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1、4.1 INVESTIGATION OF STRUCTURAL BEHAVIORInvestigating how structures behave is an important part of structural design: it provides a basis for ensuring the adequacy and safety of a design, In this section I discuss structural investigation in general. As I do throughout this book. I focus on materia
2、l relevant to structural design tasks. Purpose of Investigation Most strructturees eexisst bbecaausee thhey aree neeedeed. Anyy evvaluuatiion of a sstruuctuure thuus mmustt beeginn wiith an anaalyssis of howw efffecctivvelyy thhe sstruuctuure meeets thee ussagee reequiiremmentts. Desiggnerrs mmustt
3、coonsiiderr thhe ffolllowiing thrree facctorrs: l Functtionnaliity. orr thhe ggeneerall phhysiicall reelattionnshiips of thee sttruccturress foorm. deetaiil. durrabiilitty. firre rresiistaancee. ddefoormaatioon rresiistaancee. aand so on. l Feasiibillityy. iinclludiing cosst. avaailaabillityy off ma
4、aterrialls aand prooductts. andd prractticaalitty oof cconsstruuctiion. l Safetty. or cappaciity 10 ressistt annticcipaatedd looadss. Meanss An innvesstiggatiion of a ffullly ddefiinedd sttruccturre iinvoolvees tthe folllowwingg: 1. Deterrminne tthe strructturees phyysiccal beiing-matteriialss, ffor
5、mm, sscalle. oriienttatiion. loocattionn. ssuppportt coondiitioons, annd iinteernaal ccharractter andd deetaiil. 2. Deterrminne tthe demmandds pplacced on thee sttruccturre-tthatt iss. lloadds. 3. Deterrminne tthe strructturees defformmatiion limmitss. 4. Deterrminne tthe strructturees loaad rresppo
6、nsse-hhow it hanndlees iinteernaal fforcces andd sttresssess annd ssignnifiicannt ddefoormaatioons. 5. Evaluuatee whhethher thee sttruccturre ccan saffelyy haandlle tthe requiiredd sttruccturral tassks. Invesstiggatiion mayy taake sevveraal fformms. Youu caan l Visuaalizze ggrapphiccallly tthe strru
7、ctturees defformmatiion undder loaad. l Manippulaate matthemmatiicall moodells. l Test thee sttruccturre oor aa sccaleed mmodeel, meeasuurinng iits ressponnsess too looadss. When preecisse qquanntittatiive evaaluaatioons aree reequiiredd. uuse matthematticaal mmodeels bassed on relliabble theeoriies
8、 or dirrecttly meaasurre pphyssicaal rrespponsses. Orrdinnariily. maatheematticaal mmodeelinng ppreccedees aany acttuall coonsttrucctioon-eevenn off a tesst mmodeel. Limmit dirrectt meeasurremeenttto eexpeerimmenttal stuudiees oor tto vveriifyiing unttestted theeoriies or dessignn meethoods. Visuaal
9、 AAidss In thhis boook, I eemphhasiize graaphiicall viisuaalizzatiion; skketcchess arrc iinvaaluaablee leearnningg annd pprobblemm-soolviing aidds. Thrree typpes of graaphiics aree moost useefull: tthe freee-bbodyy diiagrram. thhe eexagggerrateed pproffilee off a loaad-ddefoormeed sstruuctuure. annd
10、 tthe scaaledd piial. A freee-bbodyy diiagrram commbinnes a ppictturee off ann issolaatedd phhysiicall cllemeen II wiith reppressenttatiionss off alll eexteernaal fforcces. Thhe iisollateed cclemmentt maay bbe aa whholee sttruccturre oor ssomee paart of it. For eexammplee. FFiguure 4.11a shhowss ann
11、 enntirre sstruuctuure-a bbeammandd-eoolummn rrigiid bbentt-annd tthe extternnal forrcess (rreprreseenteed bby aarroows). wwhicch iinclludee grraviity. wiind. annd tthe reaactiive ressisttancce oof tthe suppporrts (caalleed tthe reaactiionss). Notte: Succh aa foorcee syysteem hholdds tthe strructtur
12、ee inn sttatiic eequiilibbriuum. Figurre 44.lbb is a ffreee-boody diaagraam oof aa siinglle bbeamm frrom thee beent. Opperaatinng oon tthe beaam aare twoo foorcees: itss owwn wweigght andd thhe iinteeracctioon bbetwweenn thhe bbeamm ennds andd thhe ccoluumnss 100 whhichh thhe bbeamm iss alll aacheed
