SHEAR MECHANISM AND CAPACITY CALCULATION OF STEEL REINFORCED CONCRETE SPECIAL-SHAPED COLUMNS

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1 SHEAR MECHANISM AND CAPACITY CALCULATION OF STEEL REINFORCED CONCRETE SPECIAL-SHAPED COLUMNS Xue Jianyang, Chen Zongping, Zhao Hongtie 3 Proeor, College o Civil Engineering, Xi an Univerity o Architecture and Technology, Xi an, China Aociate Proeor, College o Civil and Architectural Engineering, Guangxi Univerity, Nanning, China 3 Proeor, College o Civil Engineering, Xi an Univerity o Architecture and Technology, Xi an, China xuejygh@xauat.edu.cn, jianyang_xue@63.com ABSTRACT : Through experiment on 7 teel reinorced concrete (SRC pecial-haped column pecimen under low-cyclic revered loading, loading proce and ailure pattern o SRC pecial-haped column with dierent teel reinorcement are oberved. From the experiment it i hown that the ailure pattern o thee column include hear-diagonal compreion ailure, hear-bond ailure, hear-lexure ailure and lexural ailure. The ailure mechanim and characteritic o SRC pecial-haped column are alo analyzed. For dierent SRC pecial-haped column, baed on the ailure characteritic and mechanim oberved rom the tet, ormula or calculating ultimate hear capacity in hear-diagonal compreion ailure and hear-bond ailure under horizontal axi and oblique loading are derived. The calculated reult how very good agreement with the actual experimental meaurement. Both the theoretical analyi and the experimental reult how that, hear capacity o T L haped column under oblique loading are larger than that under horizontal axi loading, wherea the hear capacity o -haped column under oblique loading are le than that under horizontal axi loading. KEYWORDS: teel reinorced concrete (SRC, pecial-haped column, hear mechanim, hear capacity. EXPERIMENT OUTLINE. Specimen deign and production Totally 7 pecimen, which include 9 T-haped, 4 L-haped and 4 -haped column are deigned(chen, parameter, which are hape teel, loading direction, axial compreive ratio and hear pan ratio, are ued. Shape teel include T-hape teel tru, channel teel tru, and olid hape teel. Loading direction include horizontal axi and oblique axi. Shape teel and cro-ectional geometry o the pecimen are hown in Figure. Tet parameter are lited in Table. b =50,h=5 t =tw= wire b =50,h=5 t =tw= cro diagonal bar 5 8 lat teel b =50,h=50 t =tw= olid teel T column b =50,h=5 t =tw= b =50,h=5 t =tw=8 weld olid plate 5mm plate wire b =50,h=5 t =tw= olid teel L column wire b =50,h=5 t =tw=8 6 b =50,h=5 t =tw=8 cro diagonal bar 5 8 lat teel 30 0 b =50,h=5 t =tw= hollow teel 十 column Figure Geometry and teel detail o pecimen

2 Specimen ID Shape teel Loading angle Table Tet parameter Axial compreive ratio n Shear pan ratio λ Cubic compreive trength cu /N mm - ρ /% ρ /% w T T-hape along lange T T-hape along web T3 T-hape 45 º T4 channel along lange T5 channel T6 channel along web T7 olid along lange T8 olid T9 olid along web L channel along horizontal axi L channel L3 olid along horizontal axi L4 olid T-hape along horizontal axi T-hape channel along horizontal axi channel Note: axial compreive ratio n=n/ c A, N i axial compreive orce, A i area o ection, hear pan ratio λ=l/h, L i length o pecimen, H i height o cro ection, ρ i ratio o hape teel to concrete area, ρ w i ratio o diagonal and level teel bar to concrete volume.. Failure pattern and mechanim Low cyclic revered loading tet i carried out on the parallel crohead equipment. Failure pattern o thee pecimen can be grouped into our categorie: hear-diagonal compreion ailure, hear-bond ailure, hear-lexure ailure and lexural ailure, which are hown in Figure. (a hear-diagonal compreion ailure (b hear-bond ailure (c lexural ailure Figure Failure pattern o pecimen (Shear-diagonal compreion ailure mechanim Shear-diagonal compreion ailure occur mainly on pecimen with low hear pan ratio(λ=. It ailure procedure can be divided into three tage a elatic, elatic-platic, and ailure. In elatic tage beore cracking,

