Research ArticleExperimental and Numerical Simulation Studies of RCBeams under the Actions of Equal Energy Impact Loads

Xiwu Zhou , Xiangyu Wang , Runcheng Zhang, and Wen Zhang

School of Transportation and Civil Engineering & Architecture, Foshan University, Foshan, China

Correspondence should be addressed to Xiangyu Wang; w2013754112@163.com

Received 12 September 2020; Revised 24 November 2020; Accepted 12 December 2020; Published 28 December 2020

Academic Editor: Xinyu Ye

Copyright © 2020 Xiwu Zhou et al. -is is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In this study, two groups of RC beams were subjected to low-speed drop weight impact test by using the domestic advancedultrahigh heavy-duty drop weight impact testing machine system. -e main aspects studied are the influence of the combinationof different impact velocity and mass on the dynamic response and local and global damage change of RC beam under the sameimpact energy. Next, the numerical model considering material strain rate is established using ABAQUS finite element software toverify and expand the experimental results. -e results show the following: (1) under the condition of equal energy, the peak valueof impact force measured in this experiment increases with the increase of impact velocity, yet the mid span displacement andrebar strain first increase and then decrease. In addition, when the impact velocity is 2.25m/s and the impact mass is 400 kg, thebeam has the most serious damage; (2) compared with the mass, the impact velocity has more obvious effects on the peak value ofcumulative impact force, mid span displacement, and rebar strain; (3) with the decrease of the impact velocity (the increase of themass), the local damage of the beam is gradually weakened and the overall damage is gradually exacerbated. -e failure mode ofthe beam is transformed from local punching shear failure to overall static failure type.

1. Introduction

In some special scenarios, RC beams may be impacted byheavy objects during service, such as containers falling fromport terminals and stones rolling down mountains [1]. Inorder to avoid catastrophic structural failures, impact loadsshould be additionally considered in the structural designs ofRC beams in potential special scenarios cases.

Under the conditions of impact loads, material may besubjected to the strain rate effects, and the dynamic con-stitutive will be quite different from the static constitutive.-e strain rate effects will change the strength and stiffnesslevels of the reinforcements and concrete material, resultingin the bearing capacity of the beams becoming improvedwhen compared with that under static load conditions [2].At the same time, the stress wave effects will also change thestress distribution range of the beams after impact occurs,and the stress of the beams will transition from midspan tosupport with the propagation of the stress waves [3]. -eshear effects will mainly affect the midspan. -erefore, the

higher the impact velocity is, the more obvious the sheareffects will be, and the more serious the local damages willbe. -e influencing effects on the overall failure will tend tofirst increase and then decrease [4]. It has been found thatthe inertial force effects are the key factors which will affectthe overall failure of the RC beams, and the size and range ofthe inertial force distribution are the main reasons for thechanges in the overall failure modes of the beams [5]. -esefour types of effects jointly impact the mechanical behaviorsof the beams under impact load conditions and are quitedifferent from the impacts observed under static loadconditions. -e influences of impact loads on the impactresistance behaviors of beams have always been a hot topic inthis field of research. Li [6] used falling weight impact testsand found that the higher the impact velocity is, the morequickly the stiffness of the damaged beams would decrease.However, it was observed that with enhancements of thestrain rate effect, the impact resistance bearing capacity ofthe beams had increased. Zhou et al. [7] also carried outfalling weight impact tests of stainless-steel concrete beams.

HindawiAdvances in Civil EngineeringVolume 2020, Article ID 8874097, 14 pageshttps://doi.org/10.1155/2020/8874097

mailto:w2013754112@163.comhttps://orcid.org/0000-0002-4737-0709https://orcid.org/0000-0003-2164-7420https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1155/2020/8874097

-e results revealed that the stainless-steel concrete beamsstill maintained better dynamic mechanical properties underhigh impact velocity conditions and that the impact force,displacements, and strain levels had noticeably increasedwith the increases of impact velocity. However, during theimpact process, when the impact force reaches the peakvalue, the specimen begins to displace and the specimen doesnot appear to undergo obvious damage, except for the localarea.-e impact force is transformed into the correspondinginertial force and supporting reaction force. -erefore, theimpact resistance of the beam is not accurately reflected bythe impact force. In another related study, Gholipour et al.[8] used the finite element software LS-DYNA to simulatethe influence of a close-in explosion loading, with varied-rate impact loadings on the residual capacities and damagebehavior of reinforced concrete beams. -ey proposed theresidual flexural and shear capacities model of beams basedon damage index and investigated different loading phasesso as to assess the sensitivities of the RC beams to the impactloading rate when subjected to different combinationmodes.-rough experimental testing, Fang et al. [9] found that theimpact durations were reduced with the increases in impactvelocity, and the impact durations were also increased withthe increases in impact mass. Kishi et al. [10] found that thebearing reaction force increased with increases in impactvelocity when the impact velocity was small. However, whenthe velocity reached a certain value, the bearing reactionforce had not further increased.-ese findings indicated thatthe bearing reaction force cannot precisely express theimpact bearing capacity of the beam. Ozbolt and Sharma[11] adopted numerical simulations to determine that, withincreases in impact velocity, the failure modes of the ex-amined beams had changed from bending failures to shearfailures. Dey et al. [12] observed that the peak values of theimpact force and the stiffness of fiber reinforced concretebeams gradually decreased under the same cumulativeimpact velocity conditions. Zhou et al. [13] found that thepeak values of the cumulative impact force increased withthe increases of impact velocity. In addition, the mechanicalbehavior of the beam changes with the type of impact load.-e above experiments mainly covered the influence of theloading method on the dynamic response and mechanicalbehavior of the beam under different energy impacts.However, there are relatively few experimental studiesaddressing the falling weight impact of beams, under thesame collision energy, with different loading methods. Inparticular, there remains a lack of research regarding thedevelopment and change of beam damage during single andcumulative impacts with equal energy.

At the same time, the local damages to the beam-hammer contact areas in the midspan were obvious underthe impact loads, and the local damages had affected theoverall damage to the beams. Zhang et al. [14] studied thenonlinear dynamic response and failure behavior of simplysupported beam under the action of medium velocity impactload and explosion load and found that the lower part of themiddle span of the beam was first spalled due to localpunching failure. Dou et al. [15] carried out the fallingweight impact tests by using high-strength concrete beams.