13、. Theese intteraactiionss arre nnot vissiblle iin tthe Ireeeboddy ddiaggramm off thhe wwholle bbentt. sso oone purrposse oof tthe diaagraam ffor thee beeam is to illlusttratte tthesse iinteeracctioons. Foor eexammplee. nnotee thhat thee coolummns traansmmit to theeenddsoffthee beeamss hoorizzonttal
14、andd veertiicall foorcees aas wwelll ass rootattionnal benndinng aactiionss. Figurre 44.lcc shhowss ann issolaatedd poortiion oftthe beaam llenggth. illlusstraatinng tthe beaamss innterrnall foorcee acctioons. Opperaatinng oon tthiss frree boddy aarc itss owwn wweigght andd thhe aactiionss off thhe
15、bbeamm seegmeentss onn thhe ooppoositte ssidees oof tthe sliicinng pplannes. siincee itt iss thhesee acctioons thaat hholdd thhe rremoovedd poortiion in plaace in thee whholee beeam. Figurre 44.ldd. aa tiiny seggmennt. or parrticcle. off thhe bbeamm maaterriall iss issolaatedd, iilluustrratiing thee
16、 innterracttionns bbetwweenn thhis parrticcle andd thhosee addjaccentt too itt. TThiss deevicce hhelpps ddesiigneers vissuallizee sttresss: in thiis ccasee. ddue to itss loocattionn inn thhe bbeamm. tthe parrticcle is subbjecctedd too a commbinnatiion of sheear andd liineaar ccomppresssioon sstreess
17、ees. An exxagggeraatedd prrofiile of a lloadd-deeforrmedd sttruccturre hhelpps eestaabliish thee quualiitattivee naaturre oof tthe rellatiionsshipps bbetwweenn foorcee acctioons andd shhapee chhangges. Inndeeed. youu caan iinfeer tthe forrm ddefoormaatioon ffromm thhe ttypee off foorcee orr sttresss
18、. andd viice verrsa. FIGURRE 44.1 Frree-boddy ddiaggramms.For eexammplee. FFiguure 4.laa shoows hee exxagggeraatedd deeforrmattionn off thhe bbentt inn Fiigurre 44.1 undder winnd lloaddingg. NNotee hoow yyou cann deeterrminne tthe natturee off beendiing acttionn inn eaach memmberr off thhe fframme f
19、fromm thhis figguree. FFiguure 4.2bb shhowss thhe nnatuure of defformmatiion of indivviduual parrticcless unnderr vaarioous typpes of strresss. FIGURRE 44.2 SStruuctuurall deeforrmattionnThe sscalled ploot iis aa grraphh off soome matthemmatiicall reelattionnshiip oor rreall daata. Foor eexammplee,
20、tthe graaph in Figguree 4.3 reppressentts tthe forrm oof aa daampeed iibraatioon oof aan eelassticc spprinng. It connsissts of thee pllot of thee diispllaceemennts agaainsst eelappsedd tiime t. andd reepreesennts thee grraphh off thhe eexprresssionn.FIGURRE 44.3 Graaphiicall pllot of a ddampped cycc
21、licc mootioon.Althooughh thhe eequaatioon iis ttechhniccallly ssuffficiientt too deescrribee thhe pphennomeenonn, tthe graaph illlusttrattes manny aaspeectss off thhe rrelaatioonshiip. succh aas tthe ratte oof ddecaay oof tthe dissplaacemmentt. tthe inttervval of thee viibraatioon. thee sppeciificc
22、poosittionn att soome speeciffic elaapseed ttimee. aand so on.4.2 MMETHHODSS OFF INNVESSTIGGATIION ANDD DEESIGGN Tradiitioonall sttruccturral dessignn ceenteeredd onn thhe wworkkingg sttresss mmethhod. a metthodd noow rrefeerreed tto aas sstreess dessignn orr alllowwablle sstreess dessignn (AASD). T
23、Thiss meethood. whiich relliess onn thhe cclasssicc thheorriess off ellasttic behhaviior, meeasuuress a dessignns saffetyy aggainnst twoo liimitts: an acccepttablle mmaxiimumm sttresss (callledd alllowwablle wworkkingg sttresss) andd a tollerablle eexteent of defformmatiion (deefleectiion. sttrettch
24、. errc.). TThesse llimiits reffer to a sstruuctuures rrespponsse tto sservvicee looadss-thhat is. thhe lloadds ccaussed by norrmall ussagee coondiitioons. Thhe sstreengtth mme/hhod, meeanwhiile, meeasuuress a dessignns adeequaacy agaainsst iits abssoluute loaad llimiit-tthatt iss. wwhenn thhe sstruu
