BENDING AND SHEAR ANALYSIS AND DESIGN OF DUCTILE STEEL PLATE WALLS

Transcription

1 3 th Worl Conference on Earthquake Engineering Vancouver, B.C., Canaa August -6, 004 Paper No. 77 BENDING AND SHEAR ANALYSIS AND DESIGN O DUCTILE STEEL PLATE WALLS ehi H. K. KHARRAZI, Carlos E. VENTURA, Helmut G. L. PRION 3 an Saei SABOURI-GHOI 4 SUARY or the past few ecaes gloal attention an interest has grown in the application of Ductile Steel Plate Walls (DSPW) for uiling lateral loa resisting systems. Avantages of using DSPWs in a uiling as lateral force resisting system compromise stale hysteretic characteristics, high plastic energy asorption capaci an enhance stiffness, strength an uctili. A significant numer of experimental an analytical stuies have een carrie out to estalish analysis an esign methos for such lateral resisting systems, however, there is still a nee for a general analysis an esign methoology that not only accounts for the interaction of the plates an the framing system ut also can e use to efine the yiel an ultimate resistance capaci of the DSPW in ening an shear comination. In this paper an analytical moel of the DSPW that characterizes the structural capaci in the shear an ening interaction is presente an iscusse. This propose moel provies a goo unerstaning of how the ifferent components of the system interact, an is ale to properly represent the system's overall hysteretic characteristics. The paper also contriutes to etter unerstan the structural capaci of the DPSW an of the shear an ening interaction. The simplici of the metho permits it to e reaily incorporate in practical non-linear ynamic analyses of uilings with DSPWs. To emonstrate the effectiveness of the propose moel, its preicte response is compare with results from experimental stuies performe y various researchers. INTRODUCTION This paper presents a refine moel for the shear an ening analysis of uctile steel plate walls (DSPW), which will e referre to here as the oifie Plate-rame Interaction (-PI) moel. As shown in igure, the eformation of Ductile Steel Plate Walls (DSPW) is a comination of shear an ening eformations, oth of which are consiere in the -PI moel. In this paper the moel for pure shear analysis is aresse first, followe y the pure ening moel. inally, the shear an ening interaction for the -PI moel is stuie consiering appropriate failure iteria. The iscussion also inclues the Grauate Stuent, Dept. of Civil Eng., UBC, BC, Canaa, kharrazi@civil.uc.ca Professor, Dept. of Civil Eng., Universi of British Columia, BC, Canaa, ventura@civil.uc.ca 3 Associate Professor, Dept. of Civil Eng., Uni. of British Columia, BC, Canaa, prion@civil.uc.ca 4 Professor, Dept. of Civil Eng., K.N. Toosi, Tehran, Iran

2 loa-isplacement ehaviour of DSPWs. The -PI moel explores three main phenomena occurring in the structure, namely elastic uckling, post-uckling an yieling ehaviour of the DSPW. igure. Bening an Shear Comination in DSPWs SHEAR ANALYSIS O DUCTILE STEEL PLATE WALLS To egin with, the pure shear ehaviour of a uctile steel plate wall is stuie, with the following assumptions: Basic Assumptions A pical storey of a multi-storey structure with uctile steel plates wall can e represente as an isolate panel (igure ) for which the following assumptions can e mae: The columns are assume to e rigi enough so that their eformation can e neglecte when calculating the shear eflection of the steel plate. It follows that a uniform tension fiel will evelop aoss the entire steel plate. The ifference in tension-fiel intensi in ajacent storeys is small an therefore ening of the floor eams ue to the action of the tension fiel can e neglecte. The steel plate can e consiere as simply supporte along its ounaries. The effect of gloal ening stresses on the shear uckling stress of the steel plate can e neglecte. The ehaviour of the steel plate an the steel frame can e treate as elastic-perfectly plastic. Shear loa-isplacement relationships or the steel shear wall moel shown in igure, the shear loa-isplacement iagrams for the steel plate an for the surrouning frame can e otaine separately. Then, y superimposing the two iagrams, the shear loa-isplacement of the DSPW panel can e otaine. Shear loa-isplacement iagram of steel plate A pical shear loa-isplacement iagram of a steel plate of height, with an thickness t is shown in igure 3. In this figure point C correspons to the uckling limit, an point D correspons to the yiel point of the steel plate. Both points are yet to e etermine.

