xpermental Study on Ultmate Strength of Flexural-Falure-Type RC Beams under Impact Loadng N. Ksh 1), O. Nakano 2~, K. G. Matsuoka 1), and T. Ando 1~ 1) Dept. of Cvl ngneerng, Muroran Insttute of Technology, Muroran, 5-8585, Japan 2) Muroran Development & Constructon Department, Hokkado Development Bureau, Muroran, 51-852, Japan ABSTRACT In ths paper, to estmate the ultmate strength of flexural-falure-type Renforced Concrete (RC) beams under mpact loadng, fallng-weght mpact tests were conducted. ght smply supported rectangular RC beams were used, each wth a clear-span length of 2 m. Impact load was surcharged onto the md-span by flee-fallng 2 kg steel weght. Cross sectonal dmensons, rebar rato, and mpact velocty were taken as varables. In ths experment, mpact force excted n steel weght, reacton force, and md-span dsplacement were measured and recorded by wde-band analog data recorder. The tests show that the ultmate strength of flexural-falure-type RC beams subjected to mpact load can be estmated by usng the maxmum reacton force at falure and that ths type of RC beam can be ratonally desgned wth a certan safety margn usng the relatonshp between maxmum reacton force and statc bendng capacty. INTRODUCTION Renforced Concrete (RC) and Prestressed Concrete (PC) structures such as nuclear power plants should be desgned wth a certan safety margn aganst mpact load. However, n Japan, these structures usually are constructed based on statc desgn, because desgn manuals for mpact-resstant RCPC structural members (beam, slab, column) have never yet been drafted, even for RC beams. In ths study, to establsh a ratonal mpact-resstant desgn procedure of flexural-falure-type RC beams, fallng-weght mpact tests were conducted for eght RC beams. The mpact-resstant behavor of RC beams of ths type was nvestgated by analyzng the followng expermental results: 1) tme hstores of mpact force, reacton force, and md-span dsplacement; 2) hysteretc loops of mpact force - dsplacement and reacton force - dsplacement; 3) relatonshp between dynamc responses (maxmum reacton force and cumulatve resdual dsplacement) and mpact velocty; and ) dynamc response rato of maxmum reacton force to statc bendng capacty and rato of absorbed energy to nput knetc energy. XPRIMNTAL OVRVIW Dmensons and statc desgn values of RC beams Fgure 1 shows the dmensons of RC beams used n ths study. All RC beams are of rectangular cross secton wth two deformed man rebars. The clear-span length s 2 m. The cross sectonal dmensons and rebar rato were vared. The statc desgn values for all these RC beams are lsted n Table 1. ach specmen s desgnated by cross sectonal type (A: 16 2 ram, B: 2 22 mm, C: 16 16 mm) and man rebar dameter (1, 13, 19, and 22 mm). Statc bendng capacty P, sc and statc shear capacty V, sc are calculated accordng to the Japan Concrete Standard [1], and statc shear-bendng capacty rato a s obtaned by dvdng V,,~,c by P, sc. Accordng to the manual, all RC beams consdered here wll collapse n bendng-falure mode under statc loadng because ther a ratos exceed 1.. At commencement of the experments, the average concrete compressve strength was approxmately 26.5 MPa. Test procedure ach RC beam was smply supported at a pont 25 mm nsde from the ends and was pnched on the top and bottom surface at the support ponts to prevent the beam from reboundng (Photo 1). Impact tests were conducted by teratve loadng of a free-fallng 2 kg steel weght, n whch mpact velocty was ncreased n ncrements of 1 ms from 1 ms ntal mpact velocty untl the RC beam reached the ultmate state. Impact velocty was defned as the velocty at whch the steel weght mpacts onto the RC beam. The ultmate state s assumed to be that when the cumulatve resdual dsplacement of RC beam approaches 2. % of clear-span length (Photo 1). Impact load was surcharged onto the md-span of RC beam for all test cases. Impact force excted n steel weght, reacton force, and md-span dsplacement (herenafter, dsplacement) were measured and recorded by wde-band analog data recorder. The allowable frequences of load cells and LVDT are khz and 915 Hz, respectvely. All these analog data were converted to dgtal wth 1,us samplng tme.
