Ductility and Failure Modes of Single Reinforced Concrete Columns. Hiromichi Yoshikawa 1 and Toshiaki Miyagi 2

Transcription

1 Ductility an Failure Moes of Single Reinforce Concrete Columns Hiromichi Yoshikawa 1 an Toshiaki Miyagi 2 Key Wors: seismic capacity esign, reinforce concrete column, failure moes, eformational uctility, flexural failure, shear failure, shear failure after flexural yieling, shear-egraing curve, nonlinear ynamic analysis, ranom eformation history 1 Dept. of Civil Engrg., Musashi Inst. of Tech., Tokyo, Japan. 2 Inst. of Tech., Tokyu Construction Co., Sagamihara-City, Japan.

2 Ductility an Failure Moes of Single Reinforce Concrete Columns Hiromichi Yoshikawa 3 an Toshiaki Miyagi 4 Abstract The main purpose of the seismic analysis of structures is to assess the level of risk associate with loss of serviceability, restorability an collapse. With regar to a reinforce concrete brige column, it is extremely important to ientify failure moes an to qualify the eformational uctility from the point of the capacity esign methoology (Paulay an Priestley (1992)). In this paper, types of failures of single reinforce concrete columns are classifie as flexural failure, shear failure after yieling of longituinal reinforcement, an shear failure. Proceures to etermine failure moes are presente by comparing P δ curve (push-over behavior) an the egraing capacity of shear strength along the eformational history. Nonlinear ynamic analysis is also carrie out for reinforce concrete columns 3 Dept. of Civil Engrg., Musashi Inst. of Tech., Tokyo, Japan. 4 Inst. of Tech., Tokyu Construction Co., Sagamihara-City, Japan.

3 subjecte to the recore time history of strong seismic actions. The shear-egraing curve propose by Priestley et al. (1996) is extene to a case of ranom eformation history to cope with actual seismic excitation. The propose metho is compare with ata of experimental works an numerical silations are carrie out. Introuction Seismic capacity of a substructure supporting superstructure is examine by comparing response values (loa or eformation) by earthquake motion with its strength or uctility in many cases. For example, comparison of response eformation an uctility performance of a structural system is a typical technique of seismic capacity assessment. Both these works are usually performe separately uring a esign proceure. However, this is not consiere to be a rational metho, especially in cases where seismic actions an structural uctility are affecte to each other uring a strong earthquake. When consiering reinforce concrete structures, it is important to clearly efine a failure moe an to appropriately assess the seismic capacity for each failure moe. Flexural failure an shear failure for reinforce concrete brige columns can be easily juge. However, a failure moe in-between these ( shear failure after flexural yieling ) is still open to question an often become critical in seismic esign (AIJ Design Guielines (1990), An an Maekawa (1998)). In this stuy, three failure moes of a single reinforce concrete column are efine, an ientification methos in static analyses an assessment methos for uctility factors are propose. Furthermore, comparison with test results an numerical silations were performe. A particular iscussion focuses on a egraation moel of shear strength accompanying large repeate eformation far beyon the yiel point of the main reinforcement. The egraation shear moel in ynamic ranom response is propose an ynamic nonlinear analyses by spring mass moel of a single egree-of-freeom are carrie out. The egraation process of structural members uring the time history is assesse base on an amount of amage acculate, then

4 etermination of failure/non-failure as well as failure moes are mae, an finally the maxim response isplacement is compute. Numerical silations for actual briges were performe, which offer useful an interesting information. Classification of Failure Moes of Single Reinforce Concrete Columns Now we consier the classification an efinition of failure moes of single type of reinforce concrete brige column subjecte to large cyclic eformation. We firstly consier increase cyclic tests of isplacement control type as shown in Figure 1, an efine δ y at the isplacement when longituinal reinforcement yiels an δ at the isplacement of ultimate flexural failure on the envelope curve ( P δ curve). The shear strength is, on the other han, graually reuce ue to large cyclic eformation beyon the isplacement of yieling of the main reinforcement. The shear strength are thus enote as: V yo : initial shear strength V yk : egraing shear strength ue to cyclic loaing

