Column Footing Research Articles

Effects of modeling assumptions on prediction of seismic demands of a single-story RC structure

This study investigates the seismic response of a single-story reinforced concrete (RC) structure subjected to strong ground motions. Effects of modeling assumptions used to idealize the reinforcement slip in beam-column joints and column footing are studied. For this purpose, the numerical model of a single-story, single-bay, three-dimensional asymmetric RC structure, tested on a shake table and its symmetric version, is analyzed. Two modeling approaches are considered to show the significance of rotation associated with the reinforcement slip. Bidirectional nonlinear time-history analyses are conducted using symmetric and asymmetric 3D models. In these analyses, 30 pairs of near-field ground motions, selected and scaled to match the target spectrum, are used. The findings indicate that the neglection of reinforcement slip in numerical model may result in an underestimation of almost 50% in story drift ratio demands.

Titanium Seismic Substructure Retrofit to Enable Rocking of Bridge Foundations Considering Soil–Structure Interaction: Experiments and Numerical Simulations

The cyclic performance of substandard reinforced concrete (RC) bridge substructures seismically retrofitted using titanium alloy bars (TiABs) is assessed using full-scale experiments and nonlinear numerical models. The retrofit technique uses TiAB ligaments to simply and effectively strengthen columns with inadequate flexural lap splices and provides confinement through hoop action when combined with continuous TiAB spirals. The failure characteristics, flexural ductility, and hysteretic behavior of unretrofitted substandard (i.e., vintage) and TiAB retrofitted columns were evaluated using quasi-static, reversed cyclic tests of full-scale bridge column–footing specimens modeled after the characteristics of highway bridges in Oregon constructed prior to the introduction of seismic design provisions. Foundation rocking was examined and quantified through implementation of a soil subgrade simulant. Experimental results demonstrate improved flexural response and ductility with reduced concrete damage and residual drifts of RC columns when retrofitted with TiAB. The measured responses of the test specimens were used to calibrate three-dimensional (3D), nonlinear, finite-difference models used to investigate the effect of soil–structure interaction (SSI) on the rocking moment capacity for as-built and retrofitted column–footing specimens. The model was then used to perform a parametric study to evaluate retrofit details (flexural strength and stiffness) and soil characteristics (strength and stiffness) and their relationships to engineering demand parameters such as displacement and strength, which indicated that incorporation of SSI will permit the design of more efficient and economical seismic retrofits.

Seismic performance of semi-precast high-strength recycled concrete columns with ultra-high-strength steel bar

The purpose of this study is to promote the application of high-strength reinforcement and recycled aggregate concrete in post-earthquake repairable precast structures. Three large-scale recycled concrete columns with ultra-high-strength steel bar were designed and tested under quasi-static cyclic loads. The feasibility of semi-precast columns is verified, i.e., the concrete shell of the outer tube is precast first, and then the precast external shell is used as a formwork to cast concrete into the tube. The design parameters include axial load and the addition of steel fibers. The results indicate that all specimens exhibited a good deformation capacity with an ultimate drift ratio greater than 4%. Increasing axial load will increase the lateral load capacity of the specimen by 21%, while the deformability and repairability decrease. Adding steel fibers to the precast external shell can increase the lateral load capacity by 10%, as well as the deformability and repairability of the specimen. Due to the low bond strength of ultra-high-strength steel bar, it slips at the column footing in the tensile side. Eventually, the fiber-based model simplified flexural capacity calculation model considering the ultra-high-strength steel bar slippage in the tensile zone are established.

Punching shear strength of RC column footings considering soil–footing friction

It is well recognized that various design codes and models have been developed to predict the punching shear strength of reinforced concrete column footings. Generally, the strength predictions by using current design codes and existing models are conservative, and inaccurately match the experimental results. This is because although a column footing and a flat plate (or slab) have different geometries and mechanisms, the same design method is used for them. Thus, to accurately assess and evaluate the punching shear strength of column footings, their design method should be improved. The present study paper proposes a strength model based on the compression zone failure mechanism to predict the punching shear strength of concrete footings without shear reinforcement. The punching shear at the critical section was assumed to be mainly counteracted by the intact concrete in the compression zone of the footing. In the model, the effect of the friction force between the bottom surfaces of the footings and the soil was considered. The proposed model was applied to the existing test results for verification. The predictions by the proposed model were also compared with those by current design codes and existing models. Based on the proposed model, the effects of various design parameters on the punching shear strength of the column footings were analyzed and investigated in detail.

