Experimental and Theoretical Research on Shear Strength of Seismic-Damaged SRC Frame Columns Strengthened with Enveloped Steel Jackets

,e experimental and shear strength analytical investigations carried out on seismic-damaged steel reinforced concrete (SRC) columns strengthened with enveloped steel jacket subjected to cyclic loading are presented in this paper. Four 1/2-scale SRC columns were designed and manufactured and the postearthquake damage, enveloped steel jacket-confined, and destructive tests were carried out under lateral cyclic loading. ,e effects of postearthquake damage degree and enveloped steel jacket-confined on shear capacity and ductility capacity were all well examined. Test results indicate that the ductility of seismic-damaged SRC columns strengthened with enveloped steel jacket increases with the reduction of the postearthquake damage degree. ,e results indicate that the calculation formula of shear bearing capacity of SRC columns is feasible. Based on GB50010-2010, ACI318-08, and CSA-04, three different shear models were established, and the calculated values of shear capacity are quite different, and the analysis of the shear strength of RC in the strengthened seismic-damaged SRC column cannot be ignored.,e formula is verified, and the calculated results are consistent well with the experimental results.


Introduction
As an attractive composite structure, SRC column structure has the advantages of high load-bearing capacity, excellent seismic performance, and so on [1].Worldwide, SRC structures have been widely used in the areas that are prone to earthquakes [2].However, research on seismic behavior of enveloped steel jacket-confined seismic-damaged SRC column has not been mentioned before.e impact of seismic damage and reinforcement on this kind of structure cannot be ignored, and it has very important engineering significance.In practical engineering, the mechanical properties of the enveloped steel jacket are excellent, because it is more convenient in construction [3].
e effective method of SRC structure reinforcement has been applied more and more widely in the USA, Canada, Japan and in Europe recently [4,5].Hence, for existing concrete structures, a thorough evaluation of seismic-damaged SRC columns which confined with enveloped steel jacket need to mitigate shear failure under earthquake loading, whereas for new concrete structures, the confined columns must be designed with sufficient shear capacity to sustain the whole building in an earthquake [6][7][8].e purpose of this paper is to establish a model for predicting the shear strength of enveloped steel jacket restrained columns.
Compared with ordinary concrete column, RC columns with enveloped steel jacket have different seismic behavior [9][10][11].In recent years, the seismic behavior of the seismicdamaged RC columns constrained by the enveloped steel jacket has been widely popularized, thus popularizing the use of enveloped steel jacket-confined concrete structure in earthquake regions.Nagaprasad et al. [12] presented the results obtained in the full-scale laboratory tests carried out on RC columns strengthened with steel cages.Garzón-Roca et al. [13] summarized some experimental researches on shear behavior of structures.Zhou et al. [14] indicated that under low cyclic loading, the seismic performance of columns after strengthened can reach or even exceed that of the original column within a certain extent of the damage level.Fang et al. [15] tested the shear strength and the seismic behavior of concrete-encased steel cross-shaped columns submitted to a constant axial load and cyclic lateral loads.
Existing studies mainly concentrate on the flexural performance of strengthened SRC columns under lateral cyclic loading, but little information can be used to study the shear behavior of strengthened SRC column.Some postearthquake reconnaissance has indicated that strengthened SRC columns are easily shear failure.To research the shear strength carried out on seismic-damaged SRC columns strengthened with enveloped steel jacket, four 1/2-scale SRC columns were designed and manufactured under the combined action of an axial load and reverse circulation lateral displacement.What's more, the seismic performance of enveloped steel jacket-confined SRC columns was evaluated.e proposed model was mainly used to analyze the shear strength of seismic damage degree and enveloped steel jacket reinforcement of specimen, and the rationality of the shear design codes [15][16][17] of the strengthened SRC columns need to be evaluated in the text.

Research Significance
To research the shear behavior of enveloped steel jacketconfined seismic-damaged SRC column, two main objectives were planned simultaneously to conduct the cover-all experimental program.e first objective includes making two different influence parameters for direct comparisons of seismic behavior of columns and providing new test data to the enveloped steel jacket-confined seismic-damaged SRC columns.
e second objective is mainly to evaluate the effectiveness and applicability of the proposed modes.