3 U Beam w wu D Plate Column w C igure. -PI moel plate iealization for Shear Deformation O U w U we igure 3. Shear loa-isplacement of steel plate only U w The itical shear stress, τ (see igure 4.a) is given y K π E t σ 0 τ = ( ) τ = wy () ( µ ) 3 in which t, E, µ, an σ 0 are the steel plate thickness, moulus of elastici, Poisson s ratio an the uni-axial yiel stress, respectively. K is otaine from K = ( ) for ( ) () 5.35 ( ) K = + 4 for ( ) (3) x = 0 σ xx σ xy = τ σ = τ yx + 45 O σ yy = 0 θ y x σ xx = σ sin Θ σ xy = σ sin Θ σ σ yx = σ sin Θ σ yy = σ cos Θ y a.) Stresses uring uckling.) Tension fiel stresses = x σ xx = σ sin σ = τ + σ sin Θ xy Θ σ = τ + σ sin Θ yx σ yy = σ cos Θ y The upper limit of τ σ 0 c.) Stresses after uckling igure 4. State of stresses in steel plate uring an after uckling is the yiel shear stress τ wy = (4) 3

4 The itical shear force of the we plate, w, is therefore w =τ t (5) An the itical shear isplacement, U w, is otaine from U w = τ (6) G In which G is the shear moulus of the steel plate material. Once w an U w are otaine from equations (5) an (6), respectively, point C can e efine in the shear loa-isplacement iagram (see igure 3). If it is assume that uring the post-uckling stage, a tension fiel incline at an angle Θ with respect to the horizontal, as shown in igure 4., graually evelops throughout the entire we plate. This assume stress istriution provies a lower oun for the strength of the we plate, provie that the surrouning frame memers are strong enough to sustain the normal ounary forces associate with the tension fiel. If σ enotes the value of the tension fiel stress at which yieling occurs, the total state of stress in the plate at yiel, shown in igure 4.c is efine y σ = sin Θ (7) xx σ σ = cos Θ (8) yy σ σ xy = σ yx = τ + σ sin Θ (9) Accoring to the Von ises yiel iterion, yieling of the plate occurs when ( σ xx σ yy ) + σ yy + σ xx + 6 σ xy σ 0 = 0 (0) Sustituting Eqs. (7), (8) an (9) into (0), the value of σ at which yieling of the steel plate occurs, is efine y 3 τ + 3 τ σ sin Θ + σ σ 0 = 0 () The shear strength of the we plate is now given y wu = σ xy t = t ( τ + σ sin Θ) () The limiting elastic shear isplacement U we, is otaine y U we = U w + U wp (3) U w is the itical shear isplacement as given in Eq. (6), an U wp, is the shear isplacement from the post-uckling component of the shear forces. The latter is etermine y equating the work one y the post uckle component of the shear forces to the strain energy of tension fiel. This leas to: σ ( σ sin Θ) t U wp = t (4) 4 E or σ U wp = (5) E sin Θ Sustituting U wp from Eq. (5) an U w from Eq. (6) in Eq. (3) gives τ σ U we = ( + ) (6) G E sin Θ Having etermine wu from Eq. () an U we from Eq. (6), point D is now efine in igure 3. In igure 3, lines OC an CD can e sustitute y a straight line OD, which simplifies the calculations with negligile effects on the shear loa-isplacement iagram. Thus, the slope of line OD in igure 3, which is the stiffness of the steel plate, is given y

5 ( τ + σ sin Θ) t K w = (7) τ σ ( + ) G E sin Θ As seen in Eq. (6), the limiting elastic shear isplacement, U we, is inepenent of the panel with,, ut irectly epenent on the panel height,. The columns in DSPW systems are, in general, esigne to carry gravi loas, an this is a useful characteristic for controlling uplift in the shear walls. The columns are normally assume to e rigi enough so that a uniform tension fiel is evelope throughout the entire steel plate, incline at an angle Θ=45 to the horizontal, as shown in igure 4. To ensure that the columns can sustain the normal ounary stresses associate with the tension fiel, an to make sure that a uniform tension fiel evelops aoss the entire plate, the columns will nee to have a minimum rigii (this will e iscusse further in the next section). or more etail on shear ehaviour of we plates see Saouri-Ghomi et al []. Shear loa-isplacement iagram of frame or an internal storey uctile steel plate wall as shown in igure 5, the shear loa-isplacement iagram is shown in igure 6. It is assume here that the eam-column connections are fixe an the eams ehave as rigi elements. If point E is etermine in igure 6, then the loa-isplacement iagram of the frame will e efine. rom igure 5, the shear strength of the frame, fu, is fp fu = 4 (8) in which fp is the plastic moment for the column. The limiting elastic shear isplacement of the frame, U fe, will e fp ρ + 4 U fe = (9) 6 E I f ρ + in which I f is the moment of inertia of the column an ρ = ( EI ) EI f. ρ = except for the last storey panel. fu Ufu Beam f fu E Plastic Hinge Column Kf O Ufe Uf igure 5. PI moel frame iealization igure 6. Shear loa-isplacement of frame only Point E is efine in igure 6 y otaining fu an U fe from Eqs. (8) an (9). The slope of line OE in igure 6, which is the stiffness of the frame, is 4 E I f ρ + K f = (0) 3 ρ + 4