-e results revealed that increases in the concrete strengthhad little effect on the overall dynamic responses of thebeams, yet could potentially reduce the local damage degreesof the beams. In the falling weight research conducted by Jinet al. [16], it was found that the higher the stirrup rein-forcement ratios were, the smaller the local damages wouldbe, and the beams were more prone to bending failures. -einfluences of impact velocities on local and overall damagedegrees were investigated by Zhao and Yi [17]. It was foundthat the higher the impact velocity was, the smaller theproportion of kinetic energy from the falling hammers beingconverted into overall deformation energy consumptionwould be. In addition, more energy was used for the localdamages in the beam-hammer contact areas. Due to thecomplexity and short durations of the local beam damages[18], the influences of the changes in impact velocity andmass on the scope, degree, and type of local damage requiredfurther investigation. In particular, the influencing effects ofthe local damages on the overall damage degrees remainedunclear. In addition, combinations of experimental researchtechniques and numerical simulations were believed to havethe potential to better illustrate the mechanical behaviorsand damage changes of beams under impact load conditions.At the present time, equivalent degrees of freedom methodsand simple elastoplastic impact analysis methods are themain finite element analysis methods used in the study ofbeams subjected to impact loads [19, 20]. For example, Jinet al. [21] examined the impact resistance of steel fiber-reinforced concrete beams by combining experimentalmethods and numerical simulations. It has been found thatthe addition of steel fibers to concrete beams can reduce thebeam deformation and enhance the shear resistance of thebeams. Zhang et al. [22] studied the mechanical behaviors ofthe beam under falling weight impact loads and hightemperature dead loads through experimental processes andfinite element methods.

In this investigation, a domestic advanced ultrahighheavy-type falling weight impact testing machine systemwasutilized to carry out impact tests on two groups of reinforcedconcrete beams with bending failure and shear failure, re-spectively, under static load conditions. -en, combinedwith a finite element model, the influencing effects of drophammers with different masses and velocity combinationson the mechanical behaviors and damage changes of rein-forced concrete beams under the same energy were studied.-e results obtained in this study may potentially provideimportant technical support for future impact resistancebeam designs, as well as the evaluations of the impact re-sistance of existing structures.

2. Design of the Experimental Test

2.1. Specimen Design and Testing Method. In this study’sexperimental testing processes, two groups of reinforcedconcrete rectangular beams with different reinforcementratios were designed. -e specimens were 2.0m in lengthwith net spans of 1.8m, section sizes ofb × h � 150mm × 300mm. and reinforcement cover thick-nesses of 25mm. -e longitudinal reinforcements were

2 Advances in Civil Engineering

HRB400 reinforcements with yield strength of 420MPa, andthe stirrups were HRB300 reinforcement with yield strengthof 302MPa. -e concrete strength grade was C40, and thestrength measured by the test was 43.7MPa. -e specimenswere constructed by adopting formwork pouring andmanual vibration methods and then cured at room tem-perature for 28 days. A section of the Group A beam isshown in Figure 1.

-e longitudinal reinforcement ratio of Group A wasrelatively small, the bending-to-shear capacity ratio of thebeams was 88.36KN/140.37KN, and the main failure modewas bending failure under static loads. -e longitudinalreinforcement ratio of Group B was higher than that ofGroup A, the bending-to-shear capacity ratio of the beamswas 143.26KN/140.37 KN, and the main failure was shearfailure under static loads. -e design of this study’s ex-perimental tests is shown in Table 1. -ree identical spec-imen beams from each group were impacted with the sameenergy. However, the weights and speeds of the fallingweights were different. Cumulative impact tests were carriedout on the L16-1 and L16-3 beams, and single impact testswere conducted on the remaining beams. -e impact ve-locity values and the impact force of the falling weights,midspan displacements, reinforcement strain of the mea-suring points, and damage development of the specimensduring the impact processes were collected and recorded.-en, by comparing and analyzing the two groups of beamswith different mechanical properties, the impact resistanceresponses of the RC beams under equal energy impact loadscould be accurately evaluated.

-e calculation equation of the design parameters inTable 1 is as follows:

EI �mv

2

2,

v �

����������

2(g − a) × h

,

a �F

m,

(1)

where EI is the impact energy, m is the weight of the drophammer, v is the theoretical impact velocity, g is the ac-celeration due to gravity, a is the acceleration caused byfriction, h is the measured height of the drop hammer, and Fis the measured track friction force.

2.2. TestingDevice andDataAcquisition Process. -is study’stests were carried out in the ultrahigh falling weight impactlaboratory of Foshan University, and the device used for thetesting processes is shown in Figure 2. As can be seen in thefigure, the beam was placed on a fixed hinge bearing and theimpact point of the hammer head was in the midspan area. Aforce sensor was embedded in the hammer head in order tomeasure the time history of the impact force. -e hammerwas a cylindrical flat hammer head with a diameter of200mm. -e falling hammer had gone into a free fall stateapproximately along the vertical guide rail and impacted thebeam at its midspan position. -e mass of the falling weight

could be adjusted by adding or reducing counterweightplates. Considering the friction between the falling hammerand the track, the instantaneous speed of the falling weightwas measured by a laser speed measuring device. When thehammer head contacted the beam, the instantaneous ve-locity changed and the data acquisition was triggered. -emidspan deflection under the impact load wasmeasured by apull lever-type displacement meter arranged in the midspanof the beam. In addition, a resistance strain gauge was usedto measure the strain of stressed reinforcements, and thedistribution of the measuring points is detailed in Figure 1.Among the measuring points, the No. 1 and No. 4 measuringpoints were located at the midspan position of the beam. Inorder to measure the maximum strain of the load-bearingreinforcements, the No. 2 and No. 3 measuring points werelocated at the symmetrical position of one-quarter of thebeam, and the strain under impact was relatively small.-ese findings provided important references for the sub-sequent comparisons of the reinforcement strain level ofdifferent beams. Also, a high-speed camera was adopted torecord the impact test processes.

3. Analysis of the Impact Test Results

In this study, the test results of the Group A and Group Bbeams with different reinforcement ratios under equal en-ergy impact loads were processed. -e peak values of theimpact force and rebound mechanism, peak displacements,and residual displacements, as well as the peak values of thereinforcement strain, were further analyzed. -e cumulativeimpact tests of the two beams in Group A were carried outthree times, and the impact test results are detailed inTable 2.

