Structural Analyss of Hstorcal Constructons Jerzy Jaseńko (ed) 01 DWE, Wrocław, Poland, ISSN 0860-395, ISBN 978-83-715-16-7 MECeANfCA ANAYSfS clo efstlofca MASlNoY tas SToENdTeENEa BY oefnclocea ClNCoETE AYEo ANa STEE coames Ouyang Y 1, Wang R, Yang X 3, Lu N K 4, Gu X L 5 ABSToACT Shangha s famous for ts cultural dversty, and there are a large number of hstorcal buldngs whch are expected to be preserved safely In order to study the mechancal performance and carry out safety assessment of strengthened hstorcal masonry walls, a theoretcal model, whch s based on the elastcty, was establshed n order to analyse the mechancal behavour of hstorcal masonry walls strengthened wth a steel frames and nner renforced concrete walls Under a concentrated load, a trangularly dstrbuted load, a unformly dstrbuted load, and the gravty load due to the base nclnaton, the bendng deformaton of a strengthened hstorcal masonry wall wth/wthout steel frame were nvestgated respectvely wth the actual materal parameters n an exstng hstorcal buldng It was proved that the proposed model was aduately accurate and effcent Keywords: Mechancal analyss, Hstorcal buldng, Masonry wall, Strengthenng N fntolarctfln The Andrews & George buldng, havng one hundred years hstory, s located n the Bund of Shangha It s a 3 story brck-wood structure havng rectangular plane wth length of 394 m, wdth of 10 m and heght of 15 m The façade of the buldng s preserved for ts unque archtectural style Accordng to n-stu tests and nspecton, the strength of brcks s 91 N/mm, that the strength of the mortar s about 053 N/mm, and there s no rng beams and structural columns n the buldng, whch results n the poor ntegrty The obvous damages and many vertcal cracks have been found on masonry walls For the purpose conservaton, the buldng needs to be retroftted Accordng to the retrofttng plan, the masonry walls of two facades of the buldng should be preserved and the others wll be demolshed, whch s shown n Fg 1 At the same tme, a new offce buldng wth a heght of 60 m, ncludng 14 stores above the ground and 1 story underground, wll be constructed, and the preserved masonry walls wll be connected wth the new buldng as ts enclosure walls Because the nner support members (nner walls and floor slabs) of the preserved masonry walls wll be removed, the free length of the walls wll ncrease, whch s about 15 m, and the stablty of the walls wll decrease Therefore, there s a possblty that the preserved masonry walls may be laterally collapsed, and t should be strengthened 1 Assocate Professor, Department of Cvl Engneerng, Shangha Unversty, 149 Yanchang Road, Shangha 0007, Chna, oyy_wly@snacom Post-graduate student, Department of Cvl Engneerng, Shangha Unversty, 149 Yanchang Road, Shangha 0007, Chna, 540780789@qqcom 3 Professor, Department of Cvl Engneerng, Shangha Unversty, 149 Yanchang Road, Shangha 0007,Chna, xyang@shueducn 4 Engneer, Shangha Tongru Cvl Engneerng Co Ltd, 1398 Spng Road, Room 80 of Tower B, Shangha 0009, Chna, vclunengke@163com 5 Professor, College of Cvl Engneerng, Tongj Unversty, 139 Spng Road, Shangha 0009, Chna, gxl@tongjeducn 1888
cg N Schematc dagram of the plane locaton of the preserved masonry walls Based on the comparatve analyss, the preserved masonry walls wll be strengthened wth nner renforced concrete walls and supportng steel frames The masonry walls and the renforced concrete walls are connected wth bndng steel bars, and the structural columns n renforced concrete walls wll be connected the supportng steel frames In order to understand the mechancal behavor of the strengthened composte system, a masonry wall strengthened wth a renforced concrete wall was analyzed frst, and then the analyss for the system of a masonry wall strengthened wth a renforced concrete wall and a steel frame was carred out accordngly O MECeANfCA ANAYSfS lc A MASlNoY ta SToENdTeENEa tfte A oefnclocea ClNCoETE ta ON cundamental cormula There s a masonry wall wth the heght L, the thckness h I and the elastc modulus E I, subjected to the load q(x) In order to ncrease the safety of the masonry wall, a renforced concrete wall wth the thckness h and the elastc modulus E s used to strengthen the masonry wall, and the bndng steel bars are employed to connect the two walls to form a complete connected composte wall To analyze the deformaton and the stress dstrbuton of the composte wall under load q(x), a model s establsed n Fg, n whch b uals 1 m Furthermore, followng assumptons are made o cg O Geometrc parameters of the composte wall 1) The masonry wall and the renforced concrete wall are elastc, and ther deformaton are nfntesmal 1889
