本研究係採用壓拉桿觀念建立剪力強度模式以預測鋼筋混凝土梁開榫端壓桿所能提供之剪力強度。模式之建立主要是考慮主拉力鋼筋與對角壓桿所形成的壓拉桿機制及橫向鋼筋機制來提供鋼筋混凝土梁開榫端之剪力強度，並進一步依據前人研究之130個試驗資料建立剪力強度預測公式以直接計算鋼筋混凝土梁開榫端壓桿所能提供之剪力強度。本研究並將建議模式、軟化壓拉桿模式[16,29] 及ACI 318-08附錄A壓拉桿模式[14]之預測結果作一比較，以探討各種模式對鋼筋混凝土梁開榫端剪力強度預測之適用性。研究結果顯示，本研究建議公式較能合理地預測一般強度及高強度鋼筋混凝土梁開榫端之剪力強度，預測值相當安全且偏保守，而且係以單一公式直接計算鋼筋混凝土梁開榫端壓桿所提供之剪力強度，公式本身簡單易算。
為了避免壓桿產生早期斜向劈裂破壞而無法發揮壓桿之壓力強度，在本研究中亦採用了壓拉桿觀念建立理論模式以計算鋼筋混凝土梁開榫端所須配置之最小橫向鋼筋量，並進一步依據前人研究，選擇產生對角壓桿破壞的試體130個試體，產生斜張破壞的試體25個試體，探討本研究所建議最小橫向鋼筋量計算公式之適用性。研究結果顯示，本研究所建議之最小橫向鋼筋量計算公式確能能合理地預測一般強度及高強度鋼筋混凝土梁開榫端所須配置之最小橫向鋼筋量，其計算值相當安全且偏保守，而且公式計算簡單，在工程應用上相當簡便。

A model for determining the shear strength of reinforced concrete dapped-end beams is proposed in this study. In this model, it is assumed that the shear strength of dapped-end beams is provided by the strut-and-tie mechanism and the transverse reinforcement as well. In this study, test results of 130 specimens available in the literature are compared with the results predicted separately by the proposed model, the softened strut-and-tie model, and the strut-and-tie model of ACI 318-08. The comparisons show that the proposed model can more easily and reasonably predict the shear strength of reinforced concrete dapped-end beams.
In order to prevent the dapped-end beams from premature diagonal tension failure, an analytical model for determining the minimum transverse reinforcement required for dapped-end beams is also proposed based on strut-and-tie concept. In this study, test results of 130 specimens failed by crushing of diagonal strut and 25 specimens failed by diagonal tension splitting are used to examine the applicability of the proposed model. The comparisons show that the proposed model can reasonably predict the minimum transverse reinforcement required for both low-strength and high-strength concrete dapped-end beams.

參考文獻
[1] Mattock, A. H., and Chan, T. C.,“Design and Behavior of Dapped-End Beams,”PCI Journal, Vol.24, NO.6, November-December , pp.28-45.(1979).
[2] 中國土木水利工程學會,「鋼筋混凝土學」,科技圖書股份有限公司,台北, 320pp.(2009)
[3] Schlaich,J., Schafer,K., and Jennewein, M.,“ Toweard a Consistent Design of Structural Concrete ,” Prestressed Concrete Institute Journal, Vol.32, NO.3, Mayr-June , pp.74-150.(1987).
[4] ASCE-ACI Committee 426,“The Shear Strength of Reinforced Concrete Members,”Journal of Structural Division, ASCE, Vol.99, NO. ST6, pp.1091-1187.(1973).
[5] Zhang, L. X. B., and Hsu, T. T. C.,“Behavior and Analysis of 100 MPa Concrete Membrane Elements,”Journal of Structural Engineering, ASCE, Vol. 124, No. 1, pp. 24~34 (1998).
[6] Schlaich,J., and Schafer,K.,“Druck und Querzug in Bewehrten Betonelementen,” Bericht, Institut fur Massivbau, Universitat Stuttgart, .(1987)
[7] Schlaich,J., and Schafer,K.,“ Zur Druck-Querzug-Festigkeit ded Stahibertons,” Beton-und Stahibetonst, ” Beton-und Stahlbetonbaut, . Vol.3, pp. 73~78 (1983).
[8] Miyahra, T., Kawakami, T., and Maekawa, K.,“Nonlinear behavior of crack reinforced concrete plate element under uniaxial compression,” Concrete Library International, JSCE, Vol.11, pp. 306~319 (1988).
[9] Ueda,M.,Noguchi,H.,Shirai,N.,and Morita,S.,“Introduction to activity of new RC.,”Proceedings International Workshop on Finite Element Analysis of Reinforced Concrete,Columbia University,New York. (1991).
[10] Mikame,A.,Uchida,K.,and Noguchi,H.,“A Study of compressive deterioration of crack concrete,” Proceedings International Workshop on Finite Element Analysis of Reinforced Concrete,Columbia University,New York. (1991).
[11] Vecchio,F.J.,and Collins,M.P.,“Compression response of cracked reinforced concrete,”Journal of Structural Engineering, ASCE, Vol.119, No.12, pp. 3590~3610 (1993).
[12] ASCE-ACI Committee 445, “Recent Approach to Shear Design of Structural Concrete,”Journal of Structural Engineering, ASCE, Vol.124, No.12, pp. 1375~1417 (1998)
[13] PCI Design Handbook, 5th Edition, Prestressed Concrete Institute, Chicago, Illinois (1999).
