基于尺寸效应的无腹筋钢筋混凝土梁的剪切强度公式

Shear Strength Formula for Reinforced Concrete Beams Without Web Reinforcements Against Size Effect

取无腹筋钢筋混凝土梁的临界斜裂缝及其顶端横截面所截隔离体为研究对象,根据极限平衡法,建立平衡方程组。分析临界剪压区主应力与梁斜截面破坏形式的关系,并对临界剪压区进行应力分析,再应用Baant提出的尺度律,得到同时适用于斜拉破坏和剪压破坏的无腹筋钢筋混凝土梁的剪切强度公式,其中,临界剪压区高度是该公式的未知参数。通过对Baant试验数据库进行Levenberg-Marguardt非线性最小二乘曲线拟合,得到临界剪压区高度与各参数的幂指数关系。最后经与Collins试验数据库比较可知,相对于ACI 318-08和GB 50010-2010对应的剪切强度公式,所得的剪切强度公式能更好地与试验数据吻合,且和Baant的剪切强度公式计算结果接近。

Based on the limit equilibrium method, equih＇brium equations were established by studying the free body composed of the critical inclined crack and the top cross-section from re- inforced concrete beams without web reinforcements. Analyzing the relationships between prin- cipal stresses of the critical shear compression zone and damage forms, stress analysis of the critical shear compression zone was done. Then by applying Baznt＇ s size effect law, a shear strength formula of reinforced concrete beams without stirrups for both diagonal tension failure and shear compression failure was obtained, where the critical shear compression zone height was the unknown parameter. And then by Levenberg-Marguardt nonlinear least-square curve fit- ting on Bazant＇ s test database, exponential relationship between the height of the critical shear compression zone and parameters was gotten. Finally, comparison with Collins＇ test database shows that the obtained shear strength formula can be demonstrated to agree more favorably with the test database than those from ACI 318-08 and GB 50010-2010, and close with Bazant＇ s shear strength formula.