6O 1 8O o=, Type A Type B Type C Strrup D6 I Man Rebar Type A ( D19, D22 ) Type B, C ( D1, D13, D19 ) " A 3@ 5 ] @ @ 13 5 =,15{ =3 11@ 1=11 ' I. =31 -,~ =)5 ~, 2 ] 25 25 '- (mm) Fg. 1 Dmensons of RC beams Table 1 Statc desgn values and mpact velocty Specmen A-19 A-22 B-1 B-13 B-19 C-1 C-13 C-19 Dmensons of Cross Secton (mm) 16 16 (Type A) 2 x 22 (Type B) 16 X 16 (Type C) Dameter of Man Rebar (mm) 19 22 Rebar Rato p~ (%) 1.88 2.55 Statc Bendng Capacty P.~ (kn) 6.6 83.3 Statc Shear Capacty V.~ (kn) 126.9 13.9 Shear-Bendng Capacty Rato a(=v.~ P.~) 3.1 1.9 Impact Velocty V( ms ) 1 6 1 6 1.2 16.9 98.9 5.85 1 13. 26.9 16.6 3.96 1 5 19 1.69 58.8 125. 2.13 1 6 1 13 19.7 1.32 2.98 11. 17. 37.9 68.8 7.1 87. 6..36 2.3 1 3 1 1 5!',',q!,. %~ :~:~:~:,-~::- ~: "... :.::::N... :-::-:... ~.,'... ~-~::::~... :.:...:...... :::... ::...? }:!::::!::;~ ~,~l;: ::..::~.:~;::!!!tl;~:~;:::::~;::::? ~ :7%:::~!l:;}:: ::~:~*~:::..... #:::}::::::::: :;!::; K:! ~).;!:.:;:.% %; :::>:%::::::~!!!!};::: Photo 1 xpermental setup
V= lms 2ms 3ms ms (kn) 15-15 Impact Force, P LC'2ml (kn) 15-15 - - 15 15 '... L,r-"--.,-..=..... -- - - 15 15 ~ ~ ~''~'~-...----- - 2 6 8 1 - Tme(msec) IWm_-~ Reacton Force, R ~ldlr -2-2 2 (cm) Md- Span Dsp., '' 2 ~ ~ 2. ~"~~'--'---- -2 J o -2 2 6 8 1 2 6 8 1 Tme(msec) Tme(msec) Fg. 2 Tme hstores of mpact force, reacton force and md-span dsplacement (B-IO) XPRIMNTAL RSULTS AND DISCUSSION Tme hstores of mpact force, reacton force, and md-span dsplacement Fgure 2 shows the tme hstores of mpact force P, reacton force R, and md-span dsplacement 6 for beam B-1. Here, reacton force was evaluated summng up the values obtaned from both supportng ponts. These fgures plot the mpact force as two half-sne waves: an ncdental wave havng extremely short duraton at the begnnng of mpact, and a man wave havng relatvely longer duraton rrespectve of the magntude of mpact velocty. The maxmum mpact force s ncreased and the duraton of man wave s prolonged accordng to ncrease n the mpact velocty. In contrast, reacton force s plotted as only one half-sne wave, and the confguraton of the wave durng mpact loadng resembles that of dsplacement wave. Regardng dsplacement wave, n the case of V = 1 ms mpact velocty, t can be seen that only one half-sne wave s excted. In the cases of V > 1 ms, maxmum dsplacement s ncreased and duraton of man wave s prolonged wth ncrease n mpact velocty. After mpact force s unloaded, the dsplacement fluctuates fantly accompaned by drft. Also, the resdual dsplacement s ncreased wth each ncrement of mpact velocty. Ths suggests that the damage to RC beams progresses. Hysteretc loops of mpact force - dsplacement and reacton force - dsplacement Hysteretc loops of mpact force - dsplacement P-6 and reacton force - dsplacement R,6 for beam B-1 are shown n Fg. 3. The fgure shows that n the case of V = 1 ms mpact velocty, the RC beam may behave almost elastcally because the absorbed energy estmated by ntegratng the looped area s very small. In the cases of V > 1 ms, the absorbed energy s ncreased wth each ncrement of mpact velocty. Fgure shows the hysteretc loops of P-6 and R-6 for all RC