New algorithm for fixed-angle softened-truss model

Abstract

The present paper proposes a solution methodology to predict the shear stress-shear strain curves of reinforced concrete (RC) elements (panels) using a truss model. The proposed solution procedure calculates the concrete constitutive relationships by transforming the concrete stresses and strains from the principal direction of concrete stresses to the principal direction of the applied stresses. As a result, the algorithm predicts the shear responses of RC elements having a large difference between the amounts of steel in two perpendicular directions. To check the success of the proposed methodology, the experimental shear stress-strain and shear stress-normal strain curves of 12 RC elements as well as the shear strengths of 170 beams reported in the literature are compared with their corresponding predicted results using the new algorithm of the truss model. The results show that the proposed algorithm accurately predicts the variation of the concrete strain of 12 reinforced elements and the shear strength of 170 beams. INTRODUCTIONThe post-cracking behaviour of a reinforced concrete (RC) member subjected to shear and bending was first simulated by a truss model theory at the turn of the century by Ritter and Morsch. The theory assumes that the cracked concrete separates into a series of struts, so that the shear resistance of the RC member is provided by an internal truss mechanism. Along with the original truss model theory of Ritter and Morsch, many compatibility-aided truss models, such as the compression field theory (CFT, 1,2 modified compression field theory 3 (MCFT)), the rotating-angle softened-truss model (RA-STM 4 ), and the fixed-angle softened-truss model (FA-STM 5,6 ) were developed to predict the shear strengths as well as the deformations of RC membrane elements (panels) subjected to shear and normal stresses.

Fixed-Angle Smeared-Truss Approach with Direct Tension Force Transfer Model for Torsional Behavior of Steel Fiber-Reinforced Concrete Members

“…It is worth noting that the existing fixed-angle theories (Pang and Hsu 1996;Hsu and Zhang 1997) applied the compressive stress-strain relationships of concrete determined in the principal stress direction to that in the initial fixed-crack direction. Therefore, the stresses and strains calculated by these relationships gradually differ from the actual stresses and strains in the initial fixed-crack direction because the deviation angle ( β ) between the crack angle ( 2 α ) and the principal stress angle ( α ) increases as externally applied load inceases (Lee and Mansur 2006;Lee et al 2011). To take such a deviation angle into account in this study, the stresses and strains in the crack direction (direction 2-1) were calculated by transforming the stresses and strains in the principal direction (direction d-r) by the angle of β (refer to Figs.…”

“…7. The initial value of β is taken as zero for calculations because the initial crack angle ( 2 α ) coincides with the principal stress angle ( α ) (Lee and Mansur 2006;Lee et al 2011). The stresses of concrete, steel bars, and steel fibers can be determined by selecting the average principal compressive strain ( d ε ) with assumed values of the average shear strain ( 12 γ ) and the average princi- …”

Force transfer mechanism and shear strength of reinforced concrete beams

“…The concept of MCFT can be applied to the beam design [6] as well as the analysis of load-deformation response of RC beams subjected to shear, moment, and axial load [7,8]. Besides, a new algorithm for FA-STM was proposed to be able to predict the shear response of RC beams [9]. The above methods [7][8][9] can predict the load-deformation response of RC beams very well; however, the calculation procedures are too complex [7] and the iteration for solution is inevitable [7][8][9].…”

“…Besides, a new algorithm for FA-STM was proposed to be able to predict the shear response of RC beams [9]. The above methods [7][8][9] can predict the load-deformation response of RC beams very well; however, the calculation procedures are too complex [7] and the iteration for solution is inevitable [7][8][9]. Even so, these models have made great contributions to the prediction of shear behavior of RC beams and to the other application on torsion [10].…”