The stepped shaft shown in the figure is to rotate at 900 rpm as it transmits 7000 Nm
torque from a turbine to a generator and this is the only loading case on the shaft. The material specified in the
design is A 284 Steel (grade C) and design factor is given as 2. Determine/evaluate following cases for the shaft.
a) Maximum shear stress on the shaft
b) Principal stresses on the shaft
c) Material yield criteria for selected material and occurred stresses.
Step 1 : Write down input parameters (including material properties) which are
defined in the sample example.
Step 2 : Go to "Torsion of Solid and Hollow Shafts Calculator" page to calculate maximum shear
stress on the shaft. Larger shear stresses occur on smaller diameter section of the shaft so analysis of smaller diameter section is sufficient for this example.
Step 3 : There is a shoulder fillet in the shaft design and this geometry will
raise stress . Stress concentration factor and maximum shear stress
for shoulder fillet will be calculated for torsional loading . Go to "Shoulder fillet
in stepped circular shaft" page for calculations.
Maximum shear stress of 357 MPa occurred at outer radius of shoulder
fillet. This is the answer of clause a) of the sample example.
Step 4 : To calculate principal stresses occurred on the shaft, go to the
"Principal/Maximum Shear Stress Calculator For Plane Stress" page. Note that the torsional
loading of shaft results plane stress state on the surface of shaft so this calculator
can be used.
Principal stresses are calculated as 357 MPa and -357 MPa. This is the
answer of clause b) of the sample example.
Step 5 : Selected material (A284 Steel) is ductile since elongation at break is
greater than 5%. For the evaluation of yield criteria for a ductile material
with plane stress state , we can use "Yield Criteria For Ductile Materials Under
Plane Stress(Static Loading)" page.
According to results, the design is not
safe for the given parameters and conditions. Shaft diameter or material
shall be changed to satisfy required design criteria. Steps listed above shall
be repeated to find dimensions or materials that satisfy
Note: In this example, the loading case
is static and shaft material is ductile. According to Shigley's Mechanical Engineering Design Chapter 3 ,
for ductile materials in static loading, the stress-concentration factor is not usually applied to predict the
critical stress, because plastic strain in the region of the stress is localized and
has a strengthening effect.
According to Peterson's Stress Concentration Factors
Chapter 1, the notch sensitivity q usually lies in the range of 0 to 0.1 for
ductile materials. If a statically loaded member is also subjected to shock
loading or subjected to high and low temperature, or if the part contains sharp
discontinuities, a ductile material may behave like a brittle material. These
are special cases and if there is a doubt, Kt (q=1) shall be applied.
In this example, since there is no information
about temperature and shock loading condition of the shaft,
the notch sensitivity factor q is taken as 1 and Kt is applied .
The problem is fully solved with calculators which are summarized as