In Table 2, L16-1 represents that the beam is impacted bythe first type of load, and L16-1-1 represents the first impactof the beam under the first type of load. -e reinforcementstrain is expressed by microstrain: 1 ξ � 106 μ ξ.

3.1. Analysis of Primary Impact Data. -e time-historycurves of the impact force are shown in Figure 3. -e impactforce level when the falling hammer collided with the beamwas measured by a built-in force sensor in the hammer head,and the impact force time-history curves of the three beamsin each group were merged into one chart. In this study’sexperiments, at the moment when the drop hammer collidedwith the beam, the impact force was observed to rapidlyreach a peak value and then decreased rapidly, forming awave peak. -en, the impact force vibrated and tendedtoward the horizontal. Due to the relatively large contactstiffness of the beam-hammer in the test, the signal trans-mitted by the force sensor will have overshoot phenomenon,so the impact force of some beams will appear negativevalues. By comparing the two figures, it could be seen thatunder the same energy impact load, when the impact ve-locity increased from 1.84m/s to 3.18m/s, the peak impactforce of the Group A beam increased by 70% and that ofGroup B increased by 61%. Furthermore, the peak impactforce increased by 4% from beam L16-1 to beam L20-1, and

Advances in Civil Engineering 3

the peak impact force of the four remaining beams increasedat different degrees with the increases in the reinforcementratios. In addition, during the oscillation processes of theimpact force curves after the first peak value was attained,only the impact force time history curves of the L16-1 andL20-1 beams with higher speed appeared to display sec-ondary peak values.-e secondary peak values of the impactforce of the L20-1 reinforced beam with a larger rein-forcement ratio were higher than those of the L16-1 rein-forced beam. -e main reason for this phenomenon wasthat, in the existing impact force formula [23], the power ofthe mass was secondary to the power of the velocity.-erefore, the impact velocity had greater impacts on the

trends of the impact force time-history curves than the mass.In addition, the reinforcement ratio of the L20 beam waslarger, so the overall stiffness of beam was greater. -estiffness affects the magnitude and frequency of subsequentpeaks of the beam impact force time-history curve. As aresult, the increases in velocity and stiffness were the mainreasons for the subsequent peak values of the beams underthe action of equal energy impact loads.

-e displacement time-history curve of the beam underimpact load is shown in Figure 4. After the drop hammerhad collided with the beam, the midspan displacements wereobserved to increase with the downward movement of thebeam and then decreased after reaching a peak value to form

300

25

2

450 2000

1(4)

Strain gauge

3

25150

25

300

25

2Φ10

2Φ16

⌽8@150

Figure 1: Reinforcement diagram of the Group A beam (mm).

(a)

Laser velocimeter

Hinged support

Displacementmeter

RC beam

Hammer-head

Weight plate

Pressure sensor

(b)

Figure 2: Falling weight impact test device (mm).

Table 1: Experimental test design.

Group Specimenno.Bottom

reinforcementErection

bar StirrupPrimaryimpact

energy (J)

Fallingweight(kg)

Falling height (theoretical impact velocity)

First Second -ird

AL16-1

2Φ16

2Φ10 ϕ8@150

1011.24 200 1.02m (3.18m/s) 2.04m (5.06m/s) 3.06m (6.39m/s)L16-2 1012.50 400 0.50m (2.25m/s) —L16-3 1015.68 600 0.33m (1.84m/s) 0.66m (2.92m/s) 0.99m (3.69m/s)

BL20-1

2Φ201011.24 200 1.02m (3.18m/s)

—L20-2 1012.50 400 0.50m (2.25m/s)L20-3 1015.68 600 0.33m (1.84m/s)

4 Advances in Civil Engineering

a main wave peak. Following that, the midspan displace-ments continued to decline and then rose once again afterreaching the minimum value. -is had resulted in theformation of a wave trough. When the displacements hadrisen to a certain value, the displacement curve tended to behorizontal. -e displacement time-history curve of somebeams shows negative values. -e main reason is that thefirst impact energy in this experiment is relatively small, andthe proportion of energy consumed by the elastic defor-mation of the beam has increased. So, there will be a greaterdegree of rebound.-ere were residual displacements whichwere observed in the midspan due to the plastic damage ofthe beam during the process of impact. It can be seen whencomparing the two images shown in Figure 4 that under theaction of equal energy impact loads, the peak displacementsof the beam first increased and then decreased with theincrease in impact velocity. In addition, with the increases inthe reinforcement ratios, the peak displacement of the beamhad decreased. -e residual displacements of the beam weremainly related to the reinforcement ratios and impact en-ergy. -erefore, it was indicated that the impact velocity andmass had little influence on the residual displacements.

As can be seen in Figure 5, the reinforcement strainincreased when the falling hammer collided with the beamand decreased after reaching the peak, forming a main wavepeak, and then tended to be horizontal. -e duration of themain wave peak was approximately 14 to 28ms, which wassimilar to that of the main wave peak of the displacementtime-history curve. -erefore, by comparing A and B inFigure 5, it was found that, under the action of equal energyimpact loads, the peak strain of the reinforcement first in-creased and then decreased with the increases in the impactvelocity. In addition, with the increases in the reinforcementratio, the peak strain of the reinforcement had decreased.

As detailed in Figures 3–5, the occurrence of peak valuesof the displacements and reinforcement strain was delayedrelative to the peak values of the impact force. -is wasdue to the fact that the beam was in the local responsestage before the development of the midspan displace-ments. At that stage, the impact force of the fallinghammer gradually had transformed into the inertial forceof beam itself, and the inertial force had propagated toboth ends of the beam in the form of stress waves. -en,when the stress waves reached the bearings and the beam

0.046 0.048 0.050 0.052 0.054 0.056 0.058 0.060–200000

–100000

0

100000

200000

300000

400000

500000

600000

700000

800000

L16-1 3.18m/sL16-2 2.25m/sL16-3 1.84m/s

Impa

ct fo

rce (

N)

Time (s)

(a)

L20-1 3.18m/sL20-2 2.25m/sL20-3 1.84m/s

0.046 0.048 0.050 0.052 0.054 0.056 0.058 0.060–200000

–100000

0

100000

200000

300000

400000

500000

600000

700000

800000

Impa

ct fo

rce (

N)

Time (s)

(b)

Figure 3: Time-history curves of the impact force: (a) Group A; (b) Group B.

