Residual Axial Capacity of Reinforced Concrete
Columns with Simulated Blast Damage
Bing Li1;Anand Nair2;and Qian Kai,A.M.ASCE3
Abstract:Two specimen ries[limited ismic(LS)and nonismic(NS)]were subjected to quasistatic loadings to evaluate the residual axial capacity of blast-damaged reinforced concrete(RC)columns.A validated numerical model was ud to predict the residual lateral deflection of RC columns subjected to an explosive attack.Three hydraulic actuators were installed horizontally to reproduce the target residual lateral deflection as predicted through this numerical model.Another two hydraulic actuators were installed vertically to apply the axial load and measure the residual axial capacity of the damaged columns.The effects of parameters such as axial loading and the transver reinforcement ratio are investigated through this study.The results obtained from the experimental study showed the improved performance that LS detailing provided to RC columns to resist blast or lateral loads.This subquently led columns detailed with a higher transver reinforcement ratio to have an incread residual axial capacity when laterally damaged,as compared with the NS detailed spec-imens.Axial load(rvice load)on the columns was also found to affect the residual deflection pr
ofile and residual axial capacity of the columns after the specified blast event.The validity range of a previously published function to determine blast-damaged residual axial capacity of RC columns is refined through the results obtained.DOI:10.1061/(ASCE)CF.1943-5509.0000210.©2012American Society of Civil Engineers.
山药的功效与作用及食用方法CE Databa subject headings:Concrete columns;Reinforced concrete;Finite-element method;Axial loads;Blast loads.
Author keywords:Reinforced concrete column;Residual axial capacity;Finite-element analysis;Column transver reinforcement; Column axial load.
Introduction
Background
Terrorist attacks in the past decades have drawn attention to the deficiencies in current structural design practices.The attacks rved as a call to action to reevaluate current design practices to accommodate for the vere loads where required(Li et al. 2009,2011).Failure of an individual column element could pos-sibly trigger a progressive collap of the entire frame structure. Detonati
on of explosive devices results in the generation of highly pressurized hot gass,which expand violently and displace the surrounding air,causing the reinforced concrete(RC)column element to lo its capacity as it accumulates damage.The postblast residual axial capacity of an RC column is therefore narrowed down to be an important behavior to focus on.It would be extremely important to understand the damage sustained by a, RC column element and the residual axial capacity to be able to determine if a progressive collap of the entire structure could ensue.
A ries of test was conducted by Crawford et al.(2001)to quantify the effects of explosive loads on conventional buildings. The full-scale tests were conducted on RC columns that are typi-cally found in four-storey office buildings located within Seismic Zone1of the East Coast of the United States.The test results in-dicated that the RC column element in the frame structure has a low lateral load capacity and low ductility.The explosion was t off at a short standoff distance.The looly spaced transver reinforce-ment within the RC column caud the column to fail owing to both its shear and flexure capacity to be exceeded at both ends.An addi-tional experiment was conducted by the rearch team to determine the increa in blast-loading capacity of the RC column when reinforced with a layer of carbon fiber-reinforced polymer(CFRP). It was apparent from the results obtained that the retrofitted column remained elastic and sustained no permanent deformations.The im-provement provided by the retrofit was evident from this study.
Crawford et al.(2001)furthered works and developed a column test fixture for conducting field tests.A ries of test programs were conducted with this test tup.They involved TNT-equivalent weights varying from500–1,000kg that were placed at standoff distances of3.0–6.0m.It was obrved from the results that the RC column core concrete was split into small gments by diagonal shear cracks.Crawford et al.(2001)also proceeded to carry out an experimental study in a laboratory.The aim of this experiment was to obtain detailed respon data regarding the behavior of RC col-umns under carefully controlled conditions.The study showed that the laboratory tests were capable of producing deformation results on RC columns similar to the results achieved from the field tests.