[14] ACI Committee 318,“Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary,”American Concrete Institute, Farmington Hills, Michigan (2008).
[15] 李宏仁、黃世建，「鋼筋混凝土結構不連續區域之剪力強度評估－軟化壓拉桿模型簡算法之實例應用」，結構工程，第17卷，第4期，第53-70頁 (2002)。
[16] Hwang, S.J., and Lee, H. J.,”Strength Predicton for Discontinuity Regions by Softened Strut-and Tie Model,” Journal of Structural Engineering , Vol. 128, NO. 12, pp.1519-1526(2002)
[17] Khan, M. A.,“A Study of the Behavior of Reinforced Concrete Dapped-End Beams,”MSCE Thesis, University of Washington, Seattle (1981).
[18] Chung, J. C.,“Effect of Depth of Nib on Strength of a Dapped-End Beam,”MSCE Thesis, University of Washington, Seattle (1981).
[19] 林佑鴻，「鋼筋混凝土梁開榫端之設計」，碩士論文，國立台灣科技大學營建工程系，台北 (2000)
[20] 蔡峻庭，「高強度鋼筋混凝土梁開榫端之設計」，碩士論文，國立台灣科技大學營建工程系，台北 (2001)。
[21] 黃再發，「剪跨比較大時鋼筋混凝土開榫梁之行為」，碩士論文，國立台灣科技大學營建工程系，台北 (2001)。
[22] 林詩隆，「含水平力時鋼筋混凝土開榫梁之行為」，碩士論文，國立台灣科技大學營建工程系，台北 (2002)。
[23] 郭武威，「高強度鋼筋混凝土開榫梁之行為」，碩士論文，國立台灣科技大學營建工程系，台北 (2002)。
[24] 金華如，「高強度鋼筋混凝土開榫梁之行為」，碩士論文，國立台灣科技大學營建工程系，台北 (2003)。
[25] 林宏緯，「剪力鋼筋量對鋼筋混凝土梁開榫端剪力強度之影響」，碩士論文，國立台灣科技大學營建工程系，台北 (2007)。
[26] Hwang, S. J., Lu, W. Y., and Lee, H. J.,“Shear Strength Prediction for Reinforced Concrete Corbels,”ACI Structural Journal, Vol. 97, No. 4, pp. 543-552 (2000).
[27] Hwang, S. J., Lu, W. Y., and Lee, H. J.,“Shear Strength Predicton for Deep Beams,”ACI Structural Journal, Vol. 97, No. 3, pp. 367-376 (2000).
[28] Lin, I. J., Hwang, S. J., Lu, W. Y., and Tsai, J. T.,“Shear Strength of Reinforced Concrete Dapped-end Beams,”Structural Engineering and Mechanics, Vol. 16, No. 3, pp. 275-294 (2003).
[29] Lu, W. Y., Lin, I. J., Hwang, S. J., and Lin, Y. H.,”Shear Strength of High-Strength Concrete Dapped-End Beams,” Journal of the Chinese Institute of Engineers , Vol. 26, No. 5, pp.671-680(2003)
[30] 呂文堯、黃世建、林英俊，「鋼筋混凝土梁開榫端之抗剪強度評估」，中國土木水利工程學刊，第14卷，第1期，第13-21頁 (2003)。
[31] Russo, G., Venir, R., and Pauletta, M.,“Reinforced Concrete Deep Beams-Shear Strength Model and Design Formula,”ACI Structural Journal, Vol. 102, No.3, pp. 429-437 (2005).
[32] Russo, G., Venir, R., Pauletta, M., and Somma, M.,“Reinforced Concrete Corbels－Shear Strength Model and Design Formula,”ACI Structural Journal, Vol.103, No.1, pp.3-10 (2006).
[33] Siao, W. B.,“Strut-and-Tie Model for Shear Behavior in Deep Beams and Pile Caps Failing in Diagonal Splitting,”ACI Structural Journal, Vol. 91, No. 2, pp. 123-132 (1994).
[34] Zhang, L. X. B., and Hsu, T. T. C.,“Behavior and Analysis of 100 MPa Concrete Membrane Elements,”Journal of Structural Engineering, ASCE, Vol. 124, No. 1, pp. 24~34 (1998).
[35] ENV 1992-1-1,“Eurocode 2-Design of Concrete Structures-Part 1-1：General Rules and Rules for Buildings,”Comite Europeen de Normalization CEN, 203 pp. (1992).
[36] Brown,M.,D., and Bayrak, O.,“Minimum Transverse Reinforcement for Bottle-Shaped Struts,” ACI Structural Journal, Vol.103, NO.6, pp.813-821 (2006).
[37] Brown,M.,D., Sankovich,C.L., Bayrak, O., Jirsa,J.O., Breen,J.E., and Wood,S.L., “Design for Shear in Reinforced Concrete Using Strut-and-Tie Models,” Report No. 0-4371-2, Center for Transportation Research, University of Texas at Austin,Tex. Apr. (2006)
[38] Schlaich, J., and Weischede, D.,“Detailing of Concrete Structures ,” Bulletin d’Information 150, Comite Euro-International du Beton ,Paris,163pp.(1982).