A simple method of computing the effect of a dimensional change at a particular element of a stepped shaft on two bearings, on bending deflections, and on slopes of the neutral axis at any of the nodes of interest is presented. The changes in deflection and slope of the neutral axis are derived as incremental quantities and as functions of the dimension change and the prior deflections and slopes of the neutral axis of the shaft. For shaft synthesis, the implications are that one can begin with a uniform diameter bar subjected to the loading and make a complete deflection analysis with superposed closed-form relations. Then the geometry can be modified element by element and the deflectional changes easily updated. This is computationally efficient. Further, deflections and deflection changes computed using the proposed method are identical to those obtained using a finite beam element model of the shaft.

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