6 In igure 7, the shear loa-isplacement of the panel is otaine y superimposing the iagrams shown in igures 3 an 6. In this figure, W, an P refer to the we steel plate, the frame an the steel plate panel, respectively. The steel plate panel is efine here as the comination of the plate an the frame elements. To ensure that the plate issipates more energy than the frame, it is suggeste that the steel plate walls e esigne in such a way that the following expression is satisfie: U fe > U we () As can e oserve in igure 7, y moelling the steel plate an frame separately, the esigner has significant flexiili on the selection of the memer sizes an properties. p B P (Panel) A wu D W (Plate) fu C E (rame) O Uwe Ufe igure 7. Components of PI moel shear loa-isplacement: frame only, plate only an comine effects in panel Up Effect of rigii of eams an columns on steel plate To ensure that the frame memers of the steel plate panel can sustain the normal ounary stresses associate with the tension fiel, an y assuming simple supports for the eams an columns, Eqs. () an (3) have to e satisfie (see Eqs. (7) an (8)). σ t fp cos Θ for columns () 8 σ t fp sin Θ for eams (3) 8 When checking Eq. () the axial force on the columns nees to e consiere. Eq. (3) has to e checke for the en eams of the steel plate panel. or internal storey eams, it is not always necessary to check Eq. (3) since the ifference in tension-fiel intensi is usually negligile in the ajacent stories. Nevertheless, it may e esirale to check this equation for the eams, if this ifference is consierale. BENDING ANALYSIS O DUCTILE STEEL PLATE WALLS In this section, the -PI moel for pure ening ehaviour is consiere. To moel the DSPW for the analysis of pure ening, the plate an the frame are consiere as one unit an the ening stresses in the unit section are stuie. Chapman [], Rockey an Jenkins [3], Basel an Thuerlimann [4], an many other researchers propose ifferent theories for the flexural analysis of steel wes of girers an teste several girers to verify their theoretical moels. In this section these theories are applie for the ening ehaviour, ening isplacement, an ening stress istriution of DSPWs. or the ening analysis of the shear wall, the assumptions mae are given next.

7 Basic Assumptions A pical storey of a multi-storey structure with uctile steel plate walls in ening can e represente y an isolate panel (igure 8), for which the following assumptions can e mae: The slenerness of the columns is small enough that yieling or inelastic uckling in the steel plate takes place efore any material yieling or uckling occurs in the columns. The steel plate can e consiere as simply supporte along its ounaries. The effect of gloal an inter-storey shear stresses on the ening an uckling stresses of the steel plate is neglecte. The ehaviour of the steel plate an the frame is elastic-perfectly plastic. Bening loa-isplacement relationships or the uctile steel wall moel in pure ening (igure 8), the comine loa-isplacement iagram for the steel plate an for the surrouning frame is otaine from the girer analysis theory. The moment capaci of the section is etermine from the comine loa-isplacement iagram of the panel an the frame. A pical loa-isplacement iagram for ening of a unit DSPW of height, an with, which consists of a plate an a frame, is shown in igure 9. In this figure point C correspons to the uckling limit, an point A correspons to the yiel point of the steel plate. Point B in igure 9 refers to the plastic capaci of the columns an consequently the frame. Point B is reache only when the columns oes not unergo any uckling an have higher yiel strength than the plate. These points are yet to e etermine. Critical uckling state of DSPW in pure ening To etermine the moment resistance of the DSPW at the stage of elastic itical plate uckling of the we, the itical ening stress, σ (igure 0.A), is efine as K π = E t ( ) σ 0 (4) σ ( µ ) in which t, E, µ, an σ 0 are the steel plate thickness, moulus of elastici, Poisson s ratio an the uni-axial yiel stress, respectively. K is otaine from K = 3.9 for ( ) <. 5 (5) K + = ( ) 8.6( ) for.5 (6) Beam Column Plate θ igure 8. -PI moel plate iealization for Bening Deformation