3 deormation o hape teel and concrete are the ame. It get into the elatic-platic tage when crack appear. Firtly cro diagonal crack appear in the middle egment. The number o crack increae with load increaing, and divide urace concrete into mall rhombic piece. While load continue to increae, pecimen get into the ailure tage. Surace concrete i divided into everal mall hort diagonal column through the ormation o everal main cro diagonal crack among the multiple diagonal crack. Concrete gradually cruhe and all o. The periphery part outide tirrup i cruhed irt and the cruhing expand inide until web or diagonal bar are expoed. In the end web teel yield, lateral load drop rapidly and pecimen are detroyed. According to the tet, train o hape teel and tirrup are both mall in the elatic tage, while hape teel and concrete work together a a whole element to carry load, and have the ame deormation. Concrete quit the work ater it crack. It releae elatic energy and traner it to the web teel it croed with. Shear tre reditribution occur, and hear train o hape teel and tirrup increae obviouly and how nonlinear behavior. When load reache it peak value, hape teel and tirrup yield. (Shear-bond ailure mechanim For SRC pecial-haped column with moderate hear pan ratio(λ=, hear-bond ailure occur eaily. The ailure proce include the initial appearing o horizontal crack at both end o column, and then cro diagonal crack appear in middle egment. The cro diagonal crack extend when load increae. They become teep abruptly when extend to the vicinity o teel lange, and then orm vertical bond crack. Since then, the bond crack develop ater than the diagonal crack, and they interconnect rom above to below to orm a ingle vertical bond crack through the height o a column. The crack plit the protective concrete cover, load drop rapidly and pecimen are detroyed. When load reache it peak value, web member o hape teel and tirrup almot approach yield but not yet o. (3Shear-lexure ailure mechanim For L4 pecimen with low hear pan ratio (λ=, reinorced with olid web teel and loaded in 45º, hear-lexure ailure occur. Cro diagonal crack irtly appear in middle egment. Having the characteritic o large in number and mall in ize, thee crack develop and increae in number continuouly with the increae o load. In the meantime, horizontal crack appear due to moment at both end. Then with the continuou increae o load, thee horizontal crack develop more rapid than the diagonal crack. At lat, vertical crack appear at both end o pecimen and concrete i cruhed. From ailure pattern, it can be een that the ultimate load capacity depend on the lexural capacity o normal ection. Neither the web teel nor tirrup yield when ailure occur. (4Flexural ailure mechanim Flexural ailure oten occur in pecimen with high hear pan ratio (λ=.5. Horizontal lexure crack or vertical lexure crack irtly appear at both end o pecimen. With the increae o load, minor diagonal crack appear in ome pecimen. Failure pattern i hown a the cruh o concrete at both end. Longitudinal teel and bar yield, but not web teel and tirrup.. FAILURE MECHANISM OF SRC SPECIAL-SHAPED COLUMNS UNDER OBLIQUE LOADING Experiment are carried out on T-hape pecimen under 0º (along the lange, 45º and 90º (along the web load, L-hape and -hape pecimen under 0º (along the lange and 45º load. In polar coordinate ytem, α denote the load angle and polar radiu denote characteritic value o hear capacity uα / t. Due to the low-cyclic revered loading, in the direction o 45º (45º and 5º, 0º (0º and 80º and 90º (90º and 70º, two hear capacitie are obtained in each direction. For L-hape and -hape pecimen, the hear capacity at 0º i equal to that at 90º. Baed on the tet reult, all the data point decribing hear-diagonal compreion ailure pattern are depicted in the ame polar coordinate ytem and then the polar coordinate i tranerred to rectangular coordinate ollowing

