###### Abstract  
Nonlinear analysis of structural members is vital to understand the behavior and the response of reinforced concrete members. Even though most design procedures concentrate on the ultimate stage of response towards the end of the post-yielding zone as the decisive design criterion, the structural members usually function at the service load levels within the post-cracking zone. Therefore, cracking is a critical aspect of concrete behavior that affects the overall response of reinforced concrete beams. The initiation and the propagation of the cracks are affected directly by the tension and shear stresses in the beam. In flexural beams, the tensile stresses dominate the crack onset and its growth. Cracks in reinforced concrete flexural beams leave non-cracked regions in between the cracked sections. In order to apply a consistent analysis strategy, the smeared crack approach averages the behavior of these different cracked sections and uncracked in between regions to generate an accurate global response of the entire beam. This study presents a numerical constitutive tensile model that captures the complete tensile response of the reinforced concrete flexural member, in terms of averaged/smeared crack response. As a second step, this model was examined against a large pool of experimental data to validate its accuracy. Overall, the main objective of this study is to develop a representative constitutive tensile model for reinforced concrete flexural members and validate its accuracy against experimental results. The full nonlinear sectional response is analytically realized, based on the assumed trilinear moment-curvature response and the assumed trilinear moment-extreme fiber compressive strain response. This is considered as the secondary outcome of the present study. t 21 December 202025 February 2021  
On the other hand, many researchers proposed empirical functions to estimate the tension stiffening effects. [PERSON] (1977) [4] presented a model for computing the mean strains. Between two cracked sections, the average steel strain over the entire length (\(\varepsilon_{\text{sm}}\)), is less than the bare bar strain (\(\varepsilon_{\text{s}}\)) which is the strain developed by the steel alone after cracking. The difference between (\(\varepsilon_{\text{s}}\)) and (\(\varepsilon_{\text{sm}}\)) is referred to as \"tension stiffening\". Several structural codes followed [PERSON] approach with different parameters like British standards BS 8110-1997 [5] and Eurocode2 (2004) [6]. A different approach is to estimate the tension stiffening effects by assuming a stress-strain profile beyond the cracking point of concrete. This profile includes numerical parameters calibrated against the global experimental response of beams or tensile specimens. [PERSON] and [PERSON] (1974) [7] were the first to model the tension stiffening in terms of the degraded concrete modulus. [PERSON] and [PERSON] (1977) [8] proposed a linear and a bilinear descending curve in their analysis of concrete slabs. [PERSON] and [PERSON] (2006) [9] adopted a bilinear descending function with a sudden drop of 20% of the cracking strength right at the cracking strain--see Figure 1. It is important to note here that all of the earlier tension stiffening models completely degrade the concrete contribution at a multiple of the cracking strain while this parameter seems to be related to the yielding strain of steel. In this study, the latter approach to the modeling of the tension stiffening effects is adopted to develop a newly calibrated model composed of a single mathematical expression. The controlling parameters, of a mathematical function postulated herein, are calibrated based on close agreements (minimized error) between the nonlinear numerical and the experimental load-deflection response of a set of tested beams.