Evaluation of the critical plastic region length in slender reinforced concrete bridge columns

doi:10.1016/j.engstruct.2016.07.021

Engineering Structures

Volume 125, 15 October 2016, Pages 280-293

https://doi.org/10.1016/j.engstruct.2016.07.021 Get rights and content

Highlights

•
Experimental results from tests on three slender RC bridge columns are presented.
•
The length of the plastic region (L_pr) on slender columns is evaluated.
•
Test results confirm the increase in L_pr due to the columns’ slenderness.
•
Current design guides and analysis models underestimate L_pr for slender columns.
•
A simple and accurate expression for L_pr in slender columns is proposed.

Abstract

This paper presents how the length of the critical plastic region (L_pr) in slender columns is significantly larger than what is estimated from current models, which were developed for shorter columns. Experimental results from three large-scale slender reinforced concrete columns with aspect ratios (length to depth) up to 12 were used to explore the effect of slenderness on L_pr. Components of L_pr, including linear moment gradient, nonlinear moment gradient, and tension shift effect were extracted from the test data and the contribution from each component was determined. Experimental L_pr values were compared with American, European, and New Zealand design guidelines. All design codes considered in this study significantly underestimated L_pr except for seismic design provisions provided by Caltrans. Previous expressions for the length of the plastic region were reexamined in light of the new experimental data and strong disagreement between experimental and predicted L_pr was observed. A new expression for L_pr, which correlates well with test data is thus proposed. The expression varies according to the magnitude of inelastic demands, defined by displacement ductility, and includes the effect of nonlinear moment gradient due to P-δ effects.

Introduction

Reinforced concrete (RC) bridge columns are typically designed to endure moderate to strong earthquake events by experiencing significant inelastic deformations [1], [2], [3]. These inelastic deformations, which are often associated with damage to the column, concentrate at the end regions where moment demands are maximum [4]. The portion of the column over which inelastic deformations take place is commonly known as the critical plastic region; and a ductile inelastic flexural response is necessary along this region to dissipate the seismic energy. Design guidelines [5], [6], [7], [8], [9], [10], [11] require special detailing to ensure such ductile response, by providing adequate confinement steel reinforcement over the plastic region. Also, seismic retrofitting and strengthening strategies typically involve providing additional transverse confinement over the critical plastic region of earthquake-resistant RC columns with inadequate transverse reinforcement. Having an accurate account of the length of the plastic region (L_pr) is thus essential for proper seismic design, retrofitting, and strengthening plans.

The plastic region length (L_pr) should be distinguished from the plastic hinge length (L_p) since the former represents the physical region over which plastic deformations actually spread along the RC member length; whereas, the latter is a fictitious term used in lumped plasticity models to combine all sources of inelastic deformations to determine the column’s post-yield displacement [12], [13]. Yet, the plastic hinge length is related to the length of the plastic region since L_pr captures the inelastic deformation contribution to L_p that spreads along the member due to flexure, known as the moment gradient component [14], [15], [16].

Experimental programs on large-scale test units have been typically used to determine the extent of the plastic region. Based on experimental results, empirical expressions have been proposed to predict the extent of the plastic region (L_pr). Yet, these expressions were derived from the tests mostly conducted on non-slender columns, i.e., with aspect ratios (L/D) less than 6 [17]. The significance of slenderness in contributing to the extent of the plastic region was thus generally disregarded in prior studies and the work herein shows that it was underestimated. This is contrary to the fact that slender columns considerably bend under the applied loads. The excessive member deformation away from the chord-line (δ) in conjunction with the applied axial load (P) generates additional second-order moment (P-δ) that contributes to the extent of the plastic region. The increase in L_pr due to member deformation and P-δ moment is schematically depicted in Fig. 1, in which the nonlinear moment gradient leads to a significantly larger plastic region than the one resulting from a linear moment gradient. It should be noted that the additional moment caused by P-Δ effects, which is the product of the axial load (P) and the total displacement of the column at top (Δ), is included in the linear moment gradient. Therefore, current design guidelines for the length of the critical plastic region need reevaluation for slenderness effects. This is crucial since underestimating L_pr for seismic design of RC columns leads to insufficient detailing for a ductile response and adversely affects the reliability of the structure for sustaining significant inelastic deformations before failure.