Table 2: Test results.

Group Specimenno.Impact velocity (mass)

m/s (kg)Peak value of the impact

force (N)Peak value of the displacements

(mm)Peak value of the strain

(μξ)

A

L16-1-1 3.18 (200) 505968 10.28 1620L16-1-2 5.06 (200) 883159 18.25 —L16-1-3 6.39 (200) 1139481 29.24L16-2 2.25 (400) 337214 19.46 2235L16-3-1 1.84 (600) 297582 11.02 2004L16-3-2 2.92 (600) 476215 20.00 —L16-3-3 3.69 (600) 592120 31.54

BL20-1 3.18 (200) 526625 9.51 1034L20-2 2.25 (400) 465193 16.71 1279L20-3 1.84 (600) 327335 10.70 1146

Advances in Civil Engineering 5

began to respond as a whole. -e joint action of the in-ertial force and the bearing reaction force caused theentire beam to undergo downward accelerated motion.During that process, a small part of the mechanical energyof the falling hammer was used for the impact energyconsumption in local areas of the beam-hammer contact.A large portion of the mechanical energy was stored by thebeam and consumed by the following three parts: energyconsumption by local damages; energy consumption byoverall damages; and energy consumption by the defor-mations of the reinforcements and concrete material. Inthis study’s experimental tests, the midspan displacementsand reinforcement strain of the beam were observed to

first increase and then decrease with the increases in theimpact velocity. -ese findings indicated that combina-tions of different velocities and masses had resulted in thegreatest damage and failure under the actions of equalenergy impact loads.

3.2. Analysis of Cumulative Impact Data. Figure 6 shows thetime-history curve of the impact forces of beams L16-1 andL16-3 under the actions of equal energy cumulative impactloads. -e difference between the peak impact force of theL16-1-1 and L16-3-1 beams was determined to be 208,386N.-e difference between the peak force of the L16-1-3 andL16-3-3 beams was 547,361N, which indicated that the

0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20–10

–5

0

5

10

15

20D

ispla

cem

ent (

mm

)

Time (s)

L16-1 3.18m/sL16-2 2.25m/sL16-3 1.84m/s

(a)

0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20–10

–5

0

5

10

15

20

Disp

lace

men

t (m

m)

Time (s)

L20-1 3.18m/sL20-2 2.25m/sL20-3 1.84m/s

(b)

Figure 4: Time-history curves of the displacements: (a) Group A; (b) Group B.

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16–500

0

500

1000

1500

2000

2500

Stra

in

Time (s)

L16-1 3.18m/sL16-2 2.25m/sL16-3 1.84m/s

(a)

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

–500

0

500

1000

1500

2000

2500

Stra

in

Time (s)

L20-1 3.18m/sL20-2 2.25m/sL20-3 1.84m/s

(b)

Figure 5: Time-history curves of the strain: (a) Group A; (b) Group B.

6 Advances in Civil Engineering

impact peak value of the beamwas greater when the hammervelocity was higher (lower mass) regardless of whether it wasa single impact or cumulative impacts. In regard to thecumulative impacts of a single beam, the increase rates of thethree impact force peaks of beam L16-1 were 74% and 51%,respectively, when the impact velocity increased from3.18m/s to 6.39m/s. In addition, it was observed that whenthe impact velocity increased from 1.84m/s to 3.69m/s, thethree impact peak values of beam L16-3 increased by 43%and 38%, respectively. -ese results suggested that with theincreases in the cumulative impact times, the stiffnessdamages to the beam gradually increased, and the increaserate of peak value of the impact force became smaller. Inaddition, the impact speed of beam L16-1 is higher thanbeam L16-3 each time, so that the increase rate of thecorresponding peak impact force is also greater.-erefore, itwas concluded that the velocity had greater influences on thepeak impact force than the material mass under equal energycumulative impact load conditions.

Figure 7 shows the displacement time-history curves ofthe L16-1 and L16-3 beams under the action of equal energycumulative impact loads. -e trends of the displacementtime-history curves of each beam subjected to three cu-mulative impacts were observed to be approximately thesame. In regard to the cumulative impact of a single beam,when the impact velocity increased from 3.18m/s to 6.39m/s, the increase rate of the three displacement peak values ofbeam L16-1 was determined to be 78% and 106%, respec-tively. In addition, when the impact velocity increased from1.84m/s to 3.69m/s, the increase rates of the three timesdisplacement peak values of beam L16-3 were found to be81% and 104%, respectively.-ese results indicated that withthe increases in the cumulative impact times, the stiffnessdamage of the beam had gradually become aggravated, andthe increase rate of midspan peak displacements of the beamwas greater. -erefore, the larger the midspan peak dis-placements were, the greater the residual displacementswould be, and the more serious the damage of beams wouldbe. At the same time, through numerical simulation,Wongmatar et al. [24] derived the calculation formula be-tween the maximum displacement (δmax) and the ratio ofimpact energy (Ek) to static flexural capacity (Pu):δmax � 0.72(Ek/Pu). Combined with this experiment, whenthe beam is subjected to cumulative impact load, the Ekincreases. Due to the damage of the beam in the previousimpact, the Pu decreases, so the Ek/Pu increases and the δmaxincreases. Under the same impact way, the impact energyand static bending capacity are the main factors affecting themaximum deflection of the beam. In the present study, thechanges in the cumulative impact time-history of the re-inforcement strain were found to be similar to those ofmidspan displacements.

As can be seen in Figures 6 and 7, under the condition ofequal energy impact loads, the peak value of the impact forceincreased with the increases in impact velocity (decreasedmass) according to this study’s comparison between beamsL16-1 and L16-3. However, the displacements had displayedno obvious changes. -erefore, if the local damages wereignored, the damage degrees of the beam could be expressed

by the midspan displacements [25], which indicated that itwas not accurate to express the impact bearing capacity of abeam by using the impact force. -e fact that, under equalenergy cumulative impact loads, the relative changes in thedisplacements of the beam L16-1 and beam L16-3 wereobserved to be very small, may have indicated that thedamage degrees of the beams were mainly related to theimpact energy levels.