A dynamic structure collap experiment with a1/4-scale build-ing model was conducted by Krauthammer et al.(2003).A numeri-cal study was also conducted on a model of the specimen by the rearch team.Finite-element(FE)analys using a Lagrangian
1Associate Professor,School of Civil and Environmental Engineering, Nanyang Technological Univ.,Singapore639798(corresponding author). E-mail:cbli@ntu.edu.sg
2Engineer,Land Transport Authority(LTA),Singapore408865.
3Rearch Associate,School of Civil and Environmental Engineering, Nanyang Technological Univ.,S
ingapore639798.
Note.This manuscript was submitted on June21,2010;approved on February9,2011;published online on May15,2012.Discussion period open until November1,2012;parate discussions must be submitted for individual papers.This paper is part of the Journal of Performance of Constructed Facilities,V ol.26,No.3,June1,2012.©ASCE,ISSN 0887-3828/2012/3-287–299/$25.00.
large deformation code with an explicit-dynamic FE computer code were able to predict the respon with reasonable accuracy.定义英文
To evaluate the progressive collap performance of the Alfred P.Murrah Federal Building,Oklahoma City,OK,which was -verely damaged in a 1995terrorist attack,a study was conducted by Hayes et al.(2005)to determine if current ismic design pro-visions could sufficiently improve the resistance of RC columns subjected to blast loads to possibly prevent progressive collap of the structure.The building was initially evaluated for ismic vulnerabilities as if it were located in a high-ismicity region.Strengthening schemes in the form of a pier-spandrel system,a special moment concrete frame,and a t of internal shear walls were propod.The strengthened structure was then analyzed for its respon to the same explosion that occurred in 1995.The analysis results showed t
hat the pier-spandrel and the special moment frame schemes reduced the degree of direct blast-induced damage and was capable of preventing progressive collap of the building.In a more recent parametric study conducted by Bao and Li (2010)and Wu et al.(2011),the significance of lected parameters that affected the residual axial strength of a blast-damaged RC column was revealed.Bao and Li (2010)propod a formula that was capable of providing a term v ,described as the ratio of the residual axial strength of a blast-damaged column to its initial axial capacity.This ratio is defined as follows:
v ¼
ðP r ÀP L ÞðP max ÀP L Þ
ð1Þ
where P r =residual axial capacity of a blast-damaged column;P L =axial load that the column is designed to sustain;and P max =axial capacity of an undamaged column.As such,when a column is undamaged,P r ¼P max ,and the value of v ¼1:0.Likewi,when the column has totally lost the ability to sustain its axial load,P r ¼P L ,and the value of v ¼0:0.This also refers to the ultimate state of the column.
The various parameters ud in this study provided a means of determining this residual axial strength ratio through a multivari-able regression analysis.This ratio was propod to be determined by its authors as:
v ¼
73:65ρv þ8:47ρg À0:021
L
b
þ0:104!e ½89284:22ρv À1308:64ρg À9:68ðL ÞÀ382:12 ðy r
ÞÀP L f 0c ∕A g Áð2Þwhere ρv =transver reinforcement ratio;ρg =longitudinal
reinforcement ratio;L =height of the column;b =width;y r =residual midheight deflection owing to the blast;P L =axial load;f 0c =compressive strength of the concrete ud;and A g =gross column cross-ctional area.
Some of the findings from this study included that the effect of axial load ratio is more critical for columns with lower transver reinforcement ratio and that the ratio of residual axial capacity increas as longitudinal reinforcement ratio was incread.The comparison made between the results from the propod equation and the analytical results showed that the equation was capable of predicting the residual axial capacity of blast-damaged columns with reasonable accuracy.