4 the relation o x = ρ in α, y = ρ coα. The reult i hown in Figure 3. The correlation curve o L-hape and T-hape pecimen are cloe to ellipe, and the correlation curve o -hape pecimen i cloe to rhombic. Figure 4 how hear tre ditribution o dierent SRC pecial-haped column. It can be een that, or T-hape and L-hape pecimen, the maximum hear tre under oblique load i le than that under horizontal axi load. Thi i mainly due to the enlargement o hear area under oblique load. But or -hape pecimen, the maximum hear tre under horizontal axi load i le than that under oblique load. Thi i mainly becaue that, when pecimen are loaded at horizontal axi, the vertical branch locate in the vicinity o centroid o cro ection, o the hear tre here decreae. When pecimen are under oblique load, the interection o two vertical branche i in the vicinity o centroid o the cro ection, in thi place the width o hear-reitance cro ection change abruptly (rom double ection to ingle ection to reit hear orce, which reult in the abrupt increae in the maximum hear tre. Although the width o cro ection with the maximum hear tre in the two loading direction are the ame, the ditance between the critical ection and centroid o cro ection under horizontal axi load i longer than that under oblique load, thereore it maximum hear tre i le than that under oblique load. uy /( t 4 T-hape column T 形柱 3 uy /( t 3 L-hape column L 形柱 uy /( t 4 -hape column 十形柱 ux /( t ux /( t bh o ux /( t Figure 3 Relationhip between hear-bearing capacity and loading direction or SRC pecial-haped column Figure 4 Shear tre ditribution in deerent loading direction o SRC pecial-haped column 3. CALCULATION OF SHEAR CAPACITY 3. Shear capacity o SRC pecial haped column under horizontal axi load The experiment reult how that main ailure pattern o SRC pecial-haped column are hear-diagonal compreion ailure and hear-bond ailure. The ormer one i due to the cruh o diagonal concrete hort column divided by diagonal crack, the latter one i due to the plit o concrete outide the lange. According to the aorementioned ailure mechanim, web teel yield during the hear-diagonal compreion ailure, while during the hear-bond ailure the bond between hape teel and concrete loe, hence uperimpoition method can be ued to calculate the hear capacity(zhao,00:

5 = rc + (3. Where: rc i the hear orce carried by reinorced concrete, i the hear orce carried by hape teel. 3.. Calculation o hear capacity in hear-diagonal compreion ailure For dierent hape teel, the hear orce taken by hape teel ( o olid hape SRC pecial-haped column can be calculated uing the ormula below: HM y y + M wyy H y 4( M y M wy = (3. H y + 4M wy Where: N wy = t whw, y = t whw, M wy = t whw, M y = b t ( hw + t, are repectively the 3 4 ultimate axial orce, hear orce and moment carried by web and ultimate moment o lange in the platic tage o olid hape teel in the column branche paralleling to the loading direction. H i the height o pecimen. ( o hollow hape SRC pecial-haped column For hollow hape SRC pecial-haped column, treating diagonal member a bent-up teel bar and horizontal member a tirrup, their hear capacity can be calculated uing the calculation method or RC member. Awh = w Aw coθ + wh 0 (3.3 Where: w i yield trength o web teel, A w i area o diagonal web member in the ame cro ection, θ i the angle between diagonal web member and horizontal web member which parallel to hear orce, A wh i cro ection area o horizontal web member, i the pacing o horizontal web member along the height o column, h 0 i calculated height o the ection, let h 0 =h-a, and a i depth o concrete cover o longitudinal teel. To determine hear capacity rc o reinorced concrete in SRC pecial-haped column, the current Speciication or Deign o Concrete Special-Shaped Column Structure (JGJ in China can be reerred, and the contribution o lange to the increae o hear capacity hould alo be conidered. Shear capacity o RC egment in SRC pecial-haped column under earthquake loading can be determined uing the equation below. Where RE.05 A ( k b h + h + v rc t c 0 yv 0 γ RE λ N (3.4 γ i the adjutment coeicient o eimic capacity. λ i the hear pan ratio. k i increment actor o hear tre conidering the contribution o lange. Their value are hown in Table. According to the ditribution o hear tre, hear tre o cro ection i calculated with or without the conideration o lange repectively, and the maximum value i picked, conequently the value o k are determined. t i the deign axial tenile trength o concrete. b c and h 0 repreent the width and eective height o the calculation ection repectively. yv, A v and repreent the deign yield trength, total ection area and pacing o the tirrup repectively. N i the deign value o axial compreive orce. When N > 0.3( c A c + A, ue N = 0.3( c A c + A. Here A c i the net area o concrete cro ection. Length to width ratio Table k value in dierent loading angle direction T-hape L -hape -hape Loaded along web Loaded along lange Loaded along horizontal axi Loaded along horizontal axi Calculation o hear capacity in hear-bond ailure

