Numerical Analyses of Reinforced Concrete Structures Using Spring Network Models

Abstract

(Hakozaki 6-10-1, Higashi-ku, Fukuoka 812-8581, Japan)Computer modelings are one of the most suitable and promising approaches for comprehensively understanding the mechanisms of failure in concrete. This paper presents a practical, computationally efficient procedure for analyzing fracture of reinforced concrete structures. Concrete material is represented by a rigid-body-spring model with random geometry. Rather than averaging the effects of reinforcing over a regional material volume, reinforcing material is explicitly modeled using a beam-and linkage-spring. The spring network gives reasonable predictions of fracture behavior in reinforced concrete structures.Numerical predictions are compared with experimental results of reinforced concrete piers and beams.

Modeling of Tension Stiffening Behavior in FRP‐Strengthened RC Members Based on Rigid Body Spring Networks

“…The normalized relative displacements of the two springs in the directions normal and tangential to the boundary line (i.e., δ n / h and δ s / h , where h is the characteristic length of a concrete spring element [Figure 1a]) represent the tensile/compressive and shear strains of the concrete, respectively. The normal, shear and rotational stiffnesses are set to approximate the elastic properties of concrete at the continuum levels and the rotational stiffness K φ is suggested to be zero when either the normal or the shear spring reaches its maximum strength (Saito and Hikosaka, 1999). Through the virtual work principle, the stiffness matrix associated with the two‐particle assembly, describing the relationship between the force vector ( X 1 , Y 1 , M 1 , X 2 , Y 2 , M 2 ) and the displacement vector ( u 1 ,v 1 ,θ 1 ,u 2 ,v 2 ,θ 2 ) can be obtained (Bolander and Saito, 1998).…”

“…As shown in Figure 2, the compressive response of the springs normal to adjacent concrete particles is given as follows: where E c is the elastic modulus of concrete; σ c and ɛ c , are the compressive stress and strain of the normal spring, respectively; f c is the compressive strength of concrete; is the compressive fracture energy of concrete, which can be taken as (Nakamura and Higai, 1999); h is the distance between adjacent concrete particles (Figure 1a), and is assumed in this study (Saito and Hikosaka, 1999).…”

Time-Dependent Structural Analysis Considering Mass Transfer to Evaluate Deterioration Process of RC Structures

“…Discrete method is better than the continuum models for modeling of material discontinuity. From this viewpoint, the Rigid-Body-Spring Networks approach, which is one of the discrete approaches, is used for structural analysis, since this method is an analytical technique based on discrete mechanics that easily deals with crack propagation of concrete directly (Saito et al 1999). mechanics.…”

“…The shear transfer capacity at crack interfaces depends on crack opening. Thus, the shear stress, τ, is calculated by Equation (2) (Saito et al 1999) with the function of the strain of normal spring, ε, Young's modulus, E, and shear strain, γ.…”

Crack propagation analysis of reinforced concrete wall under cyclic loading using RBSM

“…Moreover, it is assumed that the shear stress decreases with an increase in crack width at the cracked surface, in which tensile softening occurs in a normal spring by taking into consideration the shear deterioration coefficient β cr as represented in Equation (6), which is similar to Saito's model (Saito & Hikosaka, 1999). Here, ε t and ε tu are cracking strain and ultimate strain in a normal spring, respectively.…”