MINIMIZING DEFLECTION AND BENDING MOMENT IN A BEAM WITH END SUPPORTS

In this paper, heuristics are given to sequence blocks on a beam, like books on a bookshelf, to simultaneously minimize the maximum deflecti on and maximum bending moment of the beam. For a beam with simple supp orts at the ends, one heuristic places the blocks so that the maximum deflection is no more than 16/9 square-root 3 almost-equal-to 1.027 ti mes the theoretical minimum and the maximum bending moment is within f our times the minimum. Another heuristic allows maximum deflection up to 2.054 times the theoretical minimum but restricts the maximum bendi ng moment to within two times the minimum. Similar results hold for be ams with fixed supports at the ends.