Chattopadhyay, S. (2012, June), Investigation of Proportional and Non-proportional Loadings Using Mohr’s Circle  Paper presented at 2012 ASEE Annual Conference & Exposition, San Antonio, Texas. 10.18260/1-2--21616

\bibitem{asee_peer_21616}
  Chattopadhyay, S. (2012, June), \emph{Investigation of Proportional and Non-proportional Loadings Using Mohr’s Circle}
  Paper presented at 2012 ASEE Annual Conference \& Exposition, San Antonio, Texas.
  10.18260/1-2--21616

Somnath Chattopadhyay.  "Investigation of Proportional and Non-proportional Loadings Using Mohr’s Circle".  2012 ASEE Annual Conference & Exposition, San Antonio, Texas, 2012, June.  ASEE Conferences, 2012.  https://peer.asee.org/21616 Internet.  25 Apr, 2024

\bibitem{asee_peer_21616}
  Somnath Chattopadhyay.
  "Investigation of Proportional and Non-proportional Loadings Using Mohr’s Circle".
  \emph{2012 ASEE Annual Conference \& Exposition, San Antonio, Texas, 2012, June}.
  ASEE Conferences, 2012.
  https://peer.asee.org/21616 Internet.  25 Apr, 2024

@INPROCEEDINGS{asee_peer_21616
author = "Somnath Chattopadhyay"
title = "Investigation of Proportional and Non-proportional Loadings Using Mohr’s Circle"
booktitle = "2012 ASEE Annual Conference \& Exposition"
year = "2012"
month = "June"
address = "San Antonio, Texas"
publisher = "ASEE Conferences"
note = {https://peer.asee.org/21616}
number = {10.18260/1-2--21616}
}

TY  - CPAPER
AB  - Investigation of Proportional and Non-proportional Loadings Using Mohr’s Circle                                          ABSTRACTFor time-varying loads, proportional loading refers to the cases where the principal stressesmaintain constant directions and constant ratios of their values; otherwise it is non-proportional,Non-proportional loadings are especially important in the design and analysis of automotivecomponents, such as crankshafts and connecting rods. It is important to understand how externalbending and torsional loads combine to form various mixes of normal and shear stresses. Inparticular, the principal stresses play an important role in predicting material failure under staticas well as dynamic loads. Mohr’s circle is an invaluable tool in its ability to determine theprincipal stresses and principal directions. The features of proportional and non-proportionalloadings have been exemplified in this paper by studying the stresses in a shaft under combinedbending and torsion using the Mohr’s circle. The specific cases considered are: a) time varyingbending moment and time-varying torsion that are in phase, b) time varying bending momentand time-varying torsion that are 90° out of phase, c) time varying bending moment and steadytorsion, and d) steady bending moment and time-varying torsion. Making use of Mohr’s circlethe students are able to determine whether the principal stress directions remain unchanged orchange with time, and accordingly understand the proportional and non-proportional loadings.
AU  - Somnath Chattopadhyay
CY  - San Antonio, Texas
DA  - 2012/06/10
PB  - ASEE Conferences
TI  - Investigation of Proportional and Non-proportional Loadings Using Mohr’s Circle
UR  - https://peer.asee.org/21616
DO  - 10.18260/1-2--21616
ER  -