5 longituinal reinforcement yiele ultimate loa P uctility fcctor 1 isplacement (A) shear failure (B) shear failure after yiling (C) flexural failure P envelope curve (P- curve) egraation of shear strength curve Figure 1. upper: Cyclic Behavior of Single Reinforce Concrete Column, lower: Classification of Failure Moes Now that the failure moes can be efine accoring to the intersecting relationship between the P δ curve an the egraing shear capacity envelope (Priestley et al. (1996)). This is A) Shear failure: Shear failure occurs before the main reinforcement yiels B) Shear failure after flexural yieling: Shear failure occurs after the main reinforcement yieling C) Flexural failure: The P δ curve an the egraing shear capacity envelope o not intersect till reaching the ultimate flexural point ( δ = δ ). Photo 1. exhibits examples of test specimens faile in each of these failure

6 moes. The type A failure is cause when an excessive quantity of the main reinforcement is arrange or when a quantity of lateral reinforcement is insufficient, an it has been pointe out that this failure type extremely eteriorates seismic performance. On the other han, the type C failure means that shear failure oes not occur uner any excessive input of earthquake motion, an that full uctile performance is maintaine. The type B failure (flexural shear failure) locate between those types shows the limite uctile shear strength leaing to being critical concerning seismic esign. When we efine a member uctility ratio µ as µ = δ / δ y, the three failure types efine in Figure 1 are classifie as follows: (1) A) shear failure : µ < 1 B) shear failure after yieling : 1 < µ < µ C) flexural failure : µ= µ shear failure(c05) shear failure after yieling(c10) flexural failure(c20) Photo 1. Test Examples for Three Failure Moes (Hattori et al. 1998)

7 Static Nonlinear Analysis an Shear Strength Deformational Analysis obtain We will perform eformational analyses of single reinforce columns to P δ curves. The lateral isplacement δ inclues contributions of flexural eformation δ flex, shear eformation δ shear an rotating isplacement δ pullout cause by pulling out the main reinforcement at the column base. Namely, δ = δ + δ + δ (2) flex shear pullout As analytical conitions for materials, a moel was applie as the concrete constitutive law in which a confining effect by lateral reinforcement is reflecte, an the constitutive law of longituinal reinforcement was assume to be the tri- linear type moel. Shear eformation δ was neglecte in the present stuy. We assume that plastic hinge is forme in the zone from the column base to 1.0 ( is an effective height of column cross-section). The rotating isplacement δ pullout cause by pulling out the main reinforcement was calculate by applying the conventional equation. shear Shear Strength by Moifie Truss Analogy The well-known moifie truss analogy was applie for the calculation of shear strength in this stuy. This means that shear strength is obtaine by summing shear strength by lateral reinforcement V s an strength of concrete shear resisting mechanisms V (for example, JSCE Specification (1996)). In this c paper, the following expressions are use to consier initial shear strength an egraing shear strength separately.

8 initial shear strength : V y0 = Vs + Vc0 (3-a) egraing shear strength ue to cyclic loaing: V = V + V yk s (3-b) The shear strength by lateral reinforcement analogy by the following equation: V s is calculate base on the truss Vs = Aw f wy z cotθ / s (4) In which A w is the total area of shear reinforcement arrange in spacing s, an θ is a compressive strut angle. It has been pointe out that the reuction of shear strength accompanying cyclic excessive eformation is cause by egraation of the component of concrete contribution V c0. The symbol V is use as the strength in the egraation process. Here we introuce the egraation curve propose by Priestley et al. (1996) as shown in Figure 2. In Figure 2, the left vertical axis represents the shear strength τ c, the right vertical axis the shear egraation factor ζ obtaine by iviing shear strength V by the initial shear strength V c0. The initial value of this egraation factor ζ is equal to 1, an ζ < 1 for the larger eformation which is expresse such that ζ = ζ ( µ ). Thus, the relationship between the initial shear strength τ c0 an the egraing shear strength τ as well as between V an c0 V are simply written as V = ζ, τ = ζτ c0 (5) V c0 In Eq. (5), both of shear strengths V c0 an τ c0 can be relate such as