4. Numerical Simulations and Verifications

4.1. Model Establishment and Strain Rate Effect. In order tofurther study the local failure and overall damage of thebeam under equal energy impact load, the finite elementsoftware ABAQUS display dynamics module is used tocarry out three-dimensional numerical simulation of theexperiment. As shown in Figure 8, the drop hammerimpact model of the reinforced concrete beam is estab-lished. -e hammer head is simplified as a cylinder, with aradius of 200mm; the impact position is in the middle ofthe span.-emass of the falling weight can be controlled bymodifying the material density and model size, wherein it isdefined that the falling weight only moves in the verticaldirection. Additionally, through a predefined field, theimpact velocity of the falling hammer is set. -e support issimplified to the rectangular frame structure, shown inFigure 8, to simulate the pressure plate on the upper part ofthe beam during the test, and is consolidated with thebeam. Next, a coupling point is set directly below thesupport, and through the coupling point, the constrainttype of the beam is set to be simply supported. -e drophammer and the support are defined as rigid bodies. -ebond slip between rebar and concrete is not considered,and the rebar cage is embedded in the concrete matrix inthe form of Embed. -e contact between the drop hammerand beam and the beam and support is set as a universalcontact. -e concrete uses three-dimensional eight-nodelinear reduction integral solid element C3D8R and intro-duces element hourglass control. -e reinforcement baradopts the three-dimensional truss element T3D2, and theapproximate global size of the mesh is 25mm.

Due to the complexity of the dynamic responses ofreinforced concrete structures under impact load condi-tions, this study’s examination of the concrete materialadopted the damage plastic model (CDP) which was pro-posed by Lubliner et al. [26]. -e model parameters areshown in Table 3. -is model has the ability to analyze themechanical responses of concrete structures under dynamicloading conditions as well as monotonic and cyclic loadingconditions. It also considers the differences in the materialtension and compression properties. -e CDP model is ableto describe the irreversible damages to concrete material andcan also provide a description of the stiffness degradationbehaviors of the material. -e characteristic curves of theuniaxial compression and tension of the concrete charac-terized by decrease in stiffness are detailed in Figure 9. In thepresent study, the constitutive model of the longitudinalreinforcements and stirrups was the bilinear elastic-plasticmodel [27].

Advances in Civil Engineering 7

-e strain rate effect is also referred to as the sensitivityrate of the material. Due to the strain rate effects of thematerials, the strength of the reinforcements and concrete

material tend to increase under dynamic loads. -ese strainrate effects can be expressed as dynamic amplification factors(DIFs). In this study, the dynamic amplification factors(TDIFs) of the concrete tensile strength, as well as the dy-namic amplification factor model (CDIF) of the concretecompressive strength proposed by CEB [28], were used forthe numerical simulations as follows:

TDIF �fct,imp

fctm�

εctεcto

0.018

, εct

≤ 10s− 1,

0.0062εctεcto

1/3

, εct

> 10s− 1,

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)

0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20–10

0

10

20

30

40

Disp

lace

men

t (m

m)

Time (s)

L16-1-1 3.18m/sL16-1-2 5.06m/sL16-1-3 6.39m/s

(a)

0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20–10

0

10

20

30

40

Disp

lace

men

t (m

m)

Time (s)

L16-3-1 1.84m/sL16-3-2 2.92m/sL16-3-2 3.69m/s

(b)

Figure 7: Time-history curves for the displacements after cumulative impacts: (a) L16-1; (b) L16-3.

Figure 8: Numerical model diagram.

0.046 0.048 0.050 0.052 0.054 0.056 0.058 0.060–200000

0

200000

400000

600000

800000

1000000

1200000Im

pact

forc

e (N

)

Time (s)

L16-1-1 3.18m/sL16-1-2 5.06m/sL16-1-3 6.39m/s

(a)

0.046 0.048 0.050 0.052 0.054 0.056 0.058 0.060–200000

0

200000

400000

600000

800000

1000000

1200000

Impa

ct fo

rce (

N)

Time (s)

L16-3-1 1.84m/sL16-3-2 2.92m/sL16-3-2 3.69m/s

(b)

Figure 6: Time-history curves for the cumulative impact force: (a) L16-1; (b) L16-3.

8 Advances in Civil Engineering

where fct,imp is the tensile strength of the concrete underdynamic loading; fctm indicates the tensile strength of theconcrete under static loading; εct denotes the material strainrate; and εcto is the strain rate value under static loadingconditions. -e scope of the application was 10− 6 ∼ 300s− 1:

CDIF �fc,imp

fcm�

εcεco

0.014

, εc

≤ 30s− 1,

0.012εcεco

1/3

, εc

> 30s− 1,

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(3)

where fc,imp is the compressive strength of the concreteunder dynamic loading conditions; fcm indicates thecompressive strength of the concrete under static loadingconditions; εc refers to the material strain rate; and εco is thestrain rate value under static loading conditions. -e scopeof the application was −30 × 10− 6 ∼ 300s− 1.

-e Cowper-Symond model [29] was introduced in thisstudy to represent the strain rate effects of the reinforce-ments, and its expression was f•y/fy � 1 + (ε•/D)

1/P. It wasassumed that the model did not change with the strainstrengthening effects. -e values of D and P were related tothe ultimate strengths of the reinforcements, which weretaken as 40 and 5, respectively, in this study.

4.2.Model Validation. -e validity of this study’s model wasverified by comparing the damages, impact force, and

displacement results among the numerical simulations andtest results.

It can be seen in Figure 10 that part of the concrete in thelocal range of the contact area between the L16-1 concretebeam and the hammer head was crushed, and the cracking inthe concrete at the middle and lower parts of the span wasmainly formed into three oblique cracks with angles of 45°,as well as a small number of vertical cracks. In beam L16-3,mainly oblique cracks from midspan to support and verticalcracks in the midspan had formed (Figure 11). -e crushingof the concrete in the local range of the midspan of the L16-3beam was observed to be smaller than that of the L16-1beam, and themidspan displacements of the two beams weresimilar. -e inclination angles of the oblique cracks whichhad formed in the midspan and the beam ends were thelargest. -e inclination angles were observed to graduallyincrease from the bottom to the top and tended to thehorizontal in the midspan area. -e numerical simulationresults are similar to the experimental results.

