2011 Frontiers in Education Conference (FIE) 2011
DOI: 10.1109/fie.2011.6143039
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Teaching deflection of stepped shafts: Castigliano's theorem, dummy loads, heaviside step functions and numerical integration

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Cited by 9 publications
(4 citation statements)
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“…To apply this method to the stepped shaft problem, the complementary energy U needs to be computed through integration over each section in symbolic form so that suitable derivatives can be computed [22]. A direct calculation will lead to the piecewise integral shown below in Equation (8).…”
Section: Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…To apply this method to the stepped shaft problem, the complementary energy U needs to be computed through integration over each section in symbolic form so that suitable derivatives can be computed [22]. A direct calculation will lead to the piecewise integral shown below in Equation (8).…”
Section: Methodsmentioning
confidence: 99%
“…A complete stepped shaft design takes many pages of tedious computation (see Shigley [26]) and so is entirely avoided by many instructors as being too time‐consuming. The alternative is to either use Castigliano's theorem (as was done by [22]) or use a numerical solver, like the Finite Element Method (which for all purposes is a black box for the students). In the latter case, in a typical course on the design of machine elements, students fail to decipher how these equations are obtained or derived, so instructors are loathed for simply using it as a black box.…”
Section: Introductionmentioning
confidence: 99%
“…As the manipulator is quite complex having different sections, the exact model is not available in the literature. In this work, the theoretical model is derived using the Castigliano's theorem [36]. The strain energy stored in the manipulator due to bending is given by (8).…”
Section: Theoretical Analysismentioning
confidence: 99%
“…In this analysis, the numerical integration method has been chosen. This method as a successive integration is an algebraically intensive concept but can be performed with the help of many software such as MATLAB and MATHCAD [9]. The proposed shaft is loaded with a 25785 N centered force, propped by three bearings, and a keyway is mounted at its end.…”
Section: Analytical Calculationsmentioning
confidence: 99%