鋼筋混凝土扭力梁之軟化薄膜模式

Softened Membrane Model for RC Members under Torsion

施家榮(Jia-Rong Shih)

指導教授 ： 鄭全桓

國立暨南國際大學/科技學院/土木工程學系/碩士(2007年)

https://doi.org/10.6837/NCNU.2007.00113

摘要

本論文主要是以最新的剪力牆元素理論SMM(Softened Membrane Model)(Hsu and Zhu 2002) 為基礎，首度將混凝土張應力及應變梯度效應(strain gradient effect)納入考慮，發展出一新的鋼筋混凝土梁承受純扭力(pure torsion)的分析模式SMMT(Softened Membrane Model for Torsion)。由於混凝土斜壓桿承受扭力作用造成面外彎曲(out-of-plane bending)，導致在剪力流有效厚度內會產生較大的應變梯度(strain gradient)。因此，若要將應用於二維(2-D)的剪力分析模式SMM應用於三維(3-D)的扭力問題上，則必須對SMM的兩項混凝土組成關係做修正：(1)混凝土張應力-應變組成關係之混凝土張力彈性模數與開裂應變必須放大45%，即1.45倍的未修正的混凝土張力彈性模數與開裂應變 (2) Hsu/Zhu ratio必須折減20%，即扭力之Hsu/Zhu ratio等於0.8倍剪力之Hsu/Zhu ratio。本研究提出此一新的扭力分析模式SMMT，能夠準確且完整地預測混凝土開裂前及開裂後的扭矩-扭轉角曲線(torque-twist curve)，包括上升段(ascending branch)及下降段(descending branch)，且其分析結果與相關文獻之試體實驗結果比對後，結果相當一致。

關鍵字

鋼筋混凝土 ； 剪力 ； 扭力 ； 應變梯度 ； 扭矩-扭轉角曲線 ； 桁架模式

並列摘要

In this thesis the Softened Membrane Model (SMM) (Hsu and Zhu 2002), developed for predicting the behavior of RC membrane elements under shear, is extended to RC members subjected to torsion. This new analytical method, referred to as Softened Membrane Model for Torsion (SMMT), takes into account the strain gradient of concrete struts in the shear flow zone by making two modifications to the constitutive relationships of concrete: First, in the tensile stress-strain relationship of concrete, the pre-cracking stiffness and the strain at peak stress should each be increased by 45%. Second, the Hsu/Zhu ratio for torsion is taken as 80% of the Hsu/Zhu ratio for shear. As can the SMM model for shear, this new SMMT model can predict the entire torque-twist curve including the ranges before and after cracking, as well as the ascending and descending branches. The theoretical predictions from SMMT compare very well with the test data on torsion available in the literature.

並列關鍵字

reinforced concrete ； shear ； torsion ； strain gradient ； torque-twist curve ； truss model

參考文獻

1.ACI Committee 318, “Building Code Requirements for Structural Concrete（ACI 318-05）and Commentary（ACI 318R-05）,”American Concrete Institute, pp. 147-191.

2.Ashour, S. A., Samman, T. A., and Radain, T. A., 1999, “Torsional Behavior of Reinforced High-Strength Concrete Deep Beams,” ACI Structural Journal, Vol. 96, No. 6, Nov.-

Dec., pp.1049-1058.

3.Belarbi, A. and Hsu, T. T. C., 1994, “Constitutive Laws of Concrete in Torsion and Reinforcing Bars Stiffened by Concrete,” ACI Structural Journal, Vol. 92, No. 5, Sept.-Oct., pp.562-573.

4.Bradburn, J. H., “An Investigation of Combined Bending and Torsion in Rectangular Reinforced Concrete Members” Doctoral Dissertation, Department of Civil Engineering, North Carolina State University at Raleigh, 1968, (under the supervision of Prof. Paul Zia).