-e impact force time-history curves and midspandisplacement time-history curves of numerical simulationand test results for the L16-3 beam are presented in Fig-ures 12 and 13, respectively. It was concluded that the impactforce time-history curves trends were observed to be similar.In addition, the peak values of the impact force and dis-placements were similar, with errors no greater than 10%.-is study’s numerical model was able to accurately reflectthe impact responses of the beams. Figure 14 shows thekinetic energy, internal energy, and hourglass energy curvesobtained by the numerical simulation of beam L16-1. -e

Table 3: Parameter table of concrete damage plasticity model.

Mass density Young’s modulus Poisson’s ratio Dilatancy angle Eccentricity fb0/fc0 k Viscosity parameter

2450 kg/m3 3.25×104 MPa 0.2 35° 0.1 1.16 0.6667 0.0005

бt

A

B 1E0

(1 – d0)E0

C εWc = 1

D

Wc = 0

O

Wt = 1 GM

(1 – dc)E0(1 – dt)(1 – dc)E0

N

2

бt0

EC

Wt = 0

Figure 9: Concrete uniaxial tension and compression characteristic curves.

Advances in Civil Engineering 9

ratio of hourglass energy to kinetic energy is within 10%,which shows that the mesh convergence result is better. As aresult, the impact resistance of the beams and the influenceof the different control variables on the mechanical be-haviors of the beams under impact load conditions could beeffectively analyzed.

5. Analysis of the Local and Overall Damages

-e damages in the beam-hammer contact areas andpunching failure areas of the beammidspans were defined aslocal damages, and the approximate range is shown inFigure 10. -e scope, type, and degrees of the local damageswere all determined to affect the overall damages of thebeams. In the research investigation, the development oflocal damages to the beams under equal energy impact loadsand the local damages influencing effects on the overall

damages to the beams were determined by using a finiteelement method.

5.1. Analysis of Local Damages. Figure 15 shows the devel-opment process of the local damages of the L16-2 beam. Itcould be seen in the figure that, starting from the impactacting point, the stress had diffused downward and towardboth ends of the beam. -en, with the development of thetime history, the stress was mainly diffused at an obliqueangle of 45° in the local range before it was transmitted to thebearings. Next, at the end of the local responses, the stresshad propagated from the beam-hammer contact area to thebeam end bearings. Figures 16 and 17 show the compressivedamages and tensile damages of the beam at the end of thepeak impact force, respectively. At that time, the stress waveshad not yet been transmitted to the bearings, and the beam

Local failure area

(a)

Local failure area

(b)

Figure 10: Beam L16-1.

(a) (b)

Figure 11: Beam L16-3.

0.000 0.005 0.010 0.015

Impa

ct fo

rce (

N)

L16-3 simulationL16-3 test

Time (s)

–50000

0

50000

100000

150000

200000

250000

300000

350000

Figure 12: Time-history curves of the impact force.

L16-3 testL16-3 simulation

–2

0

2

4

6

8

10

12

14

Disp

lace

men

t (m

m)

0.005 0.010 0.0150.000Time (s)

Figure 13: Time-history curves of the displacements.

10 Advances in Civil Engineering

was in a local response stage. It can also be seen in the figuresthat, under the equal energy impact loads, the scope anddegrees of the local damages to the beam had increased withthe increases in impact velocity, and the local damages to thebeam decreased with increases in the reinforcement ratios.-erefore, combined with the test results displayed inFigures 10 and 11, it was clear that the oblique angles of thelocal cracks decreased with the decreases in impact velocity,and the cracks tended to be vertical cracks. -erefore, thelocal damages to the beams clearly varied with the changes inthe impact loads and reinforcement ratios and affected theoverall damage of the beam.

5.2. Analysis of the Overall Damages. -e failure modes andcrack development of beams under impact loads are gen-erally very different from those under static loads. Due to the

joint influence of four types of effects, beams subjected tobending failures under static loads may also experience shearfailures under impact loads. As detailed in Figure 18, thebeam-hammer impacts were divided into a local responsestage and an overall response stage. During the local re-sponse stage, the beam was impacted by the hammer, andthe first impact damages occurred at the contact position.-e beam-hammer contact location was covered by theconcrete of the compression area, and the damages toconcrete in the compression area led to decreases in thebending resistance of the beam, thereby influencing the

Hourglass energyInternal energyKinetic energy

0

200

400

600

800

1000

1200

Ener

gy (J

)

0.004 0.008 0.012 0.016 0.0200.000Time (s)

Figure 14: Energy time-history curve.

(a)

(b)

(c)

(d)

Figure 15: Development of the local damages: (a) 1ms, (b) 1.2ms,(c) 1.4ms, (d) 1.7ms.

(a)

(b)

(c)

(d)

Figure 16: Local compressive damages: (a) L16-3-C, (b) L16-2-C,(c) L16-1-C, (d) L20-1-C.

(a)

(b)

(c)

(d)

Figure 17: Local tensile damages: (a) L16-3-T, (b) L16-2-T, (c)L16-1-T, (d) L20-1-T.

Advances in Civil Engineering 11

failure mode of the beam. -en, the stress waves hadpropagated downward and toward the left and right ends ofthe beam. However, prior to the stress waves reaching thebearings, the connection part between the bearings and thebeam had not yet been affected by the impact load and couldbe regarded as a fixed hinge support area. As a result, theload-bearing span of the beam was reduced and concen-trated in the local midspan areas. -e bending strength ofthe beam in the midspan areas then increased with thedecreases in the load-bearing span. -erefore, it could bediscerned that the beams under impact loads had mainlyformed oblique cracks due to shear failures in the midspanareas, which appeared to be A-shaped in the local range.-iswas considered to be a unique shear effect of the beam underthe impact loading conditions and had mainly occurredduring the local response stage. When the stress waves weretransmitted to the bearings, the beam began to move in adownward direction as a whole under the joint actions ofinertia force and bearing reaction force. -is was the key todetermining the overall failure mode of the beam. It wasfound in this study that, if the resultant force of the com-bined inertia force and bearing reaction force was greaterthan the bending capacity of the entire beam, then bendingfailure would occur. Otherwise, shear failure would occur.However, if the resultant force was greater than both thebending resistance and shearing resistance of the beam, thenbending shear failure would occur.-erefore, in this study, itwas concluded that the local punching shear failure had notaccurately represented the failure types of the entire beam.

