Minimizing Deflection and Bending Moment in a Beam with End Supports*

摘要

In this paper, heuristics are given to sequence blocks on a beam, like books on a bookshelf, to simultaneously minimize the maximum deflection and maximum bending moment of the beam. For a beam with simple supports at the ends, one heuristic places the blocks so that the maximum deflection is no more than 16/9V3 #x2248; 1.027 times the theoretical minimum and the maximum bending moment is within four times the minimum. Another heuristic allows maximum deflection up to 2.054 times the theoretical minimum but restricts the maximum bending moment to within two times the minimum. Similar results hold for beams with fixed supports at the ends.