6 The tet reult how that, or SRC pecial-haped column, when hear-bond ailure occur, web teel and tirrup almot but not yield. Let σ =0.8 and take it into ormulae(3. and (3.3to calculate. Here the calculation o hear capacity o RC egment rc i dierent rom that in hear-diagonal compreion ailure. Although they are all conited o RC egment and tirrup egment, they are expreed dierently. rc here i expreed a = + (3.5 rc (Concrete hear capacity c According to the analyi o hear-bond ailure mechanim and model, c can be expreed a below: = ( b b + b ] j (3.6 c c v [ Where: i hear tre o concrete on the two ide o hape teel lange, i bond tre between concrete and hape teel lange, b i width o hape teel lange,j i arm o internal orce, which i the ditance between midpoint o concrete cover outide the compreive lange and centroid o tenile hape teel in the branch column ection paralleling to the direction o hear orce. Av N Av N = t + σ + σ (3.7 b A b A = λ ( C / d (3.8 cy + Where: C i the thickne o concrete cover or teel lange, d i the height o hape teel ection, and λ cy i the degeneration coeicient o the bond tre under revered loading. According to a previou tet reult(xue, 007, λ cy =0.83. (Shear capacity o tirrup v For SRC pecial-haped column, tirrup can not only directly reit hear orce but alo retrict core concrete to improve bond action between concrete and hape teel. Hence it i neceary to et certain amount o tirrup in uch column. The hear capacity o tirrup i: Av v = σ h 0 (3.9 Where: σ i tre o tirrup, rom thi experimental meaurement, σ =0.8 yv. A v, are repectively total area and pacing o tirrup at longitudinal direction in branch column parallel to hear orce. h0 i calculated height o the ection, h 0 =h-a, i depth o concrete cover or longitudinal bar Comparion between calculated reult and tet reult a From Table 3 we can ee that the calculated reult agree well with the tet reult. 3. Shear bearing capacity o SRC pecial haped column under oblique load 3.. Shear capacity calculation o the T-hape and L-hape pecimen under oblique load The tet reult indicate that the correlative curve o the T-hape and L-hape pecimen under oblique load i in the hape o ellipe(maruyama, 884; Wang, 006, o it equation can be written a: x y + = ux uy Where: x i projection o oblique hear orce on x axi, and x axi, y i projection o oblique hear orce on y axi, in x axi and y axi repectively when they are under hear orce alone. y x t (3.0 = coθ (θ i the angle between = inθ. ux and uy are the hear capacity

7 Table 3 Comparion o hear capacity between calculated reult and tet reult under horizontal axi load Specimen ID T T Shape teel T-hape (hollow T-hape (hollow Axial compreive ratio n Shear pan ratio λ Concrete tenile trength t /MPa T9 olid T6 L T-hape (hollow Channel (hollow channel (hollow Failure pattern hear-diagonal compreion hear-diagonal compreion hear-diagonal compreion hear-diagonal compreion Meaured value t /kn Calculated value c /kn t / c hear-bond hear-bond In the proce o diagonal hear deign, aume i hear deign value. I the deign i conducted or it projection value x and y on two main axe and treated like poitive direction hear deign, the diagonal hear capacity u i le than the hear deign value. Thereore hear deign under oblique load need to be conducted exceively in both horizontal axe direction, i.e., increae the deign hear reitance value in both horizontal axe direction to ξ x x and ξ y y repectively and treat them a hear deign in horizontal axe direction. Baed on the preent Code or Deign o Concrete Structure (GB5000 in China, hear capacity o SRC pecial-haped column under bi-directional hear loading hould atiy the requirement below: ux ux uy uy x =, y = (3. ξ x ξ y + ux uy tanθ + uy tan ux θ can be calculated uing the aorementioned method under ingle directional hear load. ux uy 3.. Shear capacity calculation o the -hape