Page 27 - 2019

Ph.D.
(Engineering & Technology)
INVESTIGATION OF OPTIMAL STRESS CONCENTRATION FACTOR FOR
SHOULDER FILLET IN ROUND BARS UNDER VARIOUS LOADING CONDITIONS

Ph.D. Scholar : Prajapati Hirenkumar Rameshbhai
Research Supervisor : Dr. Bhavesh P. Patel

Regi. No.: 14146051004
Abstract :
Many round bars (shafts) gets failure even they are designed with proper design
methodology. The prior art shows the major failures of the shaft is due to high-stress
concentrations developed at the vicinity of discontinuities presents on the shaft. Design
engineers follow the steps recommended by the Peterson, Roark’s and S M Tipton, even
though the shaft gets failure in many applications and it is a very serious issue of the
design. Many reasons are possible for the failure of the shaft but one of the reasons is
lacking in design considerations. The focus of this study is to investigate optimal stress
concentration factor (SCF) of shoulder fillet on a round bar by selecting appropriate fillet
radius (r) for a shoulder fillet under various loading conditions i.e. axial tension, bending
and torsional. First, the SCF curve’s given by a Petersons and equations are given by a
Petersons (Pilkey’s), Roark’s and S. M Tipton are studied for axial tension, bending and
torsional loading. The SCF curve’s presented by Petersons for shoulder filleted shaft are
based on four different parameters i.e. larger diameter (D), smaller diameter (d), fillet
radius (r) and SCF (k k ). In a conventional approach, to obtain SCF using Peterson curves,
t t
the ratio r/d and D/d to be considered as known. As mentioned by Peterson’s, the curves
were developed from the results obtained from experimental work and analytical work
carried out by several researchers in the past, but there is no clear discussion made
about the how these r/d ratios are taken for study and on what basis the values of r, d,
and D were taken to develop range of ratio of r/d and D/d. Therefore, in the presented
work, the efforts have made to develop a relation between fillet radius (r) and SCF (k k ) by
t t
reversing the conventional method. It is very tricky to obtain optimal SCF. First, the
equations provided by Pilkey’s, Roark’s and S M Tipton’s are modified in the form of fillet
radius for different loading conditions i.e., axial tension, bending and torsional with
different D/d ratios using similar range of h/r ratio provided by them, then the SCF is
varying from 0.1 to 7 and selecting those values of SCFs which are fall within the range of
h/r specified by Pilkey’s, Roark’s and S M Tipton. Finally, the range of SCF found is 0.9 to
7. Finite Element Analysis (FEA) of shoulder filleted shaft under axial tension, bending and
torsional loading is carried out using ANSYS 19.0 and equivalent (von Mises) stresses are
calculated and based on the definition of SCF (ratio of maximum stress to nominal
stress), stress concentration factor is calculated. Comparisons of these stress

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