9 Vc 0 = τc0 A an e V τ Ae A. e = through the effective sectional area of a member c N /mm 2 ) = 2 = = 4 = = 8 = isplacement response factor 0.0 Figure 2. Moeling of Shear Strength Degraation Curve (Priestley et al. (1996)) Shear Strength by New RC Equation The New RC equation in AIJ Design Guielines (1990) allows calculating the shear strength by superposing the truss mechanism an arch mechanism as shown in Eq. (6). V y0 B z pw f wycot + Btanθ 1 = θ ( β )( H / 2) νf ' (6) c where, B an H : section with an height (mm), respectively, z : effective height ( = j ), p w : lateral reinforcement ratio (%), f wy : yiel strength of lateral reinforcement (N/mm 2 ), β : concrete contribution ratio of compressive force in truss mechanism, ν : effective concrete factor, f ' c : concrete compressive strength (N/mm 2 ), N : axial force (N) an n: axial force ratio ( = N / BHf ' ). c The concrete egraing process is expresse by reucing the effective

10 concrete factor ν an an angle of concrete compressive struts in the truss mechanism as a single function of rotating angle R p in the plastic hinge zone of column base. This propose forla reflects the new theoretical consieration to be proven by a wie range of experimental atabase). Comparison with Test Results an Numerical Silation Comparison with Test Results In orer to verify the valiity of this propose technique, we compare analytical results with loaing test results using three specimens referre to as C05, C10 an C20 (Hattori et al. (1998)). Each specimen having cross-sectional imensions of 320 mm320 mm an a shear span ratio of 4.05 were esigne to arrange reinforcements for the above-mentione three types of failure moe (see Photo 1 again). The analytical result of specimen C05 by the propose metho shows that eformational behavior is quite similar to the test result an preicte the shear failure ientical to the test. The analytical results of specimen C10 using two shear strength egraation curves intersecte nearly at the same points on P δ envelop curve, an coincie with the failure moe of the test results (shear failure after flexural yieling). The analysis of specimen C20 shows that both of the shear egraing curves o not intersect with is assesse to be of the flexural failure. P δ curve an the failure moe

11 As an example the case for specimen C10 that faile in shear after yieling of longituinal reinforcement, is shown in Figure 3, where the test result an the (a)experimental (b)numerical lateral force:p(kn) lateral force:p(kn) isplacement: isplacement:(mm) analytical preiction are compare. Figure 3. Failure Moe an Ductility for Specimen C10 Numerical Silation It is known that the failure moe an uctility of a member are affecte by the ratio of flexural yiel strength to shear strength, concrete contribution of shear strength, main reinforcement ratio, lateral reinforcement ratio, axial force level, an so on. Then parametric silations are carrie out base on this propose technique for those affecting factors. The shape of column use is ientical to the above specimens ( A =320 mm320 mm an shear span ratio a=4.05). The New-RC Guieline equation was applie to calculate the shear strength-egraing curve. Figure 4 shows the member uctility ratio vs. the ratio of shear strength to flexural strength with parametric range use in this analysis. Here we enote the

12 ratio of shear strength to flexural strength as V / V V of y0 (flexural capacity column obtaine by iviing the ultimate flexural moment M at the column base by the shear span a ). It can be seen that the failure moe shifts from flexural to shear moe an uctility factor of columns ecreases, as the ratio of shear strength to flexural strength becomes smaller. From this figure, it may be suggeste that each failure moe can be approximately estimate by the ratio of shear strength to flexural strength in such a way that Shear failure: ratio of shear strength to flexural strength<0.8 Shear failure after yieling of longituinal reinforcement: 0.8<ratio of shear strength to flexural strength<1.5 Flexural failure: 1.5<ratio of shear strength to flexural strength Figure 5 illustrates relationship among the main reinforcement ratio, the lateral reinforcement ratio an the member uctility factor for two axial force levels. This figure implies that with increase of the axial force applie to the member, its uctility factor becomes lower an the failure moe tens to shift from the flexural to the shear moe.