) The bndng steel bars have enough stffness and strength, such that there s no slp at the nterfcace between the masonry wall and the renforced concrete wall, and the composte beam satsfes the plane deformaton assumpaton, e, the composte beam satsfes the deformaton hypothess of the classcal composte beam [1, ] It s denoted that the area and the nerta moment of the masonry wall I are A I and I I, respectvely, and the dstance from the rght sde of the masonry wall I to ts centrod s r I And t s also denoted that the area and the nerta moment of the renforced concrete wall are A and I, respectvely, and the dstance from the left sde of the renforced concrete wall to ts centrod s r The dstance between the neutral axs of the cross secton of the composte wall and the nterface of the masonry and the renforced concrete walls a set to be d, and the neutral axs s assumed to be located n the nteror of the masonry wall I Establshng a coordnate system oxyz wth the neutral axs to be oz and the axal drecton of the composte beam to be ox, and denotng the deflecton of the composte wall to be w(x), the vertcal dsplacement u I (x) of the masonry wall I and the vertcal dsplacement u (x) of renforced concrete wall can be expressed as follows, respectvely, based on the assumpton of a composte beam ì dw u( x) =-y, - h + d < y< d í dw u( x) =- y d < y < h + d î (1) and the stress on the cross secton of the composte beam s ì dw s = Ee =-Ey, - h + d < y < d í dw s = Ee =- E y d < y< d + h î () Therefore, the axal force on the cross secton of the compose beam s ò As [ ] ò A s (3) F = da + da =- E A d - r + E A d + r N Snce there s no axal force, e, F N = 0, t gves dw d = EAr-E Ar EA+ EA (4) And the bendng moment on the cross secton can be expressed as dw ò As ò A s (5) M = yda + yda =- EI where, (EI) s the uvalent bendng stffness of the composte beam, and ( EI) = E I + E I + ( r + r ) E AE A I EA + EA (6) Thus, the normal stresses on the cross secton s s EM = y, s = y (7) 1890 EM
And the correspondng narmal stran s The ulbrum uaton of the composte wall s M M e = y, e = y (8) ( EI) 4 d w 4 q = (9) It can be determned gvng the approprate boudnary condtons, and the shear force on the cross secton of the composte beam s 3 dm S ( EI dw F = ) e q 3 =- (10) cg P Shear stress of the composte beam From Fg 3, t s easy to express the shear stress at the nterface of the masonry wall I and the renforced concrete wall as and the shear force on the unt wtdth s ( + ) 1 ds E A r d t = = da FN bò (11) A EI b E A ( r + d) = = (1) T tb FS and the normal stress px at the nterface of the masonry wall I and the renforced concrete wall s where, (- + ) d d d æeiah I I ri d ö px =- b FS qx ò t = = g (13) hi+ d ç EI è ø g = E Ah r - d [ EI b] s a reducton coeffcent I I I I OO Mechancal analyss The bendng behavor of the composte wall subjected to a concentrated force, a trangularly dstrbuted load, a unformly dstrbuted load and the gravty load due to the base nclnaton, respectvely, wll be nvestgate Now the load combnaton s x q( x) = qw0 + qg + qu (14) L 1891
where, q = ( g A + g A)sna, and g g and g are specfc gravty of the masonry wall I and the renforced concrete wall, respectvely Therefore, the boundary value problem can be expressed as ì (4) x ( EI) w = q( x) = q u + qg + qw0, L íw= 0, w = 0, x = 0 M =- ( EI) w = 0, FN =- ( EI) w = P x = L î (15) The soluton the above boundary value problem s q + q q w( x) x ( x 6L 4Lx) x 0L 10L x x 4 EI 10 EI L ( - ) g u w0 3 3 = + - + - + + 6 P x L x 3 (16) Due to the base nclnaton, the fnal deflecton of the composte wall can be modfed as W( x) = w( x) + Lsn a (17) OP Numercal results Now let the heght of the masonry wall be L=15 m, thckness be h I = 510 mm, and thckness of the renforced concrete wall be h = 10 mm, respectvely, and the elastc modulus of the masonry wall be E I = 778 MPa, specfc gravty be γ I = 17000 N/m 3, and the elastc modulus of the concrete wall be E = 3 10 4 MPa, and the specfc gravty be γ = 5000 N/m 3 The followng four calculaton cases as shown n Fg 4 wll be consdered 1) Case I: P = 6kN; ) Case : q w = 08x/L kn/m; 3) Case I: tltng angle α = 4 ; 4) Case IV: q u = 08 kn/m a) Case I b) Case c) Case I d) Case IV cg 4 Schematc dagram of the load modes The deflecton dstrbutons along the wall heght for four loadng cases are shown n the Fg 5 It can be seen that the deflecton of the composte wall wthout the constrant of the steel frame s relatvely large, especally for the load case I Although the load case I may not occur n realty, t s helpful for us to understand the mechancal behavor of the composte wall Fg 6 shows the dstrbutons of the shear force along the wall heght under the four loadng cases It can be seen that the shear force wll ncrease as the loacton approachng to the base of the wall, whch 189
