmall^3)
This formula uses 1 Constants, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Nominal Stress - (Measured in Pascal) - Nominal Stress is the value of the stress at the minimum cross-section.
Bending Moment on Round Shaft - (Measured in Newton Meter) - Bending Moment on Round Shaft is the reaction induced in a circular cross-sectioned shaft when an external force or moment is applied to the element, causing the element to bend.
Smaller Diameter of Shaft with Fillet - (Measured in Meter) - Smaller Diameter of Shaft with Fillet is the diameter of the smaller round cross-section of a round shaft which has a fillet.
STEP 1: Convert Input(s) to Base Unit
Bending Moment on Round Shaft: 14000 Newton Millimeter --> 14 Newton Meter (Check conversion here)
Smaller Diameter of Shaft with Fillet: 18 Millimeter --> 0.018 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
σo = (32*Mb)/(pi*dsmall^3) --> (32*14)/(pi*0.018^3)
Evaluating ... ...
σo = 24451788.2390841
STEP 3: Convert Result to Output's Unit
24451788.2390841 Pascal -->24.4517882390841 Newton per Square Millimeter (Check conversion here)
FINAL ANSWER
24.4517882390841 24.45179 Newton per Square Millimeter <-- Nominal Stress
(Calculation completed in 00.004 seconds)

Credits

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Shri Govindram Seksaria Institute of Technology and Science (SGSITS ), Indore
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11 Round Shaft against Fluctuating Loads Calculators

Height of Shaft Keyway given Ratio of Torsional Strength of Shaft with Keyway to without Keyway
Go Height of Shaft Keyway = Diameter of Shaft with Keyway/1.1*(1-Ratio of Shaft Strength with and without Keyway-0.2*Width of Key in Round Shaft/Diameter of Shaft with Keyway)
Ratio of Torsional Strength of Shaft with Keyway to without Keyway
Go Ratio of Shaft Strength with and without Keyway = 1-0.2*Width of Key in Round Shaft/Diameter of Shaft with Keyway-1.1*Height of Shaft Keyway/Diameter of Shaft with Keyway
Width of Shaft Keyway given Ratio of Torsional Strength of Shaft with Keyway to without Keyway
Go Width of Key in Round Shaft = 5*Diameter of Shaft with Keyway*(1-Ratio of Shaft Strength with and without Keyway-1.1*Height of Shaft Keyway/Diameter of Shaft with Keyway)
Diameter of Shaft given Ratio of Torsional Strength of Shaft with Keyway to without Keyway
Go Diameter of Shaft with Keyway = (0.2*Width of Key in Round Shaft+1.1*Height of Shaft Keyway)/(1-Ratio of Shaft Strength with and without Keyway)
Torsional Moment in Round Shaft with Shoulder Fillet given Nominal Stress
Go Torsional moment on Round Shaft = (Nominal Torsional Stress for Fluctuating Load*pi*Smaller Diameter of Shaft with Fillet^3)/16
Smaller Diameter of Round Shaft with Shoulder Fillet in Tension or Compression
Go Smaller Diameter of Shaft with Fillet = sqrt((4*Load on Flat Plate)/(pi*Nominal Stress))
Nominal Torsional Stress in Round Shaft with Shoulder Fillet
Go Nominal Stress = (16*Torsional moment on Round Shaft)/(pi*Smaller Diameter of Shaft with Fillet^3)
Nominal Bending Stress in Round Shaft with Shoulder Fillet
Go Nominal Stress = (32*Bending Moment on Round Shaft)/(pi*Smaller Diameter of Shaft with Fillet^3)
Bending Moment in Round Shaft with Shoulder Fillet given Nominal Stress
Go Bending Moment on Round Shaft = (Nominal Stress*pi*Smaller Diameter of Shaft with Fillet^3)/32
Nominal Tensile Stress in Round Shaft with Shoulder Fillet
Go Nominal Stress = (4*Load on Flat Plate)/(pi*Smaller Diameter of Shaft with Fillet^2)
Tensile Force in Round Shaft with Shoulder Fillet given Nominal Stress
Go Load on Flat Plate = (Nominal Stress*pi*Smaller Diameter of Shaft with Fillet^2)/4

