Question

at what distance a should the journal bearing supports at a and b be placed so that the magnitude (absolute value) of the deflection at the center of the shaft is equal to the deflection at its ends? ei is constant.

Answer 1

The question requires using principles of engineering mechanics to determine the placement of journal bearing supports on a shaft to balance deflection constraints, assuming constant flexural rigidity.

Step-by-step explanation:

The question concerns the placement of journal-bearing supports on a shaft to achieve specific deflection constraints. Specifically, it asks for the distance at which two supports should be placed so that the deflection at the center of the shaft equals the deflection at its ends, assuming a constant EI (flexural rigidity).

To answer this question, it is necessary to utilize principles of engineering mechanics and materials, particularly those related to beam deflection, support placement, and the influence of loading conditions. By applying relevant equations and considering the symmetry of the setup, one can determine the appropriate positions for the journal-bearing supports. The problem involves understanding the relationship between forces, moments, and deflections in statically determinate systems.

Without having specific diagrams or additional context, it is challenging to provide a precise answer. Typically, such problems are solved numerically or graphically based on the given boundary conditions and load distributions.