Compressive Bracing Model for Panel Wall Used to Infill Traditional Wooden Frames

Transcription

1 Compressive Bracing Moel for Panel Wall Use to Infill Traitional Wooen rames T.. Chen, J.S. Chang & P.L. Chen epartment of Architecture, ational Cheng Kung Universit, Tainan, Taiwan SUMMARY: In this stu, in orer to investigate the contribution of earthquake resistance of wooen panel wall that often use in traitional wooen builing in Taiwan, we tr to moel the panel wall as an equivalent compressive bracing. or moeling, firstl, the loaing-isplacement relationship curve of the panel wall is calculate. The owel action of bamboo nails between two panel unit an the rocking behavior of the panel were counte in the calculation. Secon, the effective with of the equivalent bracing is efine in accorance with the stiffness of the panel wall in the elastic stage. our performance stages of the bracing have been suggeste to efine the plastic hinge properties. Using the bracing moel, a pushover analsis for a traitional woo frame builing has been execute. Accoring to the analsis, it is observe that the panel walls o improve the builing stiffness an increase ultimate resistant loaing. Besies, the analsis also shows the panel walls occurre amage visibl after the frame joints have been seriousl amage. This behavior coul be aopte to explain wh the traitional woo builings scarcel completel collapse after 1999 Chi-Chi earthquake even the frame has seriousl amage an large eformation has reache. Kewors: wooen wall, In-plane Loaing, shear wall, wooen panel, Taiwanese wooen builing 1. ITROUCTIO In Taiwan s traitional woo builing, the wooen panel wall is often aopte to partition the interior space. The panel wall is infille piece b piece in the wooen frame. Accoring to the builing amage investigation after earthquake, it is foun that these wooen panel walls were helpful to reuce the amage egree of the builing in the earthquake, especiall to avoi collapse of the traitional builing. Thus, it is reasonable to require the wooen panel wall well consiere in the analzing moel for seismic assessment. The main purpose of this stu focus on (1)moelling the panel wall as an equivalent compressive bracing an () efining the plastic hinge properties of ifferent performance stages for this bracing. urthermore, in this stu, a traitional builing is selecte to examine the structural influence of the wooen panel walls uring push-over analsis.. TE COSTRUCTIO O TE WOOE PAEL WALL ig. 1 is the traitional wooen panel wall in Taiwan. The wooen wall is constructe with a main wooen frame, an the wooen panels are infille piece b piece in the frame. or reucing the height/with ratio of the panel to avoi panel buckling, in construction, horizontal auxiliar wooen member an vertical auxiliar members are arrange, which ivie the wall into several small parts. ig. shows the connection etail of the wooen panel wall. The wooen panels are inserte into the groove of the wooen beam. Between two ajoining panels, bamboo nails are riven in both of the panels to prevent panel sliing.

2 Wooen beam Bamboo nail Wooen beam Wooen panel Wooen column igure 1. The wooen panel wall in Taiwan s traitional woo builing Wooen panel igure. Connection etails of the wooen panel wall Wooen beam 3. TE BEAVIOR O TE WOOE PAEL UER I-PLAE ORIZOTAL LOA or the wooen panel wall, because the contact surface between the panel an wooen beam can t take tensile stress, the panel will rock uner in-plane loaing. As shown in ig. 3., the iagonal of the rocking panel act as a compressive bracing to resist the in-plane loaing. The bamboo nails between two ajoining panels also provie shear strength for preventing the slie of panel interface. On the other han, the reaction from the bracing wall will cause beam to have compressive eformation. This eformation of the beam will lea the panel to have aitional rotation an increase the total horizontal isplacement of the wall. orizontal isplacement orizontal Loaing P Shear stress cause b bamboo nails Compressive bracing effect on the iagonal area igure 3. In-plane behavior of the wooen panel uner horizontal loa 3.1. Compressive Bracing Effect of Iniviual Panel iagonal Area In assessment, the iniviual panel can be simplifie as a compressive brace on the iagonal of the panel. As shown in ig. 4., we can get the expression of strain of the compressive brace(eqn. 3.1) when the horizontal isplacement of the panel unit is S. urther, we can also get the expression of stress b Eqn. 3.. The stress-strain relationship of the woo is assume as ig.5. The moulus of elasticit of the compressive brace is erive from the ankinson s equation an the moifie parameter setting for Chinese cear b Wang. S sin S W (3.1) L W S W E ( ) E (3.) W

3 E// E E (3.3) E sin E cos // L :The iagonal length of the panel unit : The height of the panel unit W : The with of the panel unit E : MOE perpenicular to woo grain E // : MOE parallel to woo grain : the angle between the iagonal line an woo grain S W s sinθ Stress Strain As shown in ig. 6., the stress of a panel element can be obtaine from the stress of the compressive brace. Eqn. 3.4 to Eqn. 3.6 are the normal stress an shear stress on the interface between wooen panel an beam. Because the interface between wooen panel an beam can t resist the tensile stress, a half with of the panel woul separate from the beam when the panel rocks. Thus we assume the effective acting with of the compressive brace is a half with of the panel. The calculate shear force P an vertical force P of the compressive brace are shown in Eqn. 3.7 an Eqn S igure 4. The eformation of iniviual panel V igure 5. The stress-strain relationship of the woo x x x x igure 6. Stress transformation of compressive brace S S W x ( ) E sin W S W ( ) E cos W S W x ( ) E sin cos W W t W t S W x ( ) E sin cos W W t W t S W ( ) E cos W (3.4) (3.5) (3.6) P (3.7) P (3.8) V