8 The upper limit of σ is the yiel ening stress σ = σ 0 (7) The itical moment force of the we plate,, is therefore = σ St (8) in which S t is the total section moulus of the panel, which is otaine from the total moment of inertia of the wall, I t, as shown elow I t 3 St = = ( I C + AC ( / ) + t /) (9) The itical ening isplacement, U m, is otaine from Um = (30) EIt Once an U m are otaine from Eqs. (8) an (30), respectively, point C in the ening loaisplacement iagram can e efine (igure 9). Ultimate yieling state of we plate in pure ening In the post-uckling state the compression stress in the we is assume not to inease eyon the itical uckling stress throughout the entire we plate, except for a very small portion close to the column in compression. or the tension stresses, uring the post-uckling stage, the tension fiel stresses graually evelop parallel to the column in tension, as shown in igure 0.B. The istriution of the stresses will not e linear any more an the neutral axis commences to move towar the tension column, which limits the we portion in tension to a smaller size than that in compression. This assume stress istriution provies a lower oun for the strength of the we plate, provie that the surrouning frame memers are strong enough to sustain the axial force associate with the ening an o not uckle. If σ enotes the tension fiel stress at which yieling occurs, the moment resistance at which the plate commences to yiel will e y = σ Seff = σ Ieff (( j) ) (3) where, j is the ratio of the istance etween the neutral axis an the compression column to, the with of the panel. S eff an I eff are the effective section moulus an the effective moment of inertia of the wall, respectively, which are as follows: I A ( j ) + t ( j ) 3 / 3 + A ( j) + α t ( j) h / α / (3) [ ] eff = C w c w C Seff = Ieff ( j) (33) where α is the length of we near the compression column, which is not uckling an is ale to carry stresses higher than the itical uckling stress. ost uctile steel plate walls have a fish-plate configuration to which the we plate is wele uring assemly. Since for thin we plates it is assume that σ = 0, the amount of α can e assume equal to the with of the fish-plate. The corresponing eflection of the panel ue to a ening moment of y is U my, which is otaine from the following equation: y Umy = (34) EI eff Once y an U my are otaine from Eqs. (3) an (34), respectively, point A can e efine in the ening loa-isplacement iagram (see igure 9). It is worthwhile to mention that the ultimate moment resistance of the wall coul e much lower than the amount otaine from Eq. 3, if the columns uckle elastically or in-elastically efore the we plate yiels. This amount is shown y yc in the ening loaisplacement iagram (see igure 9). Since it is initially assume that the columns will not uckle or yiel efore the we plate has yiel or uckle, this option is not consiere at this time.

9 p B Ultimate Plastic State y A Ultimate yiel State yc Column Buckling C Um Uyc Umy Ump Um igure 9. -PI ening moel loa-isplacement of the we plate an the frame comine If the yiel stress of the columns is larger than that of the we plate an the slenerness of the columns is relatively low, so that the section is ale to unergo axial plastification (yieling of the entire section) efore it uckles, the ultimate plastic strength can e etermine for the panel. Then the section is capale of proviing a plastic hinge, which will have a plastic moment resistance of P as efine elow: P = σ 0 Z P (35) in which, Z P is the plastic section moulus of the wall consiering only the contriution of the columns, as shown in igure 0.C. The plastic section moulus, Z P is as follow: Z P = A C (36) The corresponing eflection of the panel is U mp, an is otaine from the following equation: P U mp = (37) EI P in which I P is the plastic moment of inertia of the section, which oes not consier the contriution of the we plate. Once P an U mp are otaine from Eqs. (35) an (37), respectively, point B can e efine in the ening loa-isplacement iagram (see igure 9). It is important to note that, to reach this point, very stocky columns are neee. In most practical cases the section will likely experience uckling efore it reaches total material failure in the column sections. N.A. Plate Column Beam Plate A. B. C. igure 0. Stress istriution in the DSPW ue to pure ening, A.) Critical uckling State, B.) Ultimate Yiel Stress State of the We plate, an C.) Ultimate Plastic Stress State. Beam Plate Beam