Experimental Program
3.1.Specimen Design.Four SRC frame columns were constructed to investigate the seismic performance of seismicdamaged SRC frame columns confined with enveloped steel jacket.e test consisted of postearthquake damage loading, rehabilitation with enveloped steel jacket, and destructive tests under lateral cyclic loading.Column consisted of a 200 mm × 270 mm × 1150 mm column cast integrally and a 400 mm × 500 mm × 1000 mm foundation beam, which are shown in Figure 1.For all columns, the longitudinal bar ratio, ρ l , was equal to 1.60%, the hoop ratio, ρ sv , was equal to 0.68%, and the section steel ratio, ρ a , was equal to 4.84%.Hoop spacing was 100 mm.e SRC column was a short column.
Two main parameters of the seismic performance of the column were researched: postearthquake damage degree of specimen and enveloped steel jacket confined or unconfined.SRC-0 specimen is undamaged or named original specimen and unconfined.WSRC-0 specimen is undamaged and confined.A displacement angle of 1/100 was used to simulate the moderate damage of specimen WSRC-1, while a displacement angle of 1/50 was used to simulate the severe damage of specimen WSRC-2.Axial compression ratio, n, of all specimens is 0.32, and shear span ratio, λ, is 3.33.Postearthquake damage degree of specimen includes three parts: undamaged, moderately damaged, and severely damaged.Angle steel was selected as 4L63 × 4, and the steel plate was selected in two sizes: 240 mm × 60 mm × 4 mm and 170 mm × 60 mm × 4 mm.Angle steel and steel plate are welding the enveloped steel jacket, which is filled with sticky steel glue as connecting with concrete.e spacing of adjacent steel plate is 150 mm, and reinforcement height is 500 mm.

Material Properties.
e SRC column formulation based on a water-binder ratio of 0.39, and concrete cover was 25 mm.e compressive strength of concrete, f cu (150 mm × 150 mm × 150 mm), of the specimen was 39.6 MPa. e compressive strength, f c , was equal to 0.76f cu [16].e diameter of longitudinal bar was equaled to 16 mm, the yield stress, f y , of longitudinal bar was 376 MPa, and the ultimate stress, f u , was 515.6 MPa. e diameter of hoop was equaled to 8 mm, and the yield stress, f vy , of hoop was 312 MPa, the ultimate stress, f u , of hoop was 443.1 MPa. e yield stress, f y , of I16 section steel was 264.5 MPa, and the ultimate stress, f u , was 405.8 MPa.

Postearthquake Damage and Reinforcement of Specimens.
e specimen SRC-0, with reinforcement, and the specimen WSRC-0, without any reinforcement, are undamaged.Displacement angle of 1/100 was used to simulate moderate damage of specimen WSRC-1, while a displacement angle of 1/50 was used to simulate severe damage of specimen WSRC-2.e angle steel and the steel plate are very important reinforcement materials and can form the envelope steel jacket by welded through the electric welding, which can be used to reinforce the specimen.
According to "Regulation of building seismic strengthening technique" (JGJ 138-01) [17], the size of angle steel and steel plate, the viscose method of concrete and enveloped steel jacket, the connection of enveloped steel jacket and ground beam, etc., are all consistent with parameters and methods shown by Xu et al. [18].Angle steel extends to the ground beam and integral pouring [19].e welding plate was welded with angle steel.Enveloped steel jacket was bonded with the concrete on the surface of the specimen through the structural adhesive.
e specimen strengthened with enveloped steel jacket is shown in Figure 1.

Test Setup.
e foundation beam was completely fixed.e top of the column was allowed to move.e lateral load was implemented at the top of the specimen through doubleaction actuator with displacement and force control capabilities.
e axial load was applied all the time on the centroid of the free end section of the column and kept constant throughout the test.e sliding system consisted of thickness steel plate and pulley and kept frictional coefficient small enough.e test device is illustrated in Figure 2.
e tests of the loading system followed the JGJ 138-01 guidelines [17].e loading system is shown in Figure 3.In Advances in Civil Engineering the test, the target value of the axial load applied to maintain constantly by adjusting the hydraulic jack.e yielding displacement (∆/L × 100% 1.0%) is consistent with Xu et al. [18].Both the initial applied horizontal load and each load step of the increment were 0.25%.e yield point is employed in this study to describe the obvious change of the slope of the shear force-displacement curve.All cycles were carried out once under the force control loading procedure [20].e displacement amplitude increment was 1.0% [18].All cycles were repeated three times for each amplitude.e specimens were subjected to three successive cycles after yielding, and the increments of 1.0% for each loading step.Two cases of test stop include, that is, the load is reduced to 0.85 times the limit load and the specimen axial failure.