Figure 19 shows a schematic diagram for the beamdamages under equal energy impact loads. It can be seen inthe figure that the impact velocity of the L16-1 beam washigh, the local damages were relatively large, and no obviouscracks were observed in other parts of the beam. A large partof the mechanical energy of the falling hammer had beenconverted into energy consumed by actions of the localfailure. -is had resulted in that fact that the resultant forceof the combined inertial force and bearing reaction forceduring the overall response stage was less than that of thebending and shearing resistance capacity of the entire beam.-en, it was found that, with the decreases in impact ve-locity, the beam tended toward static load conditions, andthe local damages in the midspan areas were noticeablysmaller. In addition, more energy acted on the overall re-sponse stage of the beam. -e inertial force effects played amajor role during the overall response stage, part of whichcaused the beam to produce a downward acceleration. Also,the other part was used to generate the supporting force.-ecurve distribution of the inertial force had reduced thebending moment in the midspan of the beam, which causedthe beam to be more prone to shear failure. However, it wasobserved that with the decreases in impact velocity, theeffects of the inertial force were weakened and the beam wascloser to the failure type of static loading. -erefore, it wasindicated in this study that with the decreases in impactvelocity, the extent and scope of local failures had decreased;the inclined angles of the inclined cracks in the midspan hadalso decreased; finally, the load on the beam tended to be

(a) (b) (c)

(d) (e) (f )

Figure 18: Crack development diagram of the L16-2 beam: (a) 1ms, (b) 1.5ms, (c) 5ms, (d) 8ms, (e) 10ms, (f ) 15ms.

(a) (b)

(c) (d)

(e) (f )

Figure 19: Schematic diagram of the beam damages: (a) L16-1, (b) L16-2, (c) L16-3, (d) L20-1, (e) L20-2, (f ) L20-3.

12 Advances in Civil Engineering

static load, and the bending moment in the midspan of thebeam increased. -e Group A beam mainly experiencedbending failure under static loading conditions. With thedecrease of impact velocity, the widths of the inclined cracksfrom the beam’s midspan areas to the bearings decreasedgradually from the L16-2 beam to the L16-3 beam. In ad-dition, the bending cracks gradually increased in the mid-span areas, and the failure mode of beam tended to be thebending failure of static load. In the same way, the Group Bbeams mainly underwent shear failure under static loading,and the inclination angles of the inclined cracks in themidspan areas were observed to gradually decrease due tothe weakening of the local failures with the decreases inimpact velocity. However, the inclined cracks from thebeam’s midspan areas to the bearings were found to grad-ually widen, and the beam tended to display a shear failuremode.

6. Conclusions

In this paper, the mechanical behaviors of RC beams underequal energy impact loading conditions were examined byusing both experimental tests and numerical simulations.-e impact force, displacement, strain, and damage valuesobtained from this study’s tests were analyzed in order toobtain the following conclusions:

(1) Under the action of equal energy impact loads, thepeak values of the impact force of the beams werefound to increase with the increases of impact ve-locity. In addition, the impact velocity and stiffnesslevels of the beams had increased the size and fre-quency of subsequent peak values of the beams. -edisplacement and reinforcement strain of the beamsfirst increased and then decreased with the increasesof impact velocity. When the impact velocity is2.25m/s and the impact mass is 400 kg, the beam hasthe most serious damage.

(2) It was found that, with the cumulative impact, thestiffness of the beam decreased and the displacementincrease rates of the L16-1 beam during the last twoimpacts were 78% and 106%, respectively. Further-more, the initial impact displacement peak value andcumulative impact displacement peak value increaserates of beam L16-3 and beam L16-1 were similar.-e increase rates of the impact force peak values ofthe L16-1 beam during the last two impacts were 74%and 51% and those of the L16-3 beam were 43% and38%, respectively. -e stiffness losses of the beamsaggravated the development of cumulative impactdisplacements and reduced the increase rates of theimpact force.

(3) According to the experimental results and tensileand compression damage obtained from the nu-merical simulation results, it can be concluded that,under the same energy impact load, as the impactvelocity increases, the local damage of the beamincreases. -is is mainly reflected in the scope andextent of local damage and the development of

diagonal cracks. Additionally, as the impact massincreases, a greater amount of energy acts on theoverall response stage of the beam, and the overalldamage becomes more severe. Furthermore, thefailure mode of the beam L16 has also changed, sothat when the impact velocity is 1.84m/s, the beammainly undergoes bending failure. Secondly, whenthe impact velocity is 2.25m/s, the beam undergoesbending and shear failure; eventually, when theimpact velocity is 3.18m/s, the beam mainly un-dergoes partial punching and shear failure. -edamage development of beam L20 is similar to thatof beam L16.

In summary, in this study, the influence of differentloading types (including single loading and cumulativeloading and different combinations of impact velocity andmass) on the damage degree and failure mode of reinforcedconcrete beams under the same total impact energy isstudied by experiments and finite element simulation. -isprovides a reference for the damage assessment of thespecimen after having been subjected to the same energy anddifferent impact methods.-e specimens that are susceptibleto high-speed impact loads, which should strengthen theanti-impact protection at the point of impact, and thespecimens, which are susceptible to low-speed impact loads,should be designed to strengthen the overall shear resistance.

7. Discussion

In this study, experimental testing was carried out underlow-velocity impact conditions. It was observed that, withina certain range, the range of the local punching shear of thebeams increased with the increases in the impact velocity.-is was considered to be related to the internal bonds ofconcrete beams. However, at higher impact velocities, thechanges in the local damage ranges of the beam requirefurther study. -e impact force values can reflect the impactresistance of a beam to a certain extent. However, during theexamination of impact force in this study, the expressions ofthe impact resistance capacities of the beam were not foundto be accurate. Consequently, it was recommended that theexpressions of the impact bearing capacities of the beams befurther investigated in future research studies.

Data Availability

-e test data are included within the article and can be madefreely available.

Conflicts of Interest

-e authors declare that they have no conflicts of interest.

Acknowledgments

-e research findings described in this paper were sponsoredby the Major Project (Natural Science) of the Department of

Advances in Civil Engineering 13

Education of Guangdong Province (2014KZDXM064), theScience and Technology Innovation Project of Departmentof Education of Guangdong Province (2013KJCX0188), andthe Civil Engineering Technology Research Center ofGuangdong Province.

References

[1] C. Zhang, G. Gholipour, and A. A. Mousavi, “Blast loadsinduced responses of RC structural members: state-of-the-artreview,” Composites Part B: Engineering, vol. 195, Article ID108066, 2020.