10 BENDING SHEAR INTERACTION OR DUCTILE STEEL PLATE WALLS In a multi-storey uctile steel plate wall (DSPW), a panel unit resists not only shear forces ut also ening moments eate y the overturning action of the entire wall. To otain the capaci of the DSPW uner oth actions, the ening an shear interaction of the structure is introuce in the next section. The ening shear interaction is erive for the panel an frame at various states, such as the uckling an the yieling state of the we plate, an the frame failure state. This interaction equation is use to ajust the loa-isplacement iagram for the shear forces to account for the flexural action. Bening Shear Interaction for Critical Buckling The itical uckling shear loa resistance of the wall panel is ajuste y consiering the effect of the ening moment on the itical shear capaci of the we plate. This effect can e represente y the quaratic interaction equation: τ p + σ p = (38) τ σ where τ p an σ p are the applie stresses on the we steel plate. The itical uckling shear loa,, is then ajuste to account for the applie ening an a lower itical uckling value is otaine, which is = τ t. The total isplacement of the panel ue to the moifie itical uckling shear stress is U p τ τ σ w = + = + G EI t G E where the new ening stress, σ, is otaine from the applie moment, that is σ = / St. By etermining the elastic itical plate uckling shear loa an the total isplacement, point C is ajuste to point C in igure to account for the flexural loa effect. Bening Shear Interaction for Post-uckling Tension iel Stresses of the Plate The tension fiel eate in the uckle plate is part of the post-uckling characteristics of the steel plate. Since the gloal ening effects were ignore when eriving the pure shear capaci (as mentione in the assumptions), the ultimate yiel capaci of the steel plate in shear nees to e ajuste for the applie ening moment cause y the overturning effect. Therefore, the tension fiel stress, σ, nees to e ajuste for the ening stress, σ, eate y the ening moment in the we plate close to the tension column. As shown in igure, the ening stress, σ, in the plate ue to the ening moment is concentrate in the tension zone of the plate close to the tension column. This assume stress istriution provies a lower oun for the strength of the we plate, provie that the surrouning frame memers are strong enough to sustain the normal ounary forces associate with the tension fiel an axial forces associate with the ening moment. If σ enotes the value of the tension fiel stress at which yieling occurs, the total state of stress in the plate at yieling, shown in igure, is efine y σ = σ + σ sin Θ (40) xx σ = cos Θ (4) yy σ σ xy = σ yx = τ + σ sin Θ (4) Accoring to the Von ises yiel iterion, yieling of the plate occurs when ( σ xx σ yy ) + σ yy + σ xx + 6 σ xy σ 0 = 0 (43) (39)

11 Sustituting Eqs. (40), (4) an (4) into (43) an assuming that for thin plates τ = 0, the moifie value of σ at the yiel state of the steel plate is efine y = σ (3sin Θ ) + ( (3sin Θ )) 4( ) σ σ σ σ 0 (44) The ening stress, σ, is otaine from σ = / S eff. is the applie ening moment at the ultimate yiel state of the steel plate. The ening an shear interaction at the ultimate yiel state of the steel plate is otaine y iviing oth sies y σ = σ 0, which results in the following: σ σ (3sin ) ( σ (3sin )) 4( σ σ 0 ) Θ + Θ = (45) σ σ 0 The ajuste shear strength of the we plate is given y ( wu = σ xy t = t τ + σ sin Θ) (46) or thin plates, it is assume that τ = 0 thus the ajuste value for ultimate shear strength of the we plate is given y ( wu = t σ sin Θ) (47) The total ultimate shear resistance of the panel at the yiel state of the steel plate, wv is wv = wu + Kf Uwe (48) The ajuste limiting elastic shear isplacement U we, is otaine from U we = Uwe + (49) EI eff p B P (Panel) wu + KfUwe A A' B' ' C C' O U U' Uwe U'we Ufe U'fe Up igure. oifie loa isplacement iagram for shear resistance of the DSPW Bening Shear Interaction for Ultimate State To capture the interaction of the interstorey shear an the gloal moment for the ultimate state of the frame, the interaction equation for ening an shear of the frame is mainly ase on the axial an moment interaction of the column section. The axial an ening interaction equation of a section is usually given as a function of the following format: fn fp = f N N P (50)

