Based on the equilibrium principle of material mechanics and the geometric equation of plane problems in elasticity,the deflection differential equation and bending stress expression of cantilever tapered beams with rectangular cross-section are established.The deflection differential equation is integrated.Com-bined with the boundary conditions of bending deformation,the analytical solutions of the deflection of can-tilever tapered beams under three simple load cases of concentrated load,uniformly distributed load and ben-ding couple are derived.By taking the derivative of bending stress,the maximum bending stress value of ta-pered beams under arbitrary loads can be determined.The bending problems of cantilever beams under three simple load cases are verified respectively by using the general structural design and analysis software SAP2000.When calculating the bending deflection,it is found that the calculation methods here are all comparable to the software calculation results and are slightly larger than them.This is due to the fact that the influence of section rotation on deflection is not considered in software calculation.When calculating the maximum bending stress,it is found that when the section transformation coefficient of tapered beams is less than 0.4,the calculation method here has high calculation accuracy and can meet the design requirements of general civil engineering and has certain engineering application value.
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