Although existing literature on residual axial capacity of RC columns provides some numerical and experimental investigations,the effects of two critical factors,namely the effect of incread transver reinforcement and the effect of axial loading,have not been clearly shown.Moreover,experimental studies to determine the residual capacity of RC column subjected to blast loadings
are limited.Therefore,a ries of experimental tests were designed to be tested in the Protective Engineering Laboratory of Nanyang Technological University,Singapore.With three horizontally mounted hydraulic actuators,the damage profile attained by the model column from the numerical simulation was recreated on actual column specimens during the experimental program.The damage profile was predicted using a validated numerical model that was capable of predicting the residual lateral deflection of RC columns subjected to blast loads.Test Specimens
Two ries of RC columns,referred to as “LS ”(limited ismic detailing)and “NS ”(nonismic detailing),were constructed to be tested for this study.The variables that were lected to be studied included the spacing of transver reinforcement within the column and axial loading.Fig.1shows the schematic dimensions and detailing of all the test specimens.In the LS ries (specimens S1and S3),hoop stirrups with a 135°bend were ud as transver reinforcements.The transver reinforcement was detailed with a clor spacing as compared with the NS ries.The transver reinforcement ratio for the LS ries is 0.58%.In the NS ries (specimens S2and S4),hoop stirrups with a 90°bend were ud as transver reinforcements.The transver reinforcement ratio for the NS ries is 0.19%.Both ries of specimens had a cross-ctional dimension of 260×260mm and a vertical height of 2,400mm.A higher axial load of 0:4f 0c A g was applied on the top head of the column for specimens S1and S2,whereas for speci-mens S3and S4,a lower axial load of 0:2f 0c A g was prescribed.A summary of column specimen specifications is shown in Table 1.
Finite-Element Analysis to Predict Residual Lateral Deflection
General
The nonlinear FE modeling software LS-DYNA (Hallquist 2008)was ud in this study to carry out th
e numerical analysis.LS-DYNA (Hallquist 2008)is a fully integrated engineering analysis code specifically designed for nonlinear dynamic problems.It is particularly suited to the modeling of explosion events.Blast Loadings
An exterior explosion could produce four types of loads:impact of primary fragments,impact of condary fragments,overpressure,and reflected pressure.The effect of overpressure and reflected pressure on the target from an explosion was investigated in this study.Becau the overpressure wave strikes on the front face of a clod target,a reflected pressure is instantly developed,and this is the most destructive aspect of blast loading on a struc-ture.The loading at different points on the front surface of the column for a given charge and standoff distance is computed by LS-DYNA (Hallquist 2008)with a built-in ConWep blast model,which relates the reflected overpressure to the scaled distance and accounts for the angle of incidence of the blast wave (Randers-Pehrson and Bannister 1997).Blast incidents in recent years showed that most terrorist attacks on public structures were explo-sions within short standoff distance (<10m).Thus,in this study,the standoff distance is assumed to be 7.2m.Considering the limi-tation of the weight of explosive,which can be obtained in any particular region,an equivalent weight of 1,000kg of TNT was lected for this study.
Structural Geometry Modeling
The typical geometry FE models of LS and NS specimens are shown in Fig.2.Eight-node solid hexahedron elements were ud to reprent concrete.The reinforcing bars are modeled explicitly using two-node Hughes-Liu beam elements.Perfect bond condi-tions were assumed.This implies complete compatibility of strains between concrete and steel.The restraint at the upper end of the column provided by condary floor beams and slabs were mod-eled as a stiff block,whereas the bottom end restraint was modeled as a fixed support.A rigid plate,which is allowed to move in only the vertical direction,is attached to the top end of the model.
Material Modeling
Modeling of Concrete
The FE code LS-DYNA (Hallquist 2008)contains veral material models that can be ud to reprent concrete.The material model MAT_CONCRETE_DAMAGE_REL3,available in LS-DYNA (Hallquist 2008),is ud in this study to model the concrete.It is a plasticity-bad model that us three shear failure surfaces and includes damage and strain-rate effects (Malvar et al.1997).