13 (a)o/f c=0 (b) o/f c=0.2 Figure 5. Evaluation of Failure Moes an Ductility Ratios for Two Axial Level in Relation of Main/Shear Reinforcement Ratio Failure an Shear Degraation in Dynamic Ranom Process Classification of Failure Moes in Ranom Process Now we consier an expansion of the propose metho to ranom response of concrete columns subjecte to a seismic loa shown in Figure 6, illustrating ynamic nonlinear response. FIGURE 6 schematically epicts the time history response for (a) curvature at column base, (b) lateral force acting on the column base an (c) lateral isplacement at column top. Figure (b) escribes that

14 the amage at the base, where curvature at base excees the isplacement of the main reinforcement yieling, results in graual reuction of shear strength an finally shear failure occurs at the time when the peak amplitue of the lateral force excees the shear strength (shear failure after flexural yiel). On the other han, Figure (c) inicates that flexural failure may occur because lateral isplacement δ reaches the ultimate flexural isplacement δ. (a) curvature at column base + y time y (b) lateral force V y0 shear failure V y1 V y2 egraing shear strength V yk (t) flexural failure V(t) (c) isplacement at column top + Figure 6. (a) Curvature at Column Base, (b) Lateral Force Acting on Column Base an (c) Lateral Displacement at Column Top in Time History Response

15 Therefore the failure moes for the ynamic ranom response can be classifie into the same manner as previously efine in aition to the non-failure. Determination of ynamic failure moes an maxim response isplacement µ can be summarize as follows: max A) Shear failure: V ( t ) > V 0 ( t ) µ < 1 max B) Shear failure after yieling of longituinal reinforcement: 1 < µ max < µ y V ( t) > V ( t) C) Flexural failure: V ( t) < Vyk ( t), µ > µ µ = µ max yk D) Non-failure V ( t) < Vyk ( t), µ < µ µ = µ In these equations µ max enotes the maxim response isplacement normalize by δ y an likewise µ δ / δ y =. The value of µ max is the maxim response isplacement in the case of non-failure, or the member uctility factor once the failure occurs. Dynamic Shear Strength It is suppose that the shear-egraing moel as iscusse above has been experimentally ientifie by static tests (say, quasi-static tests by graually increase isplacement control). In programs of these tests, eformational behavior an uctility are observe on each positive an negative sie of isplacement, successively followe by δ + 1δ = y, δ = 1δ y δ = + 2δ y δ 2δ y = δ + 3δ y = δ = 3δ. Therefore we propose the following amage moel utilizing a culative amage theory to evaluate the egraation of shear

16 strength uring the ynamic ranom process. As shown in Figure 7, a factoris newly introuce in orer to express the egraation of shear strength when a column is amage by a single atta in earthquake wave. The original egraing factor ζ shown in Figure 2 is moifie by ltiplying a factor m in the form µ < 2 : ξ = 1 2 µ < 4 : ξ = µ m + 1 m 4 µ < 8 : ξ = µ m + 1 m 8 µ : ξ = mµ + 1 (7) The moification factor m is suppose to be in a range of 0 < m < 1, an ξ = ξ ( m, µ ) is referre to as the egraing factor ue to a single atta, which is ifferent from the stanar egraing curve ξ = ξ µ ). Here in the present paper, the factor m is assume to be 0.5 as a constant value through the egraation process. ( By sequentially numbering suffix i for large eformation amplitue δ (here in this stuy δ > 2δ y ) as i = 1,2,3,..., k an esignating as ξ, ξ 2, ξ 3,..., ξ k 1, the following equation of sequential ltiplication leas to the factor ς k. ζ k = ξξ 1 2ξ3... ξk = ξi k i= 1 (8) During seismic motion concrete contributions of shear strength are upate using the egraing factor ζ k obtaine from Eq. (8). V, τ

17 =() time m i=1,2,3,ksequential peak number time Figure 7. Degraation Factors for (a) Increase Displacement Control an (b) Ranom Response Displacement Nonlinear Dynamic Analysis Dynamic Failure Analysis of Brige Columns In this section numerical silation is performe on a single type of brige column that was heavily amage in the Hyogo-Ken Nambu Earthquake. Specifications of cross-sections an calculate properties of members use for silation are liste in Table 1. Three members are esignate as

