Masonry Design. = calculated compressive stress in masonry f. = masonry design compressive stress f

Transcription

1 ARCH 631 Note Set 3.1 F01n Monry Deign Nottion: A = ne or re A n = net re, equl to the gro re utrcting ny reinorceent A nv = net her re o onry A = re o teel reinorceent in onry deign A t = re o teel reinorceent in onry colun deign A v = re o concrete her tirrup reinorceent ACI = Aericn Concrete Intitute ASCE = Aericn Society o Civil Engineer = width, oten cro-ectionl = totl width o teril t horizontl ection C = copreion orce in the onry or onry deign CMU = horthnd or concrete onry unit d = eective depth ro the top o reinorced onry e to the centroid o the tenile teel D = horthnd or ded lod e = eccentric ditnce o ppliction o orce (P) ro the centroid o cro ection E = horthnd or erthquke lod E = odulu o elticity o onry E = odulu o elticity o teel = xil tre = ending tre = clculted copreive tre in onry = onry deign copreive tre = tre in the teel reinorceent or onry deign v = her tre F = llowle xil tre F = llowle ending tre F = llowle tenile tre in reinorceent or onry deign F t = llowle tenile tre F v = llowle her tre F v = llowle her tre o the onry 1 F v = llowle her tre o the her reinorceent h = ne or height = eective height o wll or colun I n = oent o inerti o the net ection j = ultiplier y eective depth o onry ection or oent r, jd k = ultiplier y eective depth o onry ection or neutrl xi, kd K = type o onry ortr L = horthnd or live lod M = internl ending oent = type o onry ortr M = oent cpcity o reinorced onry e governed y teel tre M = oent cpcity o reinorced onry e governed y onry tre MSJC = Monry Structurl Joint Council n = odulu o elticity trnortion coeicient or teel to onry n.. = horthnd or neutrl xi (N.A.) N = type o onry ortr NCMA = Ntionl Concrete Monry Aocition O = type o onry ortr P = ne or xil orce vector P = llowle xil lod in colun P e = criticl (Euler) uckling lod Q = irt re oent out neutrl xi r = rdiu o gyrtion = pcing o tirrup in reinorced onry S = type o onry ortr = ection odulu t = ne or thickne T = tenion orce in the teel reinorceent or onry deign TMS = The Monry Society V = internl her orce W = horthnd or wind lod

2 ARCH 631 Note Set 3.1 F01n β 1 ε ε = coeicient or deterining tre lock height, c, in onry LRFD deign = trin in the onry = trin in the teel ρ ρ Σ = reinorceent rtio in onry deign = lnced reinorceent rtio in onry deign = ution yol Monry Deign Structurl deign tndrd or reinorced onry re etlihed y the Monry Stndrd Joint Coittee coniting o ACI, ASCE nd The Monry Society (TMS), nd preent llowle tre deign well liit tte (trength) deign. Mteril Monry ortr re ixture o wter, onry ceent, lie, nd nd. The trength re ctegorized y letter deigntion (ro MSoNwOrK). = onry pri tet copreive trength Deigntion trength rnge M 500 pi S 1800 pi N 750 pi O 350 pi K 75 pi Deored reinorcing r coe in grde 40, 50 & 60 (or 40 ki, 50 ki nd 60 ki yield trength). Size re given noinlly # o 1/8. Cly nd concrete onry unit re porou, nd their durility with repect to wethering i n iportnt conidertion. The ount o wter in the ortr i iportnt well the orption cpcity o the unit or good ond; oth or trength nd or wetherprooing. Becue o the oiture nd tendency or hrinkge nd welling, it i criticl to provide control joint or expnion nd contrction. Monry Wll Monry wll cn e reinorced or unreinorced, grouted or ungrouted, ingle wythe or cvity, pretreed or not. Cvity wll will require tie to orce the two wll eprted y the cvity to ct one. Fro centurie o prctice, the height to thickne rtio i liited ecue o lenderne (h/t < 5 or 35 depending on code). Mot wll will ee ending ro wind or eccentricity long with ering (coined tree).

3 ARCH 631 Note Set 3.1 F01n Allowle Stree I tenion tree reult, the llowle tenile trength or unreinorced wll ut not e exceeded. Thee re reltively low (40 70 pi) nd re hown in Tle..3.. I copreion tree reult, the llowle trength (in ending) or unreinorced onry F =1/3 I copreion tree reult, the llowle trength (in ending) or reinorced onry F =0.45 Sher tre in unreinorced onry cnnot exceed F v = pi. Sher tre in reinorced onry or M/(Vd) 0.5 cnnot exceed F v = 3.0 Sher tre in reinorced onry or M/(Vd) 1.0 cnnot exceed F v =.0 Allowle tenile tre, F, in grde 40 & 50 teel i 0 ki, grde 60 i 3 ki, nd wire joint reinorceent i 30 ki.. where = peciied copreive trength o onry (F t ) (PCL) (F t ) Lod on Lintel in Monry Wll Arching ction i preent in onry wll when there i n opening nd uicient wll width on either ide o the opening to reit the rch thrut. A lintel i required to upport the weight o the wll teril ove the opening. When rching ction i preent, the weight tht ut e upported cn e deterined ro 45 degree ngle. Thi re y e tringle, or trpezoid i the wll height ove the lintel i le thn hl the opening width. The ditriuted lod i clculted height x wll thickne x peciic weight o the onry. 3