25、ctuure musst ffaill. To coonviinciinglly eestaabliish strresss. sstraain. annd ffailluree liimitts, tessts werre pperfformmed exttenssiveely in thee fiieldd (oon rreall sttruccturres) annd llaboorattoriies (onn sppeciimenn prrotootyppes. orr moodells). Noote: Reeal-worrld strructturaal ffaillurees a
26、are stuudieed bbothh foor rreseearcch ssakee annd tto eestaablissh lliabbiliity. In esssennce. thhe wworkkingg sttresss mmethhod connsissts of dessignningg a strructturee too woork at somme eestaabliisheed pperccenttagee off itts ttotaal ccapaacityy. TThe strrenggth metthodd coonsiistss off deesiggn
27、inng aa sttruccturre ttofaail. buut aat aa looad conndittionn weell beyyondd whhat it shoouldd exxperriennce. Cllearrly thee sttresss aand strrenggth metthodds aarc diffferrentt. bbut thee diiffeerennce is mosstlyy prroceedurral.The SStreess Metthodd (AASD) The sstreess metthodd iss ass foolloows: 1
28、. Visuaalizze aand quaantiify thee seerviice (woorkiing) looad conndittionns aas iinteelliigenntlyy ass poossiiblee. YYou cann maake adjjusttmennts by dettermminiing staatissticcallly llikeely loaad ccombbinaatioons (i.e , deead loaad ppluss liive loaad ppluss wiind loaad). coonsiiderringg looad dur
29、ratioon. andd soo onn. 2. Estabblissh sstanndarrd sstreess. sttabiilitty, andd deeforrmattionn liimitts ffor thee vaarioous strructturaal rrespponsses-in tennsioon. benndinng, sheear, buuckllingg. ddefllecttionn, aand so on. 3. Evaluuatee thhe sstruuctuures rrespponsse. An addvanntagge oof wworkking
30、g wiith thee sttresss mmethhod is thaat yyou foccus on thee ussagee coondiitioon (reaal oor aantiicippateed). Thhe pprinncippal dissadvvanttagee coomess frrom youur fforcced dettachhmennt ffromm reeal faiilurre ccondditiionss-moost strructturees ddeveelopp muuch diffferrentt foormss off sttresss aan
31、d strrainn ass thhey appproaach theeir faiilurre llimiits. The SStreengtth MMethhod (LRRFD) The sstreengtth mmethhod is as folllowws: 1. Quanttifyy thhe sservvicee looadss. TThenn muultiiplyy thhem by an adjjusttmennt ffacttor( eesseentiiallly aa saafetty ffacttor) too prroduuce theejacclOrred loaad
32、. 2. Visuaalizze tthe varriouus sstruuctuurall reespoonsees aand quaantiify thee sttruccturress ulltimmatee (mmaxiimumm, ffailluree) rresiistaancee inn appproopriiatee teermss (rresiistaancee too coomprresssionn, bbuckklinng. benndingg. eetc.). Sommetiimess thhis ressisttancce iis ssubjjectt too ann
33、 addjusstmeent facctorr, ccallled theeressisttanccefaacroor. Wheen yyou empployy looad andd reesisstannce facctorrs. thee sttrenngthh meethood iis nnow sommetimmes callledd fooad andd reesisstannceffaaoor ddesiign (LRRFD) (ssee Secctioon 55.9). 3. Compaare thee ussablle rresiistaancee offthee sttruc
34、ctu re to thee u ltiirnaatc ressisttancce rrequuireed (an invvesttigaatioon pprocceduure), oor aa sttruccturre wwithh ann appproopriiatee reesisstannce is proopossed (a dessignn prroceedurre). A majjor reaasonn deesiggnerrs ffavoor tthe strrenggth metthodd iss thhat strructturaal ffailluree iss reel
35、attiveely eassy tto ttestt. WWhatt iss ann appproopriiatee woorkiing conndittionn iss sppecuulattionn. IIn aany eveent, thhe sstreengtth mmethhod whiich wass fiirstt deevellopeed ffor thee deesiggn oof rreinnforrcedd cooncreete strructturees, is noww laargeely preeferrredd inn alll pproffesssionnal
36、desiggn wworkk. Neverrtheelesss, thee cllasssic theeoriies of claastiic bbehaavioor sstilll sservve aas aa baasiss foor vvisuualiizinng hhow strructturees wworkk. BBut ulttimaate ressponnsess ussuallly varry ffromm thhe cclasssicc reespoonsees, beccausse oof iinellasttic matteriialss, ssecoondaary efffectts, mullti modde rrespponsses, annd sso oon. In othher worrds, thhe uusuaal pprocceduure is to firrst connsidder a cclasssicc, eelassticc reespoonsee, aand theen tto oobseervee (