18 Case- P 1 ( P t = 1. 2%), - P 3 ( P t =1. 8%) an - P 5 ( P t = 2. 4%), in which P t enotes the ratio of longituinal reinforcement. The brige column was iealize into a system of a single egree-of-freeom with one-mass to perform a nonlinear ynamic response analysis. A skeleton curve of members in consieration was constructe base on JRA-specifications (1996) an the tri-linear type of Takea moel was use. Viscous amping coefficient was assume to be 2%. Table 1. Properties of Cross-section an Structural Member an Analytical Results(m =0.5) CASE P1 P3 P5 p t(%) T y (sec) V [=P u] (MN ) (m) (m) V s[=s s] (MN ) analytical results co (N /mm 2 ) V co (MN ) V yo[=v co+v s ] (MN ) V co/v yo V yo/v JMA-KOBE (max=800gal) V =V co (MN ) V yk/v failure moes non failure flexural failure shear failure after yieling Fig. Fig.8(a) Fig.8(b) Fig.8(c) max Earthquake motion observe at the Kobe Ocean Meteorological Observatory (hereafter referre to as JMA-KOBE) was employe as input earthquake groun motion ajuste the maxim acceleration to be 800 Gal. The Newmark- β metho ( β = 1/ 4) was use as step-by-step integration in the time omain, where the time interval was esignate as t = sec (0.002 sec when stiffness rastically change). Numerical silation was then performe an the results are shown in Table 1 an Figure 8 (a) - (c) for comparison. Since

19 the seismic input ata is base on the Hyogo-Ken Nambu Earthquake, the extremely large excitation has complete in the first 20 sec., an that the failure or non-failure was etermine uring the time of t = 510 sec in all cases. Case-P1 of Figure 8 shows that several large eformations over µ = 2 lea to reucing the shear egraing factor up to ζ k = , however neither shear failure nor flexural failure occurre after all (non- failure: µ = 4. max 31 ). On the other han, Case-P3 in Figure (b) illustrates that lateral isplacement reache the ultimate flexural uctility at the time of the initial large eformation ( µ = µ ), causing a flexural failure ( µ max = 3.94). It is interesting to see that the egraing shear strength an the response lateral force intersecte in the same amplitue. Case-P5 in Figure (c) implies a typical shear failure after flexural amage. Although the response isplacement µ was not large an then the egraation of shear strength was limite to ζ = , the shear failure was k initiate when t = sec ue to excessively large lateral force V (shear failure after flexural yieling: µ ). max = In this manner, ifferences in ynamic failure moes an maxim response isplacements are clearly recognize because of the ifference of static an ynamic characteristics accompanying the ifference of amount of the longituinal reinforcement, though the earthquake excitation an the structural configuration are ientical. It is also foun in these three cases that ratios of shear strength to flexural strength V / y V are getting small in orer of P1, P3 an P5 0 (see TABLE 1), an then the failure moe shifte from non-failure ( µ = 4. max 31 ), flexural failure ( µ = 3. max 94 ), an shear failure ( µ = 2. max 67 ). Ratio of shear strength to flexural strength is expecte to be useful to etermine the failure moe in the ynamic analysis. These analytical results mean that while the increase of longituinal reinforcement improves the static loaing capacity, the ynamic seismic capacity may be sometimes affecte aversely. It may be conclue that the columns analyze are to be high strength but low seismic capacity.

20 6 4 =4.72 no intersect =3.94 flexural failure =3.15 lateral force V isplacement egraation of shear strength Vyk(t) V(t) t=6.50sec t=6.52sec egraation of shear strength Vyk(t) no intersect -15 no intersect V(t) time (sec) time (sec) shear failure after yieling (a)case-p1: (max=4.31) ( max =2.68) (b) CASE-P3: (max=3.94) (c)case-p5: non-failure shear failure after yieling flexural failure Figure 8. Time History Response of Lateral Displacement (upper) an Lateral Force (lower) uner JMA-KOBE ( α = max 800 Gal) Numerical Silation Next we again employe earthquake motion of JMA-KOBE 1995, in which the maxim acceleration varie from 500 to 900 Gal an the contribution V ue to the lateral reinforcement change as V = 0.01, 0.5, 1.0, 1.5,...,5. 0 MN s so as to carry out nonlinear parametric ynamic analyses. Figure 9 an Figure 10 are examples of parametric silations, taking focus on the egraation process of shear strength in time-histories Figure 9 shows the egraing process of concrete contribution by the s