can be used to determne the locatons of the bndng steel bars The maxmum normal stresses of the masonry wall, the normal stresses of the renforced concrete wall at the nterface of the two walls and the maxmum normal compressve stresses of the the renforced concrete wall are shown n Fg 7, Fg 8 and Fg 9, respectvely cg R Deflecton of the composte wall cg S Shear force on the nterface wth unt wdth cg T The maxmum normal stresses of the masonry wall cg U The normal stresses of the renforced concrete wall at the nterface of the two walls cg 9 The maxmum normal compressve stresses of the the renforced concrete wall P MECeANfCA ANAYSfS lc SToENdTeENEa MASlNoY ta tfte SrmmloTfNd STEE coame PN cundamental formula Dvde the system of a masonry wall strengthened wth a renforced concrete wall and a supportng steel frame nto the sub-structure I and substructure as shown n Fg 10, and denote the nteracton forces between the two sub-structures at the nodes to be F ( = 1,,3,,8) and the correspondng horzontal dsplacements to be u ( = 1,,3,,8) (Fg 11 and Fg 1) From Fg 1, t s easy to obtan the relatonshp between the forces F ( = 1,,3,,8) and the dsplacement u ( = 1,,3,,8), whch can be expressed as [3] 1893
S where, éëk ùû { F} ék S ù{ u} = ë û (18) F = F, F, F, F, F, F, F, F, and s the stffness matrx of the steel frame, { } { }T {} u { u, u, u, u, u, u, u, u } T = 1 3 4 5 6 7 8 1 3 4 5 6 7 8 cg NM Geometrc parameters cg NN Sub-structure I cg NO Sub-structure of the composte wall and the steel frame From Fg 11, t can be obtaned that the horzontal dsplacement of the composte wall subjected to the concentrated forces F ( = 1,,3, L,8) s F ì - ³ w( xf, ) = í 6 L (3 x L) x L î x (3 L x), x L - > (19) Therefore, the fnal dsplacement of the composte wall s wth the constrant wx = w( x) - w( xf, ) 0 q 8 å = 1 8 g = x x + 6L-4 Lx - w( xf, ) + 4 = 1 qw0 3 3 P x ( 0L - 10L x+ x ) + x ( 3 L-x) 10 EI L 6 EI å (0) T { u u u u u u u u} { wl wl wl wl wl wl wl wl },,,,,,, =,,,,,,,, (1) 1 3 4 5 6 7 8 1 3 4 5 6 7 8 t yelds T L - 1 S -1 F { } = ( é ù + é ù) { } F ë K û ë û w 0 () w = w ( L), w ( L ), w ( L ), w( L ), wv( L ), w ( L ), w ( L ), w ( L ) where, { } { } T 0 0 1 0 0 3 4 5 0 6 0 7 0 8 When the force { } F s determned, the response of the composte wall can be obtaned wth the Eq (0) 1894
PO Numercal results Take the geometry and materal parameters of the masonry wall and the renforced concrete wall as that stated n the preceedng secton, and assume that the chord members of the steel frame are I-steel wth the secton dmenson of 00 mm 180 mm 55 mm 8 mm, the web members are crucform cross secton steel wth L70 5, and the elastc modulus of steel members s 06 10 5 Mpa cg NP The deflecton of the structural system The deflecton dstrbutons along the wall heght of the structural system under the four loadng cases are shown n Fg13 It can be seen that the deflectons of the composte wall wth the constrant of the steel frame for all four loadng cases are remarkably decreased compared wth those of the masonry wall strengthened wth the renforced concrete wall only cg N4 The shear force on the nterface cg NR The maxmum normal stresses of the masonry wall cg NS The normal stresses of the renforced concrete wall at the nterface of the two walls cg NT The maxmum normal compressve stresses of the the renforced concrete wall Fg 14 shows the shear force dstrbutons along the wall heght under the four loadng cases The maxmum normal stresses of the masonry wall, the normal stresses of the renforced concrete wall at the nterface of the two walls, and the maxmum normal compressve stresses of the the renforced concrete wall are shown n Fg 15, Fg 16 and Fg 17, respectvely 1895
4 ClNCrSflNS In ths paper, the mechancal analyss of a masonry wall strengthened wth a renforced concrete wall was frst conducted, and then, a masonry wall strengthened wth a renforced concrete wall and a supportng steel frame was analyzed The elementary mechancal behavor of the strengthened masonry wall was understood, and the deflectons and stresses of the strengthened masonry wall was examned It wass shown from the numercal results that the deflectons and stresses of the masonry wall strengthened wth a renforced concrete wall and a supportng steel frame were much less than those of the masonry wall only strengthened wth a renforced concrete wall The analyss model presented n ths paper was based on the elastcty, whch may mot concde wth real stuaton However, the results obtaned can be used to predct the change trend of the mechancal performances of the strengthened wall qualtatvely, whch wll provde the gudance for the retoft desgn oeceoences [1] Gere JM, Tmoshenko SP (1984) Mechancs of Materals [M] Second SI Edton Van Nostrand Renhold, New York [] Reddy JN (1993) An evaluaton of uvalent-sngle-layer and layerwse theores of composte lamnates[j] Composte Structures 1993, 5(1-4): 1-35 [3] Hulse R, Can Jack (000) Structural Mechancs [M] Second Edton Palgrave Macmllan, New York 1896