beams at the fnal mpact test. These fgures show that the dstrbuton characterstcs of P-6 and R-6 loops dffer from each other. Impact force ncreases very rapdly up to the maxmum value at very begnnng of mpact, and decreases almost to zero, rrespectve of the beam type. After that, mpact force ncreases agan to the second peak and then decreases to zero. In ths way, the confguratons of P-6 loops are complex. In contrast, reacton force ncreases lnearly up to the maxmum value. After that, almost the same value s contnuously kept untl the dsplacement reaches ts maxmum value, and then decreases to zero. The R-6 loops may be assumed to be a parallelogram whose confguraton s smple. From the precedng observatons, t s consdered that the ultmate strength of flexural-falure-type RC beams may be more ratonally estmated by usng the maxmum reacton force than the maxmum mpact force. In the followng nvestgatons, the maxmum reacton force s used for estmaton of the ultmate strength of RC beams under mpact loadng.
15[ ~'.~ 1 I V=lms V=2ms V=3ms V=ms 2 ~ ( c m ) ½ (~,.) ~ (~m) ~ (~m) Fg. 3 Hysteretc loops of mpact force - dsplacement and reacton force - dsplacement (B-l ) 25 ] v:,,. 125 P, e(cm) (a) A-19 V=Sms P-a R-# ' V= 2 a' (,:m) V-Oms r 2 ~(c~) (b) A-22 (c) B-1 V=3ms l ' V=ms r - 2 a, (cr.) (d) B-T3 25 -. I,, ' V=6ms [ V=3ms ' V=3ms ' V=Sms e~ =2 125 O 2 a' (,:m) (e) B-19 2 a (~,.) (f) C-1 2 (~) ~ (~) (g) c-13 (h) c-19 Fg. Hysteretc loops of mpact force - dsplacement and reacton force - dsplacement at fnal mpact test for all RC beams Relatonshp between dynamc responses and mpact velocty Maxmum reacton force R,d and cumulatve resdual dsplacement 3c,-each s plotted aganst mpact velocty n Fg. 5. Here, to nvestgate the effect of cross sectonal dmensons and rebar rato on dynamc response characterstcs of RC beams, two pars of RC beams (beams A-19 and B-19, and beams B-1 and C-13) are compared. ach beam n the par has a statc bendng capacty smlar to the other beam n the same par. These fgures show that the maxmum reacton force ncreases monotoncally wth the ncrease n mpact velocty. In contrast, the cumulatve resdual dsplacement ncreases steeply wth each ncrement of mpact velocty. Comparng the dynamc responses between A-19 and B-19, and between B-1 and C-13, t can be observed that the values of maxmum reacton force andor the cumulatve resdual dsplacement are almost same between the RC beams, when the statc bendng capactes of RC beams are smlar to each other. Relatonshp between the maxmum reacton force and statc bendng capacty The relatonshp between the maxmum reacton force Ru~ and statc bendng capacty Pu,~.c for each RC beam at falure s shown n Fg. 6. R,~ s obtaned from the fnal mpact tests; P,.~,c s based on Japan Concrete Standard. The dotted lne represents maxmum reacton force of 2. tmes statc bendng capacty. Ths fgure shows that the maxmum reacton force Ru~ for all RC beams exceeds 2. tmes statc bendng capacty P~.~,c. Ths suggests that the ultmate strength of flexural-falure-type RC beams under mpact loadng can be estmated by doublng the value of statc bendng capacty to ensure a margn of safety.
