负弯矩作用下结合梁挠度计算方法研究

Study of Calculation of Deflection of Composite Girders under Action of Negative Moments

钢 砼结合梁在负弯矩作用下 ,随着荷载逐渐增加 ,混凝土板中的裂缝不断产生和发展 ,梁的刚度也随之逐渐下降 ,荷载 挠度关系趋于非线性 ,因而材料力学中求挠曲线的二次积分法对负弯矩作用下的砼 钢结合梁无法获得解析解。本文提出了求钢 砼结合梁负弯矩作用下挠度的数值积分法 ,把非线性问题转化为短区间的线性问题 ,推导了计算公式 ,建立了计算模型 ,编写了电算程序 ,通过反复迭代计算先获得结合梁截面的弯矩 曲率 (M )关系 ,再根据这一关系进一步求得结合梁各截面的给定荷载下的挠度 ,从而可绘出梁的某一级荷载下的挠曲线或某一截面的荷载 挠度 (p Δ)曲线。本文利用编写的电算程序对芜湖桥的两根大型试验结合梁T1、T2梁进行了试算 ,并与实测结果进行对比 ,计算结果与实测结果吻合较好。

The two step integration method which is usually used to calculate the deflection of girders is not applicable to concrete steel composite girders under the action of negative moment. Because when the load increases, cracks in concrete slabs tend to develop and the stiffness declines, thus leading to nonlinear load deflection relation. This thesis puts forward a numerical integration method, which can be used to calculate the deflections of concrete steel composite girders under negative moment, to convert the nonlinear problem into linear problem at short interval. A program has been written by deducing a formula and establishing a calculation model. The moment curvature ( M  ) relation can be first acquired through repeated calculation, then deflections of different sections of a composite girder under given loads can be acquired according to this relation. Consequently, the curve of deflection of the girder under a certain load or the load deflection ( p Δ) curve of a certain section can be drawn. The program has been applied to two large size experimental composite girders of Wuhu Yangtze River bridge: T1 and T2. Compared with the actual measured values, the theoretical results have showed good coincidence with the actual ones.