Failure Modes and Damage Progression.
A conceptual representation of three failure modes of column using displacement ductility versus shear force diagram [21] is shown in Figure 4.In the experiment, both exural-shear failure and shear failure (showed in Figure 4) are regarded as the shear failure.
As the lateral force increased, the number and width of the diagonal cracks propagated.Moreover, as the postearthquake damage degree increased and enveloped steel jacket con ned, the value of the lateral displacement became smaller.With the lateral displacement further propagating, the concrete cover at the bottom of the specimen was ake-o when sti ness was gradually degrading, and this section was decreasing.Damage propagation and failure modes referenced [18].e concrete of the shear-compression zone was crushed, whereas the combined action of compression and shear occurred.Fracture surfaces of SRC specimen needed to be well versed in the quite smooth because of the inclined cracks through the coarse aggregate.Figure 5 shows the failure mode of all specimens.

Hysteretic Curves and Backbone Curves.
e skeleton curves of specimens are shown in Figure 6.From Table 1, compared with specimen SRC-0, the average of the ultimate load of WSRC-0 increased by 23.0% and the average of the ultimate displacement increased by 23.7% (consistent with Xu et al. [18]); the average of the ultimate load of WSRC-1 increased by 12.9% and the average of the ultimate displacement increased by 12.4%; and the average of the ultimate load of WSRC-2 increased by 7.4% and the average of the ultimate displacement increased by 8.0%.
Backbone curves shown in Figure 6 are not symmetric about the origin, because of some residual deformation after the forward cyclic loading.It was necessary to counteract the residual deformation caused by the forward cyclic loading when the reverse loading was applied.
Based on the theory of equivalent energy method, yield displacement and ultimate displacement are read from Figure 7, respectively.e feature points of the skeleton curve of the specimen are shown in Figure 6.

Ductility Coe cient.
Ductility capacity is an important seismic parameter for structures, and ductility coe cient, µ, can be used to describe it: where Δ + u /Δ − u is the positive/negative ultimate displacement and Δ + y /Δ − y is the positive/negative yielding displacement.e bearing capacity, deformation capacity and ductility coe cient of the specimen are listed in Table 1.e test results indicate that compared with the specimen SRC-0, the average ultimate bearing capacities of specimen WSRC-0 increased by 19.25% and the average limit displacement increased by 23.50%; the average ultimate bearing capacities of specimen WSRC-1 increased by 6.09% and the average limit displacement increased by 11.45%; and the average ultimate bearing capacities of test specimen WSRC-2 increased by 1.87% and the average limit displacement increased by 6.25%.
e ductility coe cient of specimen WSRC-0 is increased by 17.6%; meanwhile, ductility coe cients of the specimen WSRC-1 and WSRC-2 are lowered to 11.4% and 10.4%, respectively.e ductility of seismicdamaged specimen can be e ectively restored by enveloped steel jacket reinforcement.