2 ~e 2 = 16 LL '~ 12 = 8 O A-19 B-19 77 B-1 C-13..D,,~ Impact Velocty, V (ms) (,J e,o m_ r~ e I.'2_ r,n ~J ty = t~ l = = o n O A-19 v B-19 D B-1 C-13..v 1 2 3 t s6! Impact Velocty, V (ms) (a) Fg. 5 Maxmum reacton force (b) Cumulatve resdual dsplacement Relatonshp between maxmum reacton force and mpact velocty and between cumulatve resdual dsplacement and mpact velocty Z 3 u x.. 2 O L O = ~" A'-1'9 :A-22 A :B-1 Q :B-13 O :B-19 '.-o "C-13.C-19 O.." J J 1 a l X t~ 1 Q - A. I 2O ' ' go 2 Pusc '13' Statc Bendng Capacty, Pusc(kN) Fg. 6 Relatonshp between maxmum reacton force and statc bendng capacty Rato of absorbed energy to nput knetc energy The rato of absorbed energy to nput knetc energy a k for each RC beam at falure s plotted n Fg. 7, where a s absorbed energy estmated usng looped area of reacton force - dsplacement curve (Fg. ) and k s nput knetc energy (= mv22; m" mass of steel weght, V: mpact velocty). The fgure shows that these values are dstrbuted n the regon from.5 through.9. The mean value s about.7. PROPOSAL OF IMPACT-RSIsTANT DSIGN PROCDUR The confguraton of reacton force - dsplacement loops of RC beams at falure (Fg. ) can be smplfed as a
ua 1. U tl,b x...8.6 ua. T o.2 x_ o. - (3).8 ~e, () \ \.... ; _~:... ~, \ \ \ l (3) ~ (o) ~e' (o) (6) (5) ( )" Impact Velocty, V (ms) A9 A2 Bo B3 B9 co c3 c9 Type of Specmen - Fg. 7 Rato of absorbed energy to nput knetc energy Rud L e~ Md-Span Dsplacement r Fg. 8 A smplfed model for reacton force- dsplacement loop parallelogram (Fg. 8). Usng ths smplfed model, the requred statc bendng capacty P,.~.j of RC beams aganst mpact load can be derved settng desgn nput knetc energy ~e and resdual dsplacement 6,.j as follows: Assumng that the maxmum reacton force R,a s 2. tmes the requred statc bendng capacty P,~.a, and the absorbed energy a s.7 tmes the desgn nput knetc energy,a based on the results n sectons 3.5 and 3.6, the followng equatons are derved: R,,~ = 2.P,,, (1),, =. 7k~l (2) Here, absorbed energy, can be wrtten, by referrng to the smplfed model shown n Fg. 8, as:, = R,e6,.,t (3) Substtutng qs. (1) and (2) nto q. (3) yelds the requred statc bendng capacty P,,~,~l"
.7 ~ l _.35 ~ () P,,,l- 2 6,-,1 6,-d Usng q. (), flexural-falure-type RC beams may be ratonally desgned aganst mpact load usng the statc bendng capacty. CONCLUSIONS In ths study, toward establshment of a ratonal mpact-resstant desgn procedure of flexural-falure-type RC beams, fallng-weght mpact tests were conducted on eght RC beams. They revealed the followng: 1) Dynamc response characterstcs of flexural-falure-type RC beams are roughly the same for beams of smlar statc bendng capactes calculated based on Japan Concrete Standard. 2) Ultmate strength of flexural-falure-type RC beams subjected to mpact load can be estmated by usng the maxmum reacton force at falure. 3) Confguraton of the hysteretc loop between reacton force and the md-span dsplacement at falure of an RC beam can be approxmated by a parallelogram. ) Flexural-falure-type RC beams under mpact load may be desgned wth a margn of safety by assumng dynamc response rato as 2. and rato of absorbed energy to nput knetc energy as.7. 5) Requred statc bendng capacty for RC beams aganst mpact load may be evaluated by a proposed smple equaton. RFRNC 1. JSC, Japan Concrete Standard, 1996, n Japanese.