Strut and Tie Model Analysis in Design of RCC Deep Beams with a Different Angles Between Struts and Tie

Abstract

It is proved that the strut-and-tie model (STM) method is efficient and useful in predicting the strength of deep beams. However, the advantages of the STM approach are limited as most publications and standards lack adequate definition and have not been extensively verified a detailed analysis and design procedure for different loading cases for referring in structural analyses and designs. Therefore, this study provides detailed information and design examples for such cases to create a better understanding on the behaviour of deep beam. In this study nine simply supported reinforced concrete (RC) deep beams were modelled and analysed using a nonlinear FEA software called VecTor2, in order to investigate the behaviour of deep beam. The study variables include; load type, strut angle and shear span to depth ratio. The beams were grouped into fourseries, 𝐺𝑟𝑜𝑢𝑝 − 𝐼, 𝐺𝑟𝑜𝑢𝑝 − 𝐼𝐼, 𝐺𝑟𝑜𝑢𝑝 − 𝐼𝐼𝐼, 𝑎𝑛𝑑 𝐺𝑟𝑜𝑢𝑝 − 𝐼𝑉 considering strut angle, eccentric loading, number of point loads and size of beam, respectively. The shear span-to-depth ratio of the selected members ranges between 0.678 − 𝑡𝑜 − 2.28. The longitudinal reinforcement and vertical tie ratio used for all the RC deep beam specimens analysed using both STM and nonlinear FEA was equal with the same grade of concrete and steel. The tested members were validated by comparing to experimental predictions and comparison of the STM and NLFEA prediction. Finally, the selected deep beams are analysed using VecTor2 and computer aided strut and tie (CAST) software’s; and their load displacement diagrams were presented. The results showed that STM provided highly conservative predictions compared to NLFEA. The capacity predicted using STM was: 65.9%, 35.2%, 61.1%, 45.3%, 68.1%, 66.5%, 60.1%, 40.8% 𝑎𝑛𝑑 57.9% capacity of none-linear FEA, for specimens: CLDB1, CLDB2, CLDB3, CLDB4, ELDBWB1, ELDBWOB1, TCLDB1, FCLDB1 and HDCLDB4, respectively. Both STM and NLFEA predicted identical load transfer mechanism and failure modes for the deep beam specimens. Specimens with 𝑎/𝑑 > 1 transferred stress in truss action, whereas, specimens with 𝑎/𝑑 < 1 transferred stress in tied-arch action. Specimens with 𝑎/𝑑 > 1, 𝑎/𝑑 < 1 and 𝑎/𝑑 > 2 showed diagonal compression, splitting shear and diagonal tension failure mode, respectively.