21 egraing factors ζ an ξ in i = 1, 2, 3, an the egraing process of concrete contribution (shear strength: V an shear strength: τ ) of the shear strength can be examine. It was foun that the number of the large eformation for µ 2 an the finally obtaine ζ epen on the characteristics of the earthquake input k motion as well as the structure configuration. Figure 10 shows the egraing shear strength τ taking the maxim groun acceleration as a parameter. It was foun that, as the maxim input acceleration ( α max : inicate in the figure) increases, the column causes the more amage to become the lower shear strength τ. (a) (b) i=1 JMA-KOBE(P3, max =800Gal ) , time(sec) Figure 9. (a) Relationship of Response Displacement an Degraation Factors an ζ k, an (b) Response Displacement in The Time History ξ k

22 2.0 c (N /mm 2 ) Gal Figure 10. Comparison of Degraing Shear Strength τ an Maxim Deformation Response ratio 2 2 µ [ f ' c = 27 N / mm τ 1.51N / mm ] co = Conclusions Through the iscussions so far we summarize the conclusion of this paper as follows: Failure moes for a single reinforce concrete column were classifie into three types: shear failure, shear failure after flexural yieling an flexural failure. It is especially ifficult to moel the shear failure after flexural yieling which has been iscusse from the viewpoint of seismic esign proceure. The moifie truss analogy incorporating concrete egraing moels propose by Priestley an New RC equation from AIJ Design Guielines were utilize to preict the egraing process up to the shear failure. Comparison of this propose technique with the results of static loaing tests using three specimens (increase isplacement control test) inicate generally goo agreement concerning the failure moe an isplacement uctility. The analytical results by parametric silation suggeste usefulness of the ratio of shear strength to flexural strength. In orer to apply this analytical technique to ranom responses of a

23 column subjecte to a seismic loa, the concrete egraing moel propose by Priestley was moifie in terms of the culative amage moel. Furthermore, a ynamic nonlinear response analysis was performe using one mass an single-egree-of-freeom moel uner recore seismic action. Reuction of shear strength is upate in the time history, an it became possible to juge either failure or non-failure an to calculate the maxim isplacement. When maxim input acceleration was, for instance, α = max 800 Gal, egraing strength τ got lowere to N/mm 2 whereas initial shear strength τ co of concrete was 1.5 N/mm 2. On the other han, the shear strength τ for seismic esign in the current Japanese specifications (JRA Specification an JSCE Seismic Coe) is approximately N/mm 2, which is foun to be a more conservative value. In this moeling, however, the more aequate etermination of the factor is necessary, which has been examine in our laboratory by experimental works as well as by the analytical consieration. Further numerical silations, taking the quantity of main reinforcement, quantity of lateral reinforcement, types of earthquakes an maxim acceleration as parameters, for actual reinforcement concrete brige columns nee to be performe to obtain more comprehensive numerical information. References An, X. an Maekawa, K. (1998). Shear Resistance an Ductility of RC Columns after Yiel of Main Reinforcement. Journal of Materials, Concrete Structures an Pavements, JSCE, No.585/V-38, Architectural Institute of Japan (1990). Design guielines for earthquake resistant reinforce concrete builings base on ultimate strength concept, Japan. (In Japanese) Hattori, H., Miyagi, T., Masua, Y., Iketani, K. an Yoshikawa, H. (1998). Evaluation of Failure Moe an Ductility of Reinforce Concrete Columns. The 10 th Japan Earthquake

24 Engineering Symposium, Proceeings Vol. 2, (In Japanese) Japan Society of Civil Engineers (1996). Stanar specification for concrete structures, Seismic Design, JSCE. (In Japanese) Japan Roa Association (1996). Specification for highway briges, Part V: Earthquake-resistant esign. (In Japanese) Paulay, T. an Priestley, M.J.N. (1992). Seismic Design of Reinforce Concrete an Masonry Builings, John Wiley & Sons. Priestley, M.J.N., Seible, F., an Calvi. G.M. (1996). Seismic Design an Retrofit of Briges, John Wiley & Sons.