4 3. The isplacement of the panel cause b the compressive eformation of the beam As the panel rocks uner in-plane loaing, it will act compressive force to the beam an cause the beam to have compressive eformation. ig.7. shows the aitional isplacement R of the panel cause b the compressive eformation of the beam. In the compressive area of the beam, the eformation istribution assumption is illustrate in ig.8. The compressive eformation ecreases linearl from ege corner to the panel center, an the maximum eformation B on the beam ege corner can be formulate as Eqn W R B (3.9) R W compressive area cos (, ) ( B, B) elastic area inelastic area compressive area W / igure 7. The isplacement cause b the compressive eformation of the beam The compressive stress an eformation of the beam are relate to both the imension of the beam an the fillister(ig. 9.). or estimating the compressive force an eformation of the beam, the strength (ig. 10.) of the unit length of the beam is assume that the stress on the surface of the fillister is equal to the compression strength perpenicular to the grain. The strength BU is epene on the situation when the average stress of the beam reaches the strength perpenicular to the grain. Accoring to this assumption, the compression strength an eformation can be obtaine as: BU BU b (3.10) B igure 8. The eformation assumption of the beam B b B b B E 4b (3.11) B B (3.1) B b ( B b) E (3.13) B b illister BU B Wooen beam igure 9. The Cross-sectional etail of the beam B BU igure 10. The force-eformation relationship of the unit length of the beam

5 Then, the final expressions of compressive force following: or or Bc B 1 W B B W 8 1 W Bc R R Because the compressive force compressive brace, the relationship between BU R Bc B E ( B b) 4b of rocking panel in the range is given as BU W R BU Bc of rocking panel is the reacting force of vertical force V (3.14) (3.15) P of the Bc an P V can be got b Eqn P (3.16) V Bc 3.3 The contribution of bamboo nails rom the moment balance of the panel, as shown in ig.11., the resisting contribution of bamboo nails can be obtaine b Eqn urther, from ig.1, the relationship between the isplacement of the panel an shear eformation of the bamboo nails can be generate. The shear eformation of the bamboo nails is equal to W tan. or the angle is ver small, we can replace tan with sin an get the Eqn W P (3.17) W W tan W sin (3.18) :the owel force per bamboo nail :the number of bamboo nails In-plane loaing P Wtan W Shear force igure 11. or the owel action of bamboo nail, Chang(007) conucte a ouble shear test for the bamboo nails (ig.13). Accoring to this test, the owel force can be simplifie as following: The shear force of bamboo nails 41.6 A 318. A kgf kgf igure cm 1.3cm 4cm The shear eformation of bamboo nails (3.19)

6 isplacement 1.3cm Shear stress 318.kgf/cm igure 13. Loaing isplacement relation of bamboo nail(chang,007) igure 14. The stress-isplacement relationship of bamboo nail aopte for analsis 4. TE COMPRESSSIVE BRACE MOEL O TE WOOE WALL ig.15 shows the loa an eformation of the wooen wall. The compressive force an eformation of the compressive brace can be written with P an b using Eqn. 4.1 an Eqn.4.. ere is the angle from iagonal line to vertical line. sin (4.1) P P (4.) sin P igure 15. The force an eformation relationship between wall an compressive brace After getting the loaing-isplacement relationship of the wooen wall, the performance stages of the wall can be efine further. ig.16 is the aopte loaing-isplacement curve of the compressive brace. This curve was efine b three amage behavior of the wall, which are (1) The maximum compressive stress B of the beam reaches the strength, an the loaing an eformation of the brace is efine as P an. Accoring to the stiffness of the compressive brace at first stage, the effective with W of the compressive brace can be efine as P Ww P L W (4.3) t E sin t E sin L W w Ww (4.4) E// E E (4.5) E// sin E cos () The bamboo nail reaches ultimate shear strength an the wall usuall performs the ultimate strength P u at the same time. (3) The maximum compressive stress B of the beam reaches the strength BU, an the eformation

7 of the brace is efine as b. Then, as shown in ig.17, four plastic hinge properties of the compressive brace coul be set for nonlinear analsis. B, P ) ( u, P ) ( u b C( 0.( b ), PC ) E 1.5 b, P ) ( E igure 16. The aopte loaing-isplacement relationship curve of the moeling compressive brace P / P, S ( u Pu Pu, ) P P 1 C( B(0,1) b PC PC, ) P P 1.5 E( b PE PE, ) P P A igure 17. The plastic hinge properties setting of the moeling compressive brace 5. SEISMIC ASSESSMET APPLICATIO, S The bracing moel evelope for the traitional wooen wall has been practice in the seismic assessment of Yan-shuei Octagonal all which is a registere heritage architecture of Tainan Cit. The all is two-stores wooen builing. ig.18, ig.19 an ig.0 show the construction arrangement of wooen panel wall. / Estimate wooen rame igure 18. The first floor plan of Yanshuei Octagonal ispla all (Chang,004)

