Abstract
This paper presents an easily comprehensive method of shakedown analysis of two-span beams and symmetric three-span beams with a moving load when taking account of bending and shear. The original problem to be dealt with is a nonlinear mathematical programming due to a nonlinear interaction of bending moment and shearing force on the ultimate strength of cross section. Adoption of Mises yield condition reduces this problem to a quadratic programming. Well-known conception of quadratic inequality is introduced to find the analytical solution of the problem. Numerical results for the beams with various span-ratios, loading conditions and strengths of cross sections clarify the shakedown characteristics, particularly the influence of shearing force on shakedown loads.
