Statistical Prediction Equations for RC Deep Beam Without Stirrups

Abstract

Reinforced concrete (RC) deep beams mainly fail in shear, brittle and sudden in nature can lead to calamitous consequences. Thence, it is critical to determine the shear characteristics of RC deep beams accurately due to involving many parameters at same time. Some of the recent researches have shown that current equations for predicting ultimate shear strength are non-conservative when applied to high strength concrete (HSC) beams as well as some of design codes provisions. There are different approaches for analyzing the behavior of beams in shear. In this paper, a semi-empirical approach is adopted in which a database of existing experimental and literature results of deep beams, d > 300 mm & d < 300 mm, failing in shear under two point loads statically at mid-span, was constructed. The database, 725 deep beams, was used to propose two simplified shear equations using multiple regression analysis, IBM-SPSS-Statistics, to find out and evaluate the most important factors affecting the ultimate shear strength formulating them in a suitable predictive equation for the ultimate shear strength of deep beams without web reinforcement (stirrups). The test database covers a wide range of individual parameters as: cylindrical concrete compressive strength (20 ≤ f ′c ≤ 104 MPa), longitudinal main steel reinforcement ratio (0.17% ≤ ρs% ≤ 6.64%), effective depth of deep beams “d” (127–1000 mm), shear span to effective depth ratio (1 ≤ a/d ≤ 2.5), Beam width “b”; b/d < 1, where all database from literature were based on two point loading. This paper concluded that, the proposed equations seem to predict the ultimate shear strengths well, conservative and give lower coefficient of variation “COV” and smaller range of results when compared with the available methods of design; ECP203-2007, ACI 318-14, CSA, and BS8110 codes and other equations proposed by Sudheer Reddy, Zararis, Bazant, Zsutty and Shah.