Modeling of Strain Penetration Effects in Fiber-Based Analysis of Reinforced Concrete Structures

ACI Structural Journal, Mar/Apr 2007 by Zhao, Jian, Sritharan, Sri

Short rectangular column

The first of the two cantilever columns studied was short rectangular Column U6 that was designed and tested by Saatcioglu and Ozcebe.23 The testing of this column was part of a study that evaluated the effects of confinement reinforcement specified in ACI 318-83 on the ductility capacity of short columns. As shown in the insert of Fig. 9(a), this column had a square cross section and a clear height of 1000 mm above the footing, and was modeled using five fiber-based beam-column elements. After subjecting the column to a constant axial load of 600 kN, the lateral-load cyclic testing was performed and the measured force-displacement response is shown in Fig. 9(a). The test included sufficient instrumentation to quantify the displacement components due to member flexure, member shear, and strain penetration effects.

Also included in Fig. 9(a) are the simulated cyclic responses of the column with and without the zero-length section element to account for the strain penetration effects. (The simulation with the strain penetration effects used the following model parameters: s^sub y^ = 0.56 mm, f^sub y^ = 437 MPa, b = 0.5, and R^sub c^ = 1.0.) Between the two analyses, the one that included the strain penetration effects closely simulated the measured response. Because the response of the test unit was influenced by shear deformation, which is not included in the beam-column elements available in the fiber-based finite element program, the simulation with the strain penetration produced somewhat larger load resistance than the measured response for a given lateral displacement. The discrepancies between the measured and experimental results are even greater for the simulation that ignored the penetration effects. This particular analysis also markedly overestimated the elastic stiffness, yield strength, and the unloading stiffness of the test unit.

A further comparison between the analysis results and experimental results is presented in Fig. 9(b), which shows the lateral deflection along the column height at the yield lateral displacement (Δ^sub y^) and 4Δ^sub y^. In this figure, the measured displacements reflect the flexural displacements including the strain penetration effects, which were established by subtracting the measured shear displacements (approximately 20% at Δ^sub y^ and 10% at 4Δ^sub y^) from the measured column total displacements. The analytical displacements corresponded to the measured lateral loads of 310 kN at Δ^sub y^ and 350 kN at 4Δ^sub y^, and the contribution of the strain penetration effects to the column flexural deformation measured at the top was approximately 50% at Δ^sub y^ and 30% at 4Δ^sub y^, respectively. For both cases, the analysis simulation that included the strain penetration effects very closely captured the measured flexural displacements along the height of the column. The simulated column displacements without the strain penetration effects were significantly low.

Tall circular column

The second column investigated in this study was that tested by Smith,36 which served as the reference column for an investigation on strategic relocation of plastic hinges in bridge columns. This column had a circular section, as shown in the insert of Fig. 10(a), and a clear height of 3658 mm above the column footing. Under constant axial load of 1780 kN, the yield displacement of the column was reported to be 40 mm and the corresponding lateral load resistance was 259 kN. The failure of the column occurred due to fracture of the longitudinal reinforcing bars at the column base, after attaining lateral displacement of 323 mm with lateral resistance of 356 kN.