Bearing behavior of reinforced concrete column-isolated footing substructures

Under earthquake, the interaction between column footing and soil foundation directly affects the failure mechanism of reinforced concrete (RC) structures. In the present study, to investigate the structural performance and failure mode of RC column-isolated footing substructures on foundation, a test device using rubber-wooden composite blocks to simulate elastic foundation based on Winkler foundation model was designed. Three RC column-isolated footing substructures were tested to evaluate the load-carrying capacity, failure mode, crack distribution, footing slab deflection, subgrade reaction, and rebar strain. The test parameter was the longitudinal bar ratio of the footing slab, and axial compression and lateral loading were applied to the column. Nonlinear analysis model was established in ABAQUS, and the predictions agreed well with the test results. On the basis of the analysis model, a parametric study was performed to investigate the effects of foundation coefficient, axial compression ratio, and footing slab thickness on the load-carrying capacity, failure mode, and column constraint.

Reinforcement model considering slip effect

Reinforcement slip in the beam-column joint or column footing may significantly influence the lateral displacement of a reinforced concrete (RC) column. A simple and efficient reinforcement model to consider the reinforcement slip effect is presented in this study. The proposed model utilizes a bilinear stress-strain relationship which assumes the increase in rebar strain contributed by reinforcement slip in tensile stage. The slip is calculated by the assumption of stepped bond stress distribution along development length. Then the proposed model is simplified by an extensive parametric investigation. After that, the proposed model is implemented into a fiber beam-column element model. The results from the modified fiber model are compared with the test results of RC columns and compared with the results from the conventional fiber model and zero-length fiber model. The modified fiber model agrees well with the experimental results in the column stiffness, followed by the zero-length fiber model. However, the conventional fiber model may significantly overestimate the column stiffness. Moreover, the modified fiber model shows a good accuracy in simulating the total lateral displacement of the column and shows success in capturing the lateral displacement contributed by reinforcement slip deformation. The results confirm the reliability of the proposed model for both section and member level. Finally, a comprehensive parametric study is accomplished to evaluate the effects of concrete, rebar, section, and axial load properties on the lateral displacement response of an RC column contributed by reinforcement slip deformation.

Prediction for lateral deformation capacity of corroded reinforced concrete columns

SummaryThe deformation capacities of columns, which are the main lateral force‐resisting elements of reinforced concrete (RC) structures, have been the subject of great interest with the development of performance/displacement‐based seismic design. However, deterioration due to chloride‐induced corrosion causes a significant reduction in the seismic performance of RC columns. Although numerous investigations have focused on the deformation capacity of columns with corroded rebars and various strengthening measures have been proposed, little attention was paid to evaluating the contribution of each deformation component to the tip displacement under corrosion (i.e., bending, shear, and longitudinal bar slip at the column footing), which plays an important role in investigating and explaining the failure mechanisms of columns. This paper presents a computational prediction model to estimate the deformation capacity of RC columns with corroded rebars, and the contributions of bending and bar slip at the column footing are mainly considered in this model due to the negligible contribution of the shear deformation component for columns subjected to flexural failure mode. The calculation results obtained by the prediction model are compared with the quasistatic test results of both noncorroded and corroded RC columns. It turns out that the prediction model simulates the deformation capacity of RC columns with corroded rebars reasonably well considering its simplicity and computational efficiency, and it can be used for time‐variant capacity estimates for the lifetime seismic design and fragility assessment of RC columns exposed to corrosion.

Cyclic response of a precast composite hollow reinforced concrete column using longitudinal rebars and base plate

In this research, the precast segmental construction of composite hollow reinforced concrete (RC) columns was studied. The precast segmental construction of composite hollow RC column requires guidelines for the connections between the bent cap and column segment, connections between column segmental joints, and connections between column segment and footing. The connection methods for different precast composite hollow RC piers were experimentally studied for rational resistance against shear force and bending moments. Two types of precast composite hollow RC columns and cast‐in‐place column were studied in this paper. The performance of these columns was evaluated through experiments. The precast column erected with a base‐plate connection exhibited a performance similar to the cast‐in‐place column.