Nominal Bending Stress in Round Shaft with Shoulder Fillet Formula

Nominal Stress = (32*Bending Moment on Round Shaft)/(pi*Smaller Diameter of Shaft with Fillet^3)
σo = (32*Mb)/(pi*dsmall^3)

Some load applications that may cause stress concentration

The examples of these load applications are as follows:
(a) Contact between the meshing teeth of the driving and the driven gear.
(b) Contact between the cam and the follower.
(c) Contact between the balls and the races of the ball bearing.
(d) Contact between the rail and the wheel.
(e) Contact between the crane hook and the chain.
In all these cases, the concentrated load is applied over a very small area resulting in stress concentration.

How to Calculate Nominal Bending Stress in Round Shaft with Shoulder Fillet?

Nominal Bending Stress in Round Shaft with Shoulder Fillet calculator uses Nominal Stress = (32*Bending Moment on Round Shaft)/(pi*Smaller Diameter of Shaft with Fillet^3) to calculate the Nominal Stress, Nominal Bending Stress in Round shaft with Shoulder fillet is the amount of bending stress at the minimum cross-section in the round shaft with shoulder fillet with stress concentration arising due to the forces acting perpendicular to the shaft axis. Nominal Stress is denoted by σo symbol.

How to calculate Nominal Bending Stress in Round Shaft with Shoulder Fillet using this online calculator? To use this online calculator for Nominal Bending Stress in Round Shaft with Shoulder Fillet, enter Bending Moment on Round Shaft (Mb) & Smaller Diameter of Shaft with Fillet (dsmall) and hit the calculate button. Here is how the Nominal Bending Stress in Round Shaft with Shoulder Fillet calculation can be explained with given input values -> 2.4E-5 = (32*14)/(pi*0.018^3).

FAQ

What is Nominal Bending Stress in Round Shaft with Shoulder Fillet?
Nominal Bending Stress in Round shaft with Shoulder fillet is the amount of bending stress at the minimum cross-section in the round shaft with shoulder fillet with stress concentration arising due to the forces acting perpendicular to the shaft axis and is represented as σo = (32*Mb)/(pi*dsmall^3) or Nominal Stress = (32*Bending Moment on Round Shaft)/(pi*Smaller Diameter of Shaft with Fillet^3). Bending Moment on Round Shaft is the reaction induced in a circular cross-sectioned shaft when an external force or moment is applied to the element, causing the element to bend & Smaller Diameter of Shaft with Fillet is the diameter of the smaller round cross-section of a round shaft which has a fillet.
How to calculate Nominal Bending Stress in Round Shaft with Shoulder Fillet?
Nominal Bending Stress in Round shaft with Shoulder fillet is the amount of bending stress at the minimum cross-section in the round shaft with shoulder fillet with stress concentration arising due to the forces acting perpendicular to the shaft axis is calculated using Nominal Stress = (32*Bending Moment on Round Shaft)/(pi*Smaller Diameter of Shaft with Fillet^3). To calculate Nominal Bending Stress in Round Shaft with Shoulder Fillet, you need Bending Moment on Round Shaft (Mb) & Smaller Diameter of Shaft with Fillet (dsmall). With our tool, you need to enter the respective value for Bending Moment on Round Shaft & Smaller Diameter of Shaft with Fillet 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 Nominal Stress?
In this formula, Nominal Stress uses Bending Moment on Round Shaft & Smaller Diameter of Shaft with Fillet. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Nominal Stress = (4*Load on Flat Plate)/(pi*Smaller Diameter of Shaft with Fillet^2)
  • Nominal Stress = (16*Torsional moment on Round Shaft)/(pi*Smaller Diameter of Shaft with Fillet^3)
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