4 ARCH 631 Note Set 3.1 F01n When there re concentrted lod on the wll, the lod cn e ditriuted to width t the lintel height ed on 60 degree ngle. Reinorced Monry Meer For tre nlyi in onry lexurl eer the trin i liner the copreive tre in the onry i liner the tenile tre in the teel i not t yield ny onry in tenion i ued to hve no trength the teel cn e in tenion, nd i plced in the otto o e tht h poitive ending oent Lod Cointion D D+L D (L r or S or R) D L (L r or S or R) D + (0.6W or 0.7E) D L (0.6W) (L r or S or R) D L (0.6W) (L r or S or R) 0.6D + 0.6W 0.6D + 0.7E Internl Equiliriu C = copreion in onry = tre x re = t d grout unit BIA Teknote17 erie (kd) n.. A kd ε ρ = STRAIN A d ε /n STRESS ΣF=0: T =A C = (kd)/ jd A = M kd T = tenion in teel = tre x re = A C = T nd M = T (d-kd/3) = T (jd) nd M =C (jd) 4

5 ARCH 631 Note Set 3.1 F01n where = tre in ortr t extree ier kd = height to neutrl xi = width o ection = tre in teel t d A = re o teel reinorceent d = depth to n.. o reinorceent j = (1 k/3) For lexure deign: M M or M o, M =T(jd) = 0.5 d jk nd M = C(jd) = ρd j The deign i dequte when F in the onry nd F in the teel. Sher Strength Sher tre i deterined y v = V/A nv where A nv i net her re. Sher trength i deterined ro the her cpcity o the onry nd the tirrup: F v = F v + F v. Stirrup pcing re liited to d/ ut not to exceed 48 in. where: 1 M P Fv = where M/(Vd) i poitive nd cnnot exceed 1.0 Vd Av Fd (F Fv = 0. 5 v = 3.0 when M/(Vd) 0.5 ) v (F v =.0 when M(Vd) 1.0.) Vlue cn e linerly interpolted. Reinorceent Rtio The ount o teel reinorceent i liited. Too uch reinorceent, or over-reinorced will not llow the teel to yield eore the concrete cruhe nd there i udden ilure. A e with the proper ount o teel to llow it to yield t ilure i id to e under reinorced. A The reinorceent rtio i rction: ρ = nd ut e le thn ρ where the lnced d reinorceent rtio i unction o teel trength nd onry trength. 5

6 ARCH 631 Note Set 3.1 F01n Flexure Deign o Reinorceent One ethod i to chooe reinorceent rtio, ind teel re, check tree nd oent: 1. ind ρ nd ue vlue o ρ < ρ M. ind k, j nd clculte d = where F i llowed tre in teel. ρjf Chooe nice & d vlue. M 3. ind A = F jd 3. check deign or M < M = AF (jd) M 4. check onry lexurl tre gint llowle: = < F 0.5d jk Lod nd Reitnce Fctor Deign The deign ethodology i iilr to reinorced concrete ultite trength deign. It i ueul with high her vlue nd or eiic deign. The liiting onry trength i Force-Moent Interction β 1 c 0.80 β 1 c T C Coined tree nd the reduction o xil lod with oent i iilr to tht or reinorced concrete colun deign hown in the interction digr: Reinorceent i typiclly plced in the center o wll. Grouting i plced in hollow with reinorcing, while other hollow y e epty. Stirrup re voided. Bixil ending cn occur in colun nd tree ut tiy: + 1 F F When xiu oent occur oewhere other thn t the end o the colun or wll, virtul eccentricity cn e deterined ro e = M/P. 6

7 ARCH 631 Note Set 3.1 F01n Monry Colun Colun re cliied hving /t < 3 nd h/t > 4. Slender colun hve iniu ide dienion o 8 nd ut hve h/t 5. They ut e deigned with n eccentricity o 10% o the ide dienion, nd tiy the interction reltionhip o + 1, the tenile tre F F cnnot exceed the llowle: reinorced onry: F nd the copreive tre exceed llowle or t + F provided F. For purely xil loding, the cpcity P depend on the lenderne rtio o h/r: unreinorced h P [ = 0. 5 ] 1 or h/r r reinorced 70r P [ 0 5 =. ] or h/r > 99 h h P [ = At F ] 1 or h/r r 70r P [ 0 5 = At F ] or h/r > 99 h where h = eective length r = let rdiu o gyrtion A n = net re o onry A t = re o teel reinorceent = peciied onry copreive trength F = llowed copreive trength o reinorceent The let rdiu o gyrtion cn e ound with : 3 d 1 r = = = d 1 1 I A or rectngle with ide dienion o & d where i the ller o the two ide dienion. 7