Practical Calculation Models for Column Footing and Comparison with Experimental Data

Practical Calculation Models for Column Footing and Comparison with Experimental Data

Simplified model for compressive response of RC column footing with square cross-section

In this paper, a simplified calculus model for the prediction of the compressive response of RC column footing with a square cross-section is presented. As it is well-known RC concrete footing are designed adopting uniform contact pressures on the substrate and assuming a strut and tie model in deep members and a cantilever beam or slab model in flexible members. Deep and flexible members are distinguished in literature only based on the tangent of the angle expressed as the ratio between the depth and the shear span of the footing.In this paper, several subgrade contact pressures distribution for column footings (rigid or soft soils) were considered in developing a mechanical model able to derive the complete load displacement curves of RC deep and flexible footing in compression. The objective of the research was the more appropriate choice of the calculus model to predict the compressive response of single column footing. In particular, if the angle, expressed as the ratio between the depth and the shear span of the footing, is higher than 45° the strut and tie model was suggested for best prediction, while, if the angle is lower than 45°, the beam or the slab models with punching shear were adopted. For both cases simplified loading soil profiles corresponding to rigid, flexible or winker model were adopted. Effects of main parameters such as geometry (depth, width) and shape of footing (single or shaped), the mechanical ratio of longitudinal reinforcement and type of soil are investigated both numerically and analytically. Numerical results and available experimental results were utilized to verify the model. The comparison between analytical and numerical results allows one to validate the proposed model and to define the range of application of the strut and tie or beam model depending on the footing geometry, the mechanical ratio of longitudinal reinforcement and type of soil. Finally, the comparison between analytical and experimental results available in the literature gives a further confirmation on the reliability of the proposed model.

Performance of bridge piers under vehicle collision

Both the peak dynamic force (PDF) and the equivalent static force (ESF) of a vehicle collision with reinforced concrete bridge columns were examined as part of an extensive finite element (FE) analyses study. An extensive parametric study of 13 parameters, including the concrete material model, the unconfined concrete compressive strength fc′, the material strain rate, the percentage of longitudinal reinforcement, the hoop reinforcement, the column span-to-depth ratio, the column diameter, the top boundary conditions, the axial load level, the vehicle’s velocity, the vehicle’s mass, the roadside distance between errant vehicle and unshielded bridge column, and the soil depth above the top of the column footing was conducted. Three approaches were used to investigate the ESF. The ESF in the first (stiffness-based) approach was defined as the static force producing the same maximum displacement that is produced by a vehicle collision at the point of impact. The ESF examined in the second approach was calculated according to the Eurocode. The ESF studied in the third approach was defined as the Peak of the Twenty-five Milli Second moving Average (PTMSA). The different ESFs were compared to the ESF in the American Association of State Highway and Transportation Officials-Load and Resistance Factor Design (AASHTO-LRFD; 2670kN [600kips]). In general, the ESF calculated according to the Eurocode presented the lower bound while those from the stiffness-based approach presented the upper bound. Furthermore, the recommended ESF of the AASHTO-LRFD was found to be non-conservative for heavy and/or high speed vehicle impacts; it was found to be too conservative for light and/or slow vehicle impacts. Hence, rather than a constant design impact force, a variable design impact force should be used. An equation was developed to calculate a design impact force, which is the function in the vehicle’s mass and velocity. A simplified equation based on the Eurocode equation of the ESF was proposed. These equations, however, do not require cumbersome FE analyses.