pecimen under oblique load For -hape pecimen, the tet reult indicate that hear capacity under load in oblique direction i le than that in horizontal axi direction, and the correlative curve i in the hape o rhombu. There i hear tre concentration in the center o the interection o two column branche, thu it i the weak part o a pecimen, a hown in Figure 5. It i mainly here that the cracking rom hear-diagonal compreion ailure and the inal ailure pattern take place, which ha been veriied by experimental reearch. From calculation it i ound that the maximum hear tre in the weak part o ection under load in oblique direction i identical to that under load in horizontal axi direction without taking the vertical branch column into eect. However, or a -hape pecimen, becaue it two branche interect at center, their hear tre ditribution in the cro ection i aected each other. Thi i taken into account with the introduction o the aorementioned increment actor k. Thereore, hear capacity under oblique loading hould be /k o the hear capacity in any horizontal axi direction, that i: = / ux k (3. Where: k i the increment actor conidering the inluence o lange. alue can be ound in Table. ux and uy are hear capacity in the direction o x and y axe repectively when they are under hear load

8 individually. They are equal becaue o the ymmetry o cro ection. Uing the above method, hear capacity o the T-hape, -hape pecimen under oblique load are calculated and compared with actual meaured value rom experiment (ee Table 4. It can be een that the two reult it very well. Table 4 Comparion o hear capacity between calculated reult and tet reult under oblique load Axial Shear Concrete Calculated Tet Specimen Shape compreive pan tenile trength ID teel ux /kn uy /kn value value ratio n ratio λ t /MPa c /kn t /kn t / c T5 channel tru channel tru Concluion (Under low-cyclic revered loading, ailure pattern o SRC pecial-haped column mainly include hear-diagonal compreion ailure, hear-bond ailure, hear-lexure ailure and lexural ailure. Shear pan ratio i the main inluencing actor o ailure pattern. The ailure pattern which i mainly in the orm o hear deormation occur eaily in pecimen with low hear pan ratio. (Flange in SRC pecial-haped column can enhance the hear capacity. The degree o enhancement i related with loading direction and length to width ratio o column branche, but ha nothing to do with width o branche when the length to width ratio i ixed. (3Under oblique load, the hear capacity veru loading direction curve are ellipe or T-hape and L-hape column and rhombic or -hape column. For L-hape and T-hape column, a long a the hear capacitie in the two horizontal axe direction are atiied repectively, the hear capacity in the oblique direction can alo be atiied. But or -hape column, becaue the diagonal hear capacity i lightly le than the hear capacitie in two horizontal axe direction, ulilling the required hear capacitie in two horizontal axe direction doe not mean the hear capacity in oblique direction i atiied. (4For SRC pecial haped column with dierent teel reinorcement, baed on the hear mechanim in hear-diagonal compreion ailure and hear-bond ailure pattern, ormulae or calculating hear capacity under horizontal axi load and oblique load are derived. The calculated reult how very good agreement with the tet reult. The author would like to thank the Foundation o Educational Department o Shaan xi Province (Granted No. 07JK30 and State Education Minitry (Granted No.[007]08 or their upport o thi reearch project. REFERENCES Chen Z.P., Xue J.Y., and Zhao H.T.(007. Experimental reearch on eimic behavior o teel reinorced concrete pecial-haped column. Journal o Building Structure, 8:3, Maruyama K., Ramirez H., Jira J.O.(984. Short RC column under bilateral load hitorie. Journal o tructural engineering. 0:, Wang L.J., Wang T.C., and Wang S.(006. Experimental tudy on hear behavior o reinorced concrete rame column under bilateral horizontal load. Journal o Building Structure, 7:4, Xue J.Y., Zhao H.T.(007. Bond-lip theorem o teel reinorced concrete tructure and it application, Science Pre, Beijing, China. Zhao H.T.(00. Steel and concrete compoite tructure, Science Pre, Beijing, China.