Research endeavors have also led to proposed expressions for L_pr (and moment gradient component of L_p) in RC beams [18], [19], [20] and columns [12], [21], [22], [23]. However, linear moment gradients along the member’s height were assumed for developing these L_pr (and L_p) expressions. Therefore, the effect of nonlinear moment gradients due to P-δ moments is not fully captured in current L_pr models. This explains, to the authors’ knowledge, the reason that most of the available L_pr expressions lack any term to include the effects of slenderness. Therefore, developing an expression for L_pr that includes the effect of slenderness and second-order nonlinear moment gradient on the extent of the plastic region is essential for the proper design of slender RC columns.

Section snippets

Current seismic design guidelines

Seismic design guidelines require special detailing and enhanced confinement steel reinforcement in the plastic regions of RC columns in order to ensure stable ductile response. The ACI code (ACI-318-11) [9] and Eurocode 8 for buildings (EN 1998-1:2004) [6] specify the length of the critical region (l_o and l_cr as referred to by ACI and EN-1, respectively) in columns of ductile moment frames to be the larger of: (a) maximum dimension of the cross section, (b) one-sixth of the clear span, or (c)

Experimental program

Experimental data to evaluate the effects of slenderness on L_pr was extracted from tests conducted by the authors on three large-scale specimens of slender RC bridge columns. Only pertinent information and results from the tests are provided in this paper. A more detailed account of the test procedures and results can be found in Ref. [25].

Curvature profile

Curvature profiles were calculated from the relative vertical extensions and contractions, measured by the vertical DTs, between multiple sections along the height. The average (from push and pull directions) curvature profiles along the test columns are shown in Fig. 3(a). The plastic region length, L_pr, was found from the length of the region over which the curvature values exceeded the yield curvature (ϕ_y), indicated by a vertical dashed line in Fig. 3(a). In this paper the use of the

Experimental evaluation of L_pr

Previous experimental research on determining the length of the critical plastic region used either visual evaluation of the damaged region [33], [34] or curvature profiles along the columns’ height [12], [13], [35]. In addition to the aforementioned methods, moment profiles are utilized in this paper to assess L_pr and its components.

Comparison of experimental L_pr with previous research

Current knowledge about the extent of the plastic region due to moment gradient is reevaluated herein for slender RC columns in light of the new experimental evidence from the tests conducted by the authors.

Proposed expression for L_pr

The development of an expression for the extent of the plastic region due to linear moment gradient (L_pr,L) is presented. The L_pr,L expression can be adjusted for the effect of member deformation and nonlinear moment gradient due to P-δ effect. Consequently, a closed-form relationship between L_pr,NL and μ_Δ is also proposed.

Conclusions

The extent of the critical plastic region in slender RC bridge columns was experimentally evaluated via test data from three large-scale columns with aspect ratios up to 12. Current design guidelines for the length of the potential plastic region that requires special detailing were reassessed in light of the experimental results reported in this paper and the following conclusions were derived:

(1)
Use of curvature profiles is the most viable method to experimentally assess the extent of the

Acknowledgements

The research described in this paper was carried out with funding from the U.S. National Science Foundation under Grant numbers CMMI-1000549 and CMMI-1000797.

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Evaluation of the critical plastic region length in slender reinforced concrete bridge columns

Highlights

Abstract

Introduction

Section snippets

Current seismic design guidelines

Experimental program

Curvature profile

Experimental evaluation of Lpr

Comparison of experimental Lpr with previous research

Proposed expression for Lpr

Conclusions

Acknowledgements

Eng Struct

Eng Struct

Scientia Iran

Eng Struct

Procedia Eng

Seismic design and retrofit of bridges

Efficient beam-column element with variable inelastic end zones

J Struct Eng

Eurocode 8: design of structures for earthquake resistance. Part 1: General rules, seismic actions and rules for buildings. EN 1198-1

Eurocode 8: design provisions of structures for earthquake resistance. Part 2: Bridges. EN 1998-2

The design of concrete structures. Concrete structures standard, Part 1: Code of practice

Building code requirements for structural concrete (ACI 318-11) and commentary (ACI 318R-11)

Guide specifications for LRFD seismic bridge design

Seismic design criteria 1.7

Force-displacement characterization of well-confined bridge piers

ACI Struct J

Seismic design of reinforced concrete and masonry buildings

Inelastic hyperstatic frames analysis

Flexural Mech Reinf Concr

Plastic hinge lengths of normal and high-strength concrete in flexure

Adv Struct Eng

Experimental evaluation of L_pr

Comparison of experimental L_pr with previous research

Proposed expression for L_pr