Structural design of isolated column footings

Superstructure loads are transmitted to the underlying soil strata through a suitably designed foundation. Therefore, the foundation of a structure is considered the most crucial structural element in a building. The foundation may be classified into two main categories, shallow and deep foundations. Shallow foundation comprises isolated column footings, combined footings and reinforced concrete mat. The design of isolated column footing is accomplished through the application of geotechnical and structural analysis concepts. So that, the input research into isolated column footings comes from two different disciplines, geotechnical and structural. This may be one of the main causes that attributed to the limited research input to the subject. Therefore, the structural design of isolated column footings is based on empirical rules and the calculations of bending moments (BM) and shearing forces (SF) induced in a footing are based on the rules of beam theory, which is questionable. On the other hand, punching theory was developed on relatively thin floor slab, even though the theory is implemented for the calculation of punching shear in relatively thick footings. Also experimental research on isolated column footings is scarce, due to the difficulties involved in the setup of the laboratory models and the cost of experiments. The work presented in this article deals with the correlation between failure loads predicted by different code provisions, ECP203-11, ACI318-08, BS 8110.1-1997 and EC2-2004, of isolated column footings, and the corresponding measured values.The study showed that shear span to depth ratio of a footing and distributions of contact stress at footing–soil interface are key factors in the structural design of the footing. ECP203-11, ACI318-08, and EC2-2004 code provisions, underestimate the structural failure loads of isolated column footings, while BS 8110.1-1997 overpredicts the failure loads of isolated column footings, if punching provisions at perimeter of column are pulled out from the code.

Numerical Simulation of FRP-Jacketed RC Columns Subjected to Cyclic and Seismic Loading

This paper presents a numerical model for the cyclic/seismic behavior of reinforced concrete (RC) columns retrofitted with fiber-reinforced polymer (FRP) confining jackets. Such a column model has previously been unavailable despite the popularity of FRP jacketing as a seismic retrofit method for RC columns. The proposed numerical column model is based on a recent stress-strain model for FRP-confined concrete subjected to cyclic axial compression and a hysteretic moment-rotation model to account for the effect of strain penetration of the longitudinal steel bars in the column footing (i.e., effect of fixed-end rotations). This column model was implemented into OpenSees (Open System for Earthquake Engineering Simulation) using its fiber-section force-based nonlinear beam-column element. Predictions of the numerical column model for three FRP-jacketed RC columns subjected to either double-curvature bending or single-curvature bending are shown to be in close agreement with the test results.

Rapid repair of a severely damaged RC column having fractured bars using externally bonded CFRP

Research on rapid repair of reinforced concrete (RC) columns has been limited to columns with slight or moderate damage. Moreover, few studies have been conducted on repair of severely damaged columns, particularly with buckled or fractured reinforcing bars. In those studies, however, the techniques used involve considerable time and effort and are not considered “rapid”. The goal of this study was to develop an effective technique to rapidly repair severely damaged RC columns for temporary service use with externally bonded carbon fiber reinforced polymer (CFRP). This paper describes the repair and retest of three half-scale severely damaged square RC bridge columns within 4 or 5 days. Damage to each column included buckled longitudinal bars, and one column had fractured bars near the column base. The repairs were designed to restore the column strength using longitudinal and transverse CFRP. A novel anchorage system was designed to anchor the longitudinal CFRP to the column footing. This study illustrates the effectiveness and limitations of this repair technique. The technique was found to be successful in restoring the strength of the columns without fractured bars, but only partially successful for the column with fractured bars located near the base because of CFRP anchorage limitations.

Theoretical Analysis of the Sole Plate of Semi-Rigid Light Steel Column Footings on the Basis of Winkler Model of Elastic Foundation Beam

To obtain the pressure distribution model on the sole plate of semi-rigid light steel column footing, the deflection formulas of beams with free ends on elastic foundation subjected to arbitrarily concentrated load and arbitrarily trapezoidal load were developed by applying the Winkler model of elastic foundation beam and initiate-parameter expressions of deformation and internal force by presetting boundary condition and calculating with Maple software. The sole plate of semi-rigid square steel tube column footing was converted into elastic foundation beam which is supported by concrete foundation, the mechanical model of the sole plate subjected to eccentric load was obtained, and the theoretical solution of pressure distribution on the sole plate was presented. Then the theoretical solution was compared with the numerical solution via an example. The results show that the two solutions meet well with each other, and there is much great difference between the pressure distribution on sole plate of semi-rigid light steel column footing and the linear pressure distribution model in common use. As a result, the semi-rigid column footing stiffness would be overestimated by using linear pressure distribution model. The fruits presented in this paper are useful and convenient to the design of semi-rigid light steel column footing.