The model has a default parameter generation function using the unconfined compressive strength of the concrete and provides a robust reprentation of complex concrete laboratory respon (Sch
wer and Malvar 2005).In this model,the stress tensor is ex-presd as the sum of the hydrostatic stress tensor and the deviatoric stress tensor.The hydrostatic tensor changes the concrete volume,and the deviatoric stress tensor controls the shape deformation.The compaction model for the hydrostatic stress tensor is a multilinear approximation in internal energy.Pressure is defined by
p ¼C ðεv ÞþγT ðεv ÞE
ð3Þ
where E =internal energy per initial volume;and γ=ratio of specific heats.The volumetric strain εv is given by the natural log-arithm of the relative volume and is shown in Fig.3.The model contains an elastic path from the hydrostatic tension cutoff to the point T of elastic limit.When the tension stress is greater than the hydrostatic tension cutoff,tension failure occurs.When the volu-metric strain exceeds the elastic limit,compaction occurs,and the concrete turns into a granular kind of material.The bulk unloading modulus is a function of volumetric strain.Unloading occurs along the unloading bulk modulus up to the pressure cutoff.Reloading always follows the unloading path to the point at which unloading began and continues along that loading path.
Table 1.Summary of Model Specifications and Numerical Results Test Height (mm)Cross-ction (m
m ×mm)
Longitudinal rebar (%)
Transver reinforcement (%)
Axial load (kN)X FEM midheight (mm)
MHDR (%)
naga
S12,400260×260 2.300.5881028.3
1.18S22,400260×260
2.300.1981041.2 1.94S32,400260×260 2.300.5840652.8 2.20S4
2,400
260×260
2.30katherine
0.19
406
64.8
2.69
Note:MHDR =the ratio of the midheight deflection to the height of the column;X FEM midheight =predicted residual deflection in the midheight of the
column.
(a)(b)
Fig.1.Specimen reinforcement detail and dimensions:(a)LS ries;(b)NS ries
A three-curve model is ud to analyze the deviatoric stress
tensor;the upper curve reprents the maximum strength curve,the middle curve is the initial yield strength curve,and the lower curve is the failed material residual strength curve.
To consider that concrete would exhibit an incread strength under higher loading rates,a dynamic increa factor (DIF),the ratio of the dynamic -to -static strength,is employed in this analy-sis.The expressions propod by Malvar and Crawford (1998)are ud.The DIF for the concrete compressive strength is given as
DIF ¼
8><>: _ε_ε
s
1:026αs _ε≤30s À1γs _ε_εs
13_ε
>30s À1ð4Þ
where _ε
=strain rate in the range of 30×10À6to 300s À1;_ε
s ¼30×10À6s À1(static strain rate);log γs ¼6:156αs À2;αs ¼1∕ð5þ9f c ∕f co Þ;f co ¼10MPa;and f c =static compressive strength of concrete.
The DIF for concrete in tension is given by
DIF ¼
8><>: _ε_εs
δ_ε≤1:0s À1β _ε_εs
13_ε>1:0s À1ð5Þ
where ε=strain rate in the range of 10À6s À1to 160s À1;_ε
pleasure的用法s ¼10À6s À1
(static strain rate);log β¼6δÀ2δ¼1∕ð1þ8f c ∕f co Þ;f co ¼10MPa;and f c =static compressive strength of concrete.Different rate enhancements are specified for “tension and com-pression ”in the concrete material model employed in this study owing to the tensile respon being more nsitive to strain rate in contrast to the compressive respon.
The strain-rate effect in the numerical model is incorporated at any given pressure by expanding the failure surfaces with a rate enhancement factor in accordance to the effective deviatoric strain rate.Defining the strain-rate enhancement factor as r f and the pres-sure as p ,an “unenhanced ”pressure p ∕r f is first obtained.Then the unenhanced strength Δσðp ∕r f Þis calculated for the specified failure surface.Finally,the enhanced strength is obtained by
Δσe ¼r f Δσ
p
r f ð6ÞStrength is equally enhanced along any radial stress path that includes uniaxial,biaxial,and triaxial tension and uniaxial and biaxial compression.The effective strain rate versus deviatoric strength enhancement is given by an LS-DYNA DEFINE_CURVE keyword.
