竖向预应力作用下PC箱梁腹板应力场分析

Analysis on stress field of box girder webs under vertical prestress load

为了研究箱梁腹板在竖向预应力作用下应力分布的特点,以狭长薄板模拟腹板,导出其在单根竖向预应力筋作用下的解析解、数值解,并与有限元计算对比,结果吻合较好。在多对力作用下叠加原理成立,模拟腹板在竖向预应力作用下的应力场,导出竖向正应力的解析解,并采用最小二乘法原理得其数值解。引入应力均匀度参数λ和应力水平系数κ,计算得相应截面的λ值和κ值,表明λ值和κ值对竖向预应力筋间距s较为敏感;当预应力间距与腹板半高之比s/c<0.5时,在x=0.5s处截面上不同高度处均能保持较高的预应力度,且应力比较均匀,λ接近于1;当s/c=0.5时,仅能保证x=0.5s截面上1/4高度处的λ值和κ值分别度达到0.95和0.96。在保证λ值和κ值大于0.95的前提下,计算得适合工程精度的腹板竖向预应力扩散角α,进而得出竖向预应力筋合理间距s=2h.tanα。

In order to study stress distribution of box girder webs under vertical prestress load,the box girder webs were regarded as narrow thin rectangular plates to obtain analytic and numerical solutions under the action of a couple of vertical forces,and the solutions were compared with those given by the finite element method.Good agreement among the solutions was observed.Superposition principle is used to attain the stress field of the box beam web affected by various vertical prestress forces,and the analytical solution of vertical normal stress is derived.The numerical solution is given by the least squares method.Uniformity parameter λ and stress level parameter κ were introduced and calculated,and the results turned out that λ and κ were sensitive to vertical prestressed tendon spa-cing.If s/c0.5,the stresses at different height were uniform and kept in a state of high prestress;if s/c=0.5,it could be ensured that λ is 0.95 and κ is 0.96 at 1/4 height.On the condition that κ and λ were larger than 0.95,the diffusion angle α was calculated,and the reasonable vertical prestress tendon spacing was given as s=2h·tanα.