钢-混凝土组合梁界面滑移效应变分法求解

Solution of slip effect of steel-concrete composite beam with variational principles

为了求解钢-混凝土组合梁的界面滑移效应,以弹性理论为基础,建立平衡方程;利用最小势能原理,结合变分方法,分别推导了简支钢-混凝土组合梁在受均布荷载和集中荷载时,组合梁的界面相对滑移、组合梁挠度以及附加弯矩的计算方法。结果表明:此方法使相对滑移微分方程基本形式得到统一;附加弯矩与相对滑移趋势成正比,而与相对滑移量无关;界面相对滑移量与抗滑移刚度、截面剪力有关,并且会增加组合梁挠度;简支组合梁相对滑移在梁两端部达到最大值,而向跨中减小。最后通过算例验证了给出的解析解的正确性。

In order to solve the simple steel-concrete composite equation was built with the theory of elasticity. The analytic expressions of interface slip and deformation, which were caused by point load or distributed load, were derived by using the principle of minimum potential energy and variational method. The method for calculating additional bending moment was derived, too. The results show that the method unifies the basic form of the relative slip differential equation. Additional moment has nothing to do with the amount relative slip, while it is proportional to the trend of relative slip. Relative slip is associated with anti-slip and the cross-section shear, and will increase the deflection of composite beam. While the maximum interracial slip is at the end of beam and decreases to zero at he mid-span. The suggested formulas are in good agreement with the measured results. 7 figs, 15 refs.