Modeling of Reinforcement
The material model MAT_PLASTIC_KINEMATIC is ud to model the steel.It is an elastic-plastic material model with strain-rate effect.The stress-strain curve is assumed bilinear,to reprent the elastoplastic behavior with linear isotropic hardening.The ex-pressions propod by Malvar and Crawford (1998)are ud to incorporate for strain-rate nsitivity.The adopted DIF formulation was for both yield and ultimate
stress
Fig.2.Illustrations of models:(a)LS ries;(b)NS
ries
Fig.3.Pressure versus volumetric strain curve
DIF¼
_ε
10À4
α
ð7Þ
whereα¼αf y andαf y¼0:074À0:040f y∕414for yield stress; andα¼αf u andαf u¼0:019À0:009f u∕414for ultimate stress. Eq.(7)is valid for reinforcement with yield stress between 290–710MPa and for strain rates between10À4and225sÀ1.
Erosion Criterion
The simulation is t to display erosion of elements.As such,when the inherent capacity of any element is exceeded during the sim-ulation,it would result in erosion of the element in the model.The principal tensile strain criterion was ud to determine the erosion of the elements in this study.
Validation of Finite-Element Models
An explosive loading laboratory testing program conducted at the University of California,San Diego ud a hydraulic-bad blast simulator to simulate explosive events without using explosive materials Hegemier et al.(2006).Several tests have been performed to investigate the dynamic respon of the RC columns when sub-jected to such impulsive loads.
The dynamic respons of the test specimens subjected to impul loads of5.3,12.1,13.1,and15.9kPa-c were analyzed using propod FE models.Three cas of positive duration, reprentative of typical energy dissipation time of a clo-in explosion,were3,4,and5ms,and their respective peak pressures were ud in the analysis,becau the detailed peak pressure and duration for the corresponding impul loads were not reported.
Fig.4shows the comparisons of residual deformations of numerical,laboratory,and field test results.The comparisons show that the numerical result is much higher than the laboratory test result when subjected to an impul load of12.1kPa-c.For the
deformation at one point.The effective strain contours reveal the strain localization at which failure propagates.The failure is local-ized near the column top and bottom ends owing to diagonal shear failure,which is consistent with field and laboratory test results. This validates the FE model to be able to predict the residual de-flection of RC columns subjected to blast loadings.
Analysis Steps and Load Patterns
The purpo of the validated FE simulation was to obtain the residual deflection of the column specimen at three specific loca-tions at which the actuators were positioned in the laboratory.This deflection would then be programmed into the displacement-controlled actuator ttings during the experimental study pha to achieve a column deflection profile to simulate the effect from a blast load.As shown in Fig.6,the analysis step would begin by applying the rvice loadings onto the column model.An axial load of0:4f0c A g is intended to be applied on specimens S1and S2, whereas an axial load of0:2f0c A g is intended to be applied on spec-imens S3and S4.The gravity loading was initially applied in a quasi static method on the steel plate that is on top of the RC col-umn model.Subquently,dynamic blast pressures were applied to Fig.5.Comparison of numerical and experimental respon of rein-forced concrete columns subjected to impulsive loadsbabolat
Fig.6.Loading steps in simulation
the front face of the column model.The last stage from the numeri-cal modeling program involved determining the residual lateral de-flection profile attained by the column model.The target residual deflection of each specimen is shown in Table 1.Moreover,the residual deflections attained by the models are shown in Fig.7.