8 igure 19. The partition wall on 1 st floor plan igure 0. The partition wall on n floor plan 5.1 The analsis moel of the wooen frame Table 5.1 lists the material properties of woo an bamboo nail use in the seismic assessment. ig.1 is the analsis moel of the wooen frame. In the moel, the equivalent compressive bracing of wooen panel walls were given corresponing axial force plastic hinge setting. Besies, all beam-column joints also has been assigne with ifferent moment plastic hinge b the metho given in the reference (Chang et.al,011). Table 5.1 The material propert The ensit of the woo 0.43 MOE parallel to woo grain kgf/cm Compressive strength parallel to woo grain 10 kgf/cm MOE perpenicular to woo grain 800 kgf/cm Compressive strength perpenicular to woo grain 40 kgf/cm The shear stiffness of the bamboo nail(chang,007) kgf/cm Release moment W1 W3 W4 W5 W6 moment plastic hinge axial force plastic hinge W8 W W7 5. The pushover analsis result an iscussion 5..1 The amage moe igure 1. Analsis moel of the wooen frame ig. is the istribution of plastic hinges as rift angle of the roof reache The circle plastic hinges of the member excees the ultimate strength ( stage ). Uner the in-plane push loa, the joints in the porch area amage first, an then the wooen wall brace in the porch area exceee the ultimate strength. The main wooen wall in the first floor amage until the rift angle of the builing

9 reache 16.65%, which is much later than the amage of beam-column joint. Obviousl, uring earthquake excitation, this wooen panel wall will help avoiing the builing collapse, even the woo frame has performe consierable large eformation. This phenomena also has been observe ver often in the 1999 Chi-Chi earthquake. 7.(5.18ton,15.97%) 4.(6.40ton,11.79%).(6.04ton,9.6 5.(6.64ton, (6.64ton,1.98 %) East sie 1.(5.6ton,8.14%) 1.(5.6ton,8.14.(6.04ton,9.6%) 6.(6.56ton,14.37%) West sie 3.(6.51ton, (5.16ton, iscussion igure. The amage moe of the frame when the rift angle on the roof reach ig.3 shows the comparison of the wooen panel walls uner in-plane loaing. The ultimate resistant loaing an the stiffness of the frame with wooen panel wall is much higher than that without wooen panel wall. The ultimate resistant loaing of the frame with wooen panel wall is 1.74 times of the pure frame. This result explains that the wooen panel wall is inee an important element to resist the seismic loaing an nees to be consiere in the seismic assessment of traitional wooen builing. Besies, as shown in ig.4, the store stiffness of the secon floor is higher than that of the first floor. At maximum loa, the store rift angle of secon floor is onl 83% of the first floor. This is because some seconar wooen beams an columns are arrange in the wooen wall of secon floor. The wall is ivie into four small parts(w1~w4), an for each part(w1~w4), the height/with ratio becomes smaller. This result also means that changing the construction of the wall, especiall reuce height/with ratio of the panel, can effectivel improve the stiffness of the traitional wooen frame. igure 3. The contribution of the wooen panel wall

10 igure 4. The comparison of the rift angle of ifferent store 6. COCLUSIOS In this stu, the panel wall use to infill the wooen frame of traitional builing is moele as an equivalent compressive bracing, which is base upon the etail behavior of unit panel. The plastic hinge properties of the bracing are efine for nonlinear analsis, which is relate to the compressive amage of the wooen beam an the owel action of bamboo nails. The evelope bracing moel has been use in the seismic assessment of Yan-shuei Octagonal all in Tainan Cit. The analsis shows the panel walls will increase the structure stiffness an the ultimate resistant loa. In aition, the panel wall is helpful to avoi the frame totall collapse after the beam-column joints of the frame has suffere seriousl amage. This phenomena also has been observe ver often in the 1999 Chi-Chi earthquake. REERECES 1. Wang S.Y. (1993). Woo phsics (in Chinese). ational Institute of Compilation an Translation, Taipei,. Chang J.S., Chen T.., Shih C.., Lin Y.C. (011), The Seismic Assessment Report of The Yanshuei Octagonal all, ational Cheng Kung Universit, Tainan Cit, Taiwan 3. Chang W.S., Komatsu K., su M.., Chen W.J.(007).On mechanical behavior of traitional timber shear wall in Taiwan II: simplifie calculation an experimental verification, Journal of Woo Science, 53, ankinson R.L. (191).Investigation of crushing strength of spruce at varing angles of grain, Air Service Information Circular, o.3(59), Material Section Report o Svante W.(004).Stress-Strain Relationships for Spruce Woo: Influence of Strain Rate, Moisture Content an Loaing irection, Societ for Experimental Mechanics, 44:1,44-48