Elastic-plastic bi-layer beams on Winkler foundation under a concentrated load
To improve the theoretical basis of elastic-plastic beams on elastic foundations,assuming that the beams are ideal elastic-plastic and the bi-layer beams are connected by vertical springs between the layers,the differential equations of the bi-layer elastic-plastic beams on Winkler foundation were formulated based on force equilibrium and constitutive relationships,and generalized solutions were given.Subsequently,an analy-sis was conducted on the bi-layer beams with an infinite length and a centralized load at its center.The entire loading process of the bi-layer beams with uniform quality and width was investigated,and the effects of pa-rameters such as beam thickness and interlayer vertical modulus on the beam's maximum load-bearing capacity were analyzed.The results indicate that if the upper and lower beams have same thickness or the lower beam is thinner,the upper beam will give first,independent of the interlayer vertical modulus.As the interlayer verti-cal modulus approaches infinity,the deflection curves of the upper and lower beams become identical,and the ultimate load carrying capacity approaches that of the bi-layer stacked beams.Then,the structure transforms into bi-layer stacked beams.When the ratio of the interlayer's vertical modulus to the reactive modulus of the foundation is greater than 5 000,the effect of the vertical tensile and compressive deformation of the upper and lower beams on the ultimate bearing capacity of the beams exceeds 3％and should be considered.It is appro-priate to employ the generalized modulus to account for the effect of vertical tensile and compressive deforma-tion of the beam section.
foundation elastic-plastic beamultimate bearing capacitybi-layer beamWinkler foundationanalytical solution
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