Study on the Frame Structure under Nonuniform Settlement

In this paper, the effect of the non-uniformity settlement of ground foundation on the upper frame structure is studied. It takes a four-story space frame structure with two spans as an example. The different pedestals are installed at the joint of column footing, which respectively form the fixed supported model and the elastic supported model. Basin shaped settlement is applied in each model. The result shows that the beams are principally suffered with the bending moment and the columns principally suffered with axial force, shear force and bending moment, and that the elastic support model has certain economy.

Experimental Study on Strength of Connections to Concrete Filled Tubular in Fire

Concrete filled tubular columns are widely used all over the world, due to their significant advantages, including attractive appearance, structural efficiency, reduced column footing, fast construction and high fire resistance without external fire protection. An experimental study has been carried out on the performance of joints between steel beams and concrete filled tubular columns in simple construction under fire conditions. The failure modes of the test specimens were always in the joint regions. Therefore, if the joints are appropriately designed and protected so that they possess sufficient strength, it is possible for the steel beam to develop catenary action and survive very high temperatures even without fire protection.

Fire Resistance of Axially Loaded Slender Concrete Filled Steel Tubular Columns – Development of a Three-Dimensional Numerical Model and Comparison with Eurocode 4

In recent years, concrete filled tubular (CFT) columns have become popular among designers and structural engineers, due to a series of highly appreciated advantages: high load-bearing capacity, high seismic resistance, attractive appearance, reduced column footing, fast construction technology and high fire resistance without external protection. In a fire, the degradation of the material properties will cause CFT columns to become highly nonlinear and inelastic, which makes it quite difficult to predict their failure. In fact, it is still not possible for analytical methods to predict with enough accuracy the behaviour of columns of this kind when exposed to fire. Numerical models are therefore widely sought. Many numerical simulations have been carried out worldwide, without obtaining satisfactory results. This work proposes a three-dimensional numerical model for studying the actual fire behaviour of columns of this kind. This model was validated by comparing the simulation results with fire resistance tests carried out by other researchers, as well as with the predictions of the Eurocode 4 simplified calculation model.

Hysteretic Behavior of Anchorage Slip in R/C Members

Large-scale reinforced concrete columns were tested to investigate hysteretic behavior of anchorage slip in reinforced concrete structures. The columns were subjected to constant axial compression and unidirectional and bidirectional lateral-deformation reversals. The results indicate a significant increase in column rotation due to anchorage slip. Penetration of yielding into the column footing was observed in the tension reinforcement, while the compression yielding was localized at the column-footing interface. Axial compression resulted in early closure of the crack associated with anchorage slip, reducing related deformations. An analytical model was developed for hysteretic moment-anchorage slip-rotation relationship. The model consists of a primary curve and a set of rules defining unloading and reloading branches. The primary curve is constructed by computing the extension and slippage of tension reinforcement in the adjoining member. This is accomplished by considering inelastic strain distribution along the embedment length of reinforcement, as well as the local bond-slip relationship. Hysteretic rules are obtained from experimental observations, and incorporate pinching of hysteresis loops as well as the effect of axial compression. Comparisons of experimental and analytical hysteretic relationships indicate excellent agreement.

Strength and Deformability of Steel Column Footing

The hysteretic loops of the embedded‐type column‐to‐footing connection, subjected to seismic loading, can be classified into three types, namely (1) Elastic‐plastic with sufficient deformability; (2) pinching type with large deformability; and (3) pinching type with poor deformability. Fracture modes of the types are: type A, where a plastic hinge is formed in the steel column at the top surface of the footing; type C, where punching shear failure of the footing concrete occurs, in which the side wall breaks out laterally at the girder‐free side of the footing, preceding the yielding of the column member; or type B, which is a combined mode of types A and C. The maximum strength of the connections of type C is analyzed theoretically based on the test results hitherto reported in Japan. And, to ensure avoiding failure in type C, a design guide for details of the connection is presented, together with a parametric study.