12 The ultimate shear resistance of the frame section is moifie ase on this interaction equation. Since the ultimate shear resistance of the frame is otaine form fu = 4 fp an it is reasonale to assume that the ultimate plastic moment of the frame is otaine from P = σ 0 ZP, an Z P = AC given that N P = A C σ 0, then P = N P, an Eq. 50 can e re-written as fu N = f fu P (5) If the frame is mae of I-section columns Eq. 50 ecomes: N N = k o P N P for N.A. in the we of column (5) N k = otw N f c N P C N P AC N P for N.A. in the flange of column (53) where c, t w, an f are height, we thickness an flange with of the column respectively, an ko ctw. Eqs. 63 an 64 ecome: fu N = k o fu P for N.A. in the we of column (54) fu N k = otw f c for N.A. in the flange of column (55) fu C P AC P Using the moifie shear resistance of the frame an aing it to the moifie shear resistance of the steel plate results in the ultimate shear resistance of the panel, P : = + (56) P wu wu fu N where is the moifie ultimate yiel state of the steel plate an fu N is the moifie ultimate capaci of the frame, ajuste for ening shear interaction. Accoringly, the total isplacement U fe is moifie to consier the moment effect, which results in U p fe = U fe + (57) EI p The applie moment loa at this stage is p, which is not necessarily equal to the total plastic moment capaci. With this information, the loa-isplacement curve OCAB is ajuste to OC A B as shown in igure. It is important to mention that for esign purposes point A has to e etermine since it is the yiel point, whereas point B is use to etermine the total shear resistance of the DSPW. igure 3 shows the ening an shear interaction iagram for a given DSPW, which has a shear an ening capaci of P an P respectively. x σ yy = σ cos σ = τ + σ sinθ xy Θ σ = τ + σ sin Θ yx σ = σ + σ sin Θ igure. Bening an shear interaction of stresses in the steel panel xx y

13 EECTIVENESS O THE -PI ETHOD Results from tests conucte at the Universi of Alerta, Canaa y Driver [5] an Behahanifar [6] were use to evaluate the effectiveness of the -PI metho. Details of the specimens teste are shown in igure 4. The reason that these experimental stuies were chosen is ecause they teste multi-storey DSPWs that experience a significant amount of ening. or the large-scale steel plate wall shown in igure 4 (see Driver et al. [5]), the -PI metho leas to very satisfactory results when the moment contriution is accounte for, as shown in igure 5.a. The wall teste y Behahanifar [6], was Driver s specimen, excluing the first floor panel. or this specimen the -PI metho also provies satisfactory results when the moment contriution is accounte for, as shown in igure 5.. rom these comparisons it can e conclue that for steel plate walls mae of steel plates wele to column an eam memers, with rigi column to eam connections an aequate column capaci, the -PI metho provies satisfactory results. Note that for the specimens investigate the angle of inclination for tension fiel was assume to e 45 (Θ =45 ). '/ p'/p wu'+kfuwe/p Intaili in the frame an uckling of the column '/p O '/p 'cy/p y'/p p'/p igure 3. oifie loa isplacement iagram for shear resistance of the DSPW CONCLUSIONS In this paper an analytical moel, the oifie Plate-rame Interaction (-PI) metho, has een introuce, an it has een emonstrate that the metho preicts accurately the structural ehavior of multi-storey steel plate walls. A significant avantage of this metho is that many esign parameters, such as the shear loa-isplacement values, strength, stiffness an limiting elastic isplacement for the steel plate, an plate-frame interaction can e evaluate iniviually, an their effect on the overall wall capaci can easily e etermine. It is also important to mention that the -PI moel consiers the ehavior of DSPW not only for shear forces ut also for overturning moments. This provies the esigner with great flexiili for the esign of uctile steel plate walls. An ae enefit is that the metho is suitale for incorporation in practical seismic esign provisions. '/

14 89 mm 836 mm W30X8 P=70 kn P=70 kn W530X8 t = 3.4 mm W30X60 t = 3.4 W30X60 t= mm 89 mm W30X60 W30X8 t = mm igure 4. Details of specimens teste at Universi of Alerta test y Driver et al. (997) (Photo courtesy of R. Driver) igure 5. Comparison of -PI moel preiction an experimental results from tests conucte at Universi of Alerta, a).after Driver et al. (997) (top) an ). after Behahanifra (003) (ottom)

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