الفهرس 
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Abstract
For better strength prediction using strut-and-tie models (STM), it is essential to use reliable strength parameters of the components of the model; e.g., struts, ties, and nodes. Among all the elements of the STM, the strength of the bottle-shaped struts is not well quantified. The purpose of this study is to develop more accurate formulas for the calculation of the effectiveness factors for bottle-shaped struts in 2D, that are unreinforced struts, reinforced with minimum reinforcement, and reinforced with sufficient transverse reinforcement, also, develop more accurate formulas for the calculation of the bearing stress for 3D struts. The nonlinear finite element analysis, with the aid of the software ABAQUS, has been utilized in this study, which has been verified against experimental tests. The study has been carried out for many different grades of concrete varying from 20 to 100 𝑀𝑃𝑎. The obtained formulas have been verified against experimental tests, and have been compared with the ACI 318-19 provisions in case of 2D D-regions, and with Adebar and Zhou provisions for 3D structures like pile caps. The predictions from the developed formulas are more accurate than the predictions with the ACI 318-19, and Adebar and Zhou provisions. Also, the results from these formulas are always on the safe side. On the other hand, the ACI 318-19 provisions lead to unsafe results in the case of high-strength concrete and very conservative results for the case of unreinforced struts with normal-strength concrete.