Calculation of Shear Strength of Strengthened Columns.
Wei and Zhang [22] developed the traditional truss-arch model.When the tests need to explore the shear bearing capacity of solid-webbed SRC short column, based on the truss-arch model, the solid-webbed SRC short column can divide SRC and section steel two parts to study.Lu et al. [23] provided the calculation method of sheer capacity of the strengthened column and considering the in uence of enveloped steel jacket-con ned (the in uence of CFRPcon ned ignored in this place).Hence, the proposed shear strength, V m , of the seismic-damaged SRC columns con ned with enveloped steel jacket can be expressed as Based on the rules of the GB50010-2010, the ACI318-08, and the CSA-04, three di erent shear models were established, and the analysis of the shear strength of reinforcement seismic-damaged SRC column cannot be ignored [16,24,25].Based on the rules of the GB50010-2010 [16], the RC column contribution, V cr , is given by where f t is the design value of concrete axial tensile strength; ρ v is the stirrup rate of column section; A is the e ective area of the concrete section of seismic damage column.
Based on ACI318-08 [24], the RC column contribution, V cr , is given by where f c is the axial compression strength of concrete; ρ s is the reinforcement ratio of longitudinal reinforcement; V u1 h 0 /M m is the the generalized shear span ratio of calculating section; h 0 is the e ective height of column section.
Based on CSA-04 [25], the RC column contribution, V cr , is given by  Advances in Civil Engineering where β * is the contribution coe cient of concrete; d v is the longitudinal reinforcement diameter; f c is the axial compression strength of concrete.e enveloped steel jacket contribution, V g , is given by equation (3b) [23].
e section steel contribution, V a , is given by equation (3c) [22]: where f yv is the yield stress of hoop; A sv is the gross area of hoop; ρ sv is the hoop ratio; s is the hoop spacing; f g is the yield stress of enveloped steel jacket; N is the the axial load; t w and h w are the section steel thickness and height, respectively, and f a is the the original strength of section steel before postearthquake damage of test columns.And the shear coe cient, v g , can be computed by equation ( 4) [26,27]: e tensile strength, f t , needs to be rede ned because the constraint action of the enveloped steel jacket is simpli ed to be the same as the restraint of the hoop.f t [23,28] is expressed as where x and y are the width and height of the e ective restraint area of concrete, respectively.h 1 is the height of enveloped steel jacket-con ned; A z is the angle steel area; s z is the plate spacing; E sv and E z are the modulus of elasticity of the hoop and enveloped steel jacket, respectively, ε sv and ε z are the e ective strain of hoop and enveloped steel jacket, respectively.However, based on the area of the section columns tested by Lu [29], Zhang [30], and Liu [31] that the area of the postearthquake damaged columns is not equal to bh 0 .To solve the problem, Yang [14] gave a simpli ed method to calculate the strength of the hoop, longitudinal reinforcement, and section steel after earthquake damage.Divided, the column section consists of two parts with hoop as boundaries: core-zone area, A 1 , and non-core-zone area, A 2 , and the cross-sectional area of the column, A, is expressed as where D 1 is the damage index of the non-core-zone area of the section column D 1 0.5 for moderate damage and D 1 1 for severe damage.e strength reduction factor, a F , can be computed by equation ( 7) [24]: where D is the damage index of specimen, which was proposed by Park-Ang in 1985 [32] and β 1 and β 2 are correlation coe cients and can be computed by the following equations [24]:  Yang [26] gave a simpli ed method to calculate the strength of the hoop, longitudinal reinforcement, and section steel after earthquake damage.
where f yv , f ck , and f a is the original strength of hoop, longitudinal reinforcement, and section steel before postearthquake damage of test columns, respectively, and f yv ′ , f ck ′ , and f a ′ is the strength of the hoop, longitudinal reinforcement, and section steel after postearthquake damage of the test columns, respectively.erefore, equation ( 2) can be expressed as where V gu v g ρ sv f g bh 0 , (14) 4.3.2.Shear Strength Modes. Figure 8 shows the comparison of experimental and other methods from the ACI [24], the CSA [25], the GB (GB50010) [16], and proposed model.From Figure 8, the mean ratio and coe cient of variation are 1.43 and 0.24, 1.36 and 0.18, 1.13 and 0.16, and 1.07 and 0.13, respectively.e results indicate that the proposed model can predict the shear strength reasonably, and the code provisions are relatively conservative at the same time.e mean ratio of the GB50010 is about 1.0, which demonstrates that this code may tend to over-valuation of the shear strength.
e predicted shear strength of the ACI318-08 and the CSA-04 is commonly conservative, because they neither consider the arch action nor base on the truss model and MCFT.As the shear span-depth ratio, λ, decreases, the conservative increases.e e ect of arch action increases as the shear span-depth ratio, λ, decreases.It con rms that the proposed method is slightly conservative and safe.

Conclusions
rough the design and manufacture of four 1/2-scale SRC column models, the postearthquake damage, enveloped steel jacket-con ned and destructive tests under lateral cyclic loading were carried out.e damage model, force-displacement relationship, deformation capacity, and shear strength are compared and discussed.Conclusions can be drawn after the tests and the predicted results comparison.
(1) Overall seismic behavior of strengthened columns was observed to be stronger compared with that of 6 Advances in Civil Engineering nonstrengthened column under the same conditions, displayed a relatively high ductility and energy dissipation capacity, and obtained higher shear capacity.(2) Similar e ect can be found between the enveloped steel jacket and the stirrups, which can e ectively restrain the spalling of concrete cover at the bottom of the column and the increase of concrete cracks.(3) Compared with the specimen SRC-0, the average of the ultimate load of the WSRC-0 increased by 23.0% and the average of the ultimate displacement increased by 23.7%; the average of the ultimate load of WSRC-1 increased by 12.9% and the average of the ultimate displacement increased by 12.4%; and the average of the ultimate load of WSRC-2 increased by 7.4% and the average of the ultimate displacement increased by 8.0%.(4) e result of the prediction of shear strength is relatively conservative, because the arch action has been ignored by most code provisions.us, the condition of compatibility between seismic damage degree and enveloped steel jacket-con ned needs to be considered.

Data Availability
e data used to support the ndings of this study are available from the corresponding author upon request.

Figure 4 :
Figure 4: De nition of column failure modes.

Table 1 :
Characteristic points of backbone curves.