[2] Y. B. Guo, G. F. Gao, L. Jing, and V. P. W. Shim, “Quasi-staticand dynamic splitting of high-strength concretes-tensilestress-strain response and effects of strain rate,” InternationalJournal of Impact Engineering, vol. 125, pp. 188–211, 2019.

[3] X. Guo, Stress Wave Propagation in Concrete Structure underImpact Loading, National University of Defense Science andTechnology, Changsha, China, 2010.

[4] S. Saatci and F. Vecchio, “Effects of shear mechanisms onimpact behavior of reinforced concrete beams,” ACI Struc-tural Journal, vol. 106, no. 1, pp. 78–86, 2009.

[5] F. Liu, Q. Luo, B. Yan et al., “Numerical study on the failuremode of RC column subjected to lateral impact,” Vibrationand Shock, vol. 36, no. 16, pp. 122–127, 2017.

[6] M. Li, Effects of Rate-dependent Properties of Material onDynamic Properties on Reinforced Concrete Structural, DalianUniversity of Technology, Dalian, China, 2011.

[7] X. Zhou, R. Zhang, R. Xiong, G. Zhang, and X. Wang, “Anexperimental study of the impact mechanical properties of RCbeams following replacements of stainless steel reinforce-ments of equal strength,” Advances in Materials Science andEngineering, vol. 2019, Article ID 3635974, 16 pages, 2019.

[8] G. Gholipour, C. Zhang, and A. A. Mousavi, “Loading rateeffects on the responses of simply supported RC beamssubjected to the combination of impact and blast loads,”Engineering Structures, vol. 201, Article ID 109837, 2019.

[9] Y. Fang, J. Qu, and F. Xiang, “Experimental and numericalsimulation of beammembers under low velocity impact load,”Heilongjiang Science and Technology Information, vol. 25,no. 13, pp. 116-117, 2015.

[10] N. Kishi, H. Mikami, and T. Ando, “Impact-rsistint behaviourof shear-failure-type RC beams under falling-weight impactloading,” in Proceedings of the 7th International Conference onStructures under Shock and Impact, pp. 499–508, Montreal,Canada, 2002.

[11] J. Ozbolt and A. Sharma, “Numerical simulation of reinforcedconcrete beams with different shear reinforcements underdynamic impact loads,” International Journal of Impact En-gineering, vol. 38, no. 12, pp. 940–950, 2011.

[12] V. Dey, A. Bonakdar, and B. Mobasher, “Low-velocity flexuralimpact response of fiber-reinforced aerated concrete,” Cementand Concrete Composites, vol. 49, no. 1, pp. 100–110, 2014.

[13] X. Zhou, R. Zhang, G. Zhang, and X. Wang, “Experimentalstudy on impact mechanical properties of RC beams replacedby stainless steel bars with constant cross section,” Journal ofXinyang Normal University, vol. 32, no. 3, pp. 487–491, 2019.

[14] C. Zhang, G. Gholipour, and A. A. Mousavi, “Nonlineardynamic behavior of simply-supported RC beams subjected tocombined impact-blast loading,” Engineering Structures,vol. 181, pp. 124–142, 2019.

[15] G. Dou, X. Du, and L. Liang, “Experimental study on thebehavior of high strength reinforced concrete beams under

impact load,” Journal of Tianjin University, vol. 47, no. 12,pp. 1072–1080, 2014.

[16] L. Jin, J. Xu, R. Zhang, and X. Du, “Numerical study on theimpact performances of reinforced concrete beams: amesoscopic simulation method,” Engineering Failure Analy-sis, vol. 80, pp. 141–163, 2017.

[17] D. Zhao andW. Yi, “Anti-impact behavior and designmethodfor RC beams,” Vibration and Impact, vol. 34, no. 11,pp. 139–145, 2015.

[18] W. Zhao andQ. Jiang, “Study on local response characteristicsof RC beams under impact loading,” Journal of HunanUniversity, vol. 46, no. 3, pp. 25–32, 2019.

[19] K. Fujikake, T. Senga, N. Ueda, T. Ohno, and M. Katagiri,“Study on impact response of reactive powder concrete beamand its analytical model,” Journal of Advanced ConcreteTechnology, vol. 4, no. 1, pp. 99–108, 2006.

[20] A. Q. Bhatti, N. Kishi, H. Mikami, and T. Ando, “Elasto-plastic impact response analysis of shear-failure-type RCbeams with shear rebars,” Materials & Design, vol. 30, no. 3,pp. 502–510, 2009.

[21] L. Jin, R. Zhang, G. Dou, J. Xu, and X. Du, “Experimental andnumerical study of reinforced concrete beams with steel fiberssubjected to impact loading,” International Journal of DamageMechanics, vol. 27, no. 7, pp. 1058–1083, 2018.

[22] R. Zhang, J. Liu, X. Du, and G. Dou, “Mechanical behavior ofSFRC beams subjected to both impact and fire loadings,”Explosion and Shock, vol. 39, no. 9, pp. 63–75, 2019.

[23] G. Woisin, “Design against collision,” Schiff & Hafen, vol. 31,no. 2, pp. 1059–1069, 1979.

[24] P. Wongmatar, C. Hansapinyo, V. Vimonsatit, and W. Chen,“Recommendations for designing reinforced concrete beamsagainst low velocity impact loads,” International Journal ofStructural Stability and Dynamics, vol. 18, no. 9, p. 1850104,2018.

[25] S. Tachibana, H. Masuya, and S. Nakamura, “Performancebased design of reinforced concrete beams under impact,”Natural Hazards and Earth System Sciences, vol. 10, no. 6,pp. 1069–1078, 2010.

[26] J. Lubliner, J. Oliver, S. Oller, and E. Oñate, “A plastic-damagemodel for concrete,” International Journal of Solids andStructures, vol. 25, no. 3, pp. 299–326, 1989.

[27] T. B. Zhan, Study on Mechanical Behavior of ReinforcedConcrete Beams under Static and Dynamic Loads, BeijingUniversity of Technology, Beijing, China, 2016.

[28] Euro-Intemational Committee for Concrete, CEB-fip modelcode 2010, Fib Bulletin, Euro-Intemational Committee, Lau-sanne, Switzerland, 2010.

[29] N. Jones, Structural Impact, Cambridge University Press,Cambridge, UK, 2011.

14 Advances in Civil Engineering