Experimental Program
Material Proprieties
Each of the four specimens was cast with ready-mixed concrete that was specified to be able to achieve a characteristic strength of no lower than 25MPa within 28days.The aggregates were specified to have a size of 13.0mm,and the concrete pour was required to produce a slump of 125.0mm to ensure its workability.Twelve 150×300-mm test cylinders (three per individual specimen)were also cast and cured under the same conditions to make them reprentative of their respective column specimens.The cylinders were individually tested for their compressive strength f 0c to deter-mine the compressive strengths of the concrete ud to cast the specimens.The results obtained from the cylinder compressive tests are shown in Table 2.The compressive strengths of the respec-tive specimens were ud to carry out the numerical simulations as well.
酒的英文
High tensile strength steel bars of 16.0-mm diameter with nominal yield strength of 460MPa made up the longitudinal
reinforcement,and mild steel bars of 6.0-mm diameter with nominal yield strength of 250MPa were provided as transver reinforcement for all column specimens.The two batches of spec-imens had variations in terms of the amount of transver reinforce-ment.The first batch had double hoops formed by R6bars placed at 100.0-mm spacing.The cond batch had single hoops formed by R6bars placed at 175.0-mm spacing.Table 1shows the specimen reinforcement specifications.Test Setup
The experiment tup required a loading frame that was capable of maintaining axial loads on the column specimens initially,subquently followed by the application of lateral loads to enable the specimens to take up the deflected shape as achieved from the numerical study conducted on the models of the specimens.Once the specimens had achieved the deflected shape as if they had been damaged from a blast load,their axial loads were gradually in-cread to determine the additional amount of residual axial capac-ity available on sustaining this simulated blast damage.A sketch and photograph of the test tup are shown in Fig.8.The two vertical actuators shown in Fig.8worked together with a transfer beam to apply the axial load and measure the residual capacity
of the column specimens.Three horizontal actuators were ud to deform the column to simulate the effects of blast loadings.Three horizontal rollers were ud to constrain the rotation and horizontal freedom of the top head.Instrumentation
Extensive measuring devices were ud to monitor the respon of the test specimens on the specimens and within the actuators.The built-in load cells in the actuators were ud to measure the axial load and residual axial capacity of the specimens.Three LVDTs capable of a travel distance of 300mm were ud to mon-itor the horizontal deflection of the column.
Experimental Results and Obrvations
2017高考数学答案Specimen S1
A target midheight deflection of 27.8mm,or a midheight deflec-tion ratio (MHDR)(defined as the ratio of the midheight deflection to the height of the column)of 1.16%,was to be attained on this specimen.The axial load of 811kN (0:4f 0c A g )was applied through a displacement-controlled mode through the vertically placed ac-tuators.Once the preaxial load was maintained,the lateral actuators were controlled through a displacement-controlled mode to achieve the targeted displacement profile of this specimen.The crack de-velopment pattern that was obrved during the experiment is shown
柚子的英文in Fig.9(a).As shown in Fig.9(a),the flexural cracks were obrved in the midheight of the column at an MHDR of 0.2%.The first diagonal shear crack occurred in the bottom end of the column when the MHDR reached 0.5%.The diagonal shear cracks at the bottom of the column became wider,and the midheight flexural cracks developed toward the top end of the column when the MHDR was further incread to 1.0%.As the MHDR neared the targeted value of 1.18%,diagonal shear cracks were also ob-rved at the top of the column.Photographs of specimen S1being subjected to the lateral loads are shown in Fig.10.A plot of the experimental deflected profile of specimen S1and the other spec-imens are shown in Fig.11.
Fig.12(a)shows the applied axial loads against the respective vertical deformations of specimen S1.The initial axial load of 811kN,as shown in Fig.12(a),caud a vertical shortening
of
Fig.7.Numerical residual x displacement of each specimen after blast load attack
Table 2.Compressive Strength from Cylinder Tests Test Cylinder 1f 0c
(MPa)
Cylinder 2f 0c
(MPa)
Cylinder 3f 0c
(MPa)
Average f 0c (MPa)S127.834.832.731.8S235.330.931.832.6S332.632.734.733.3S4
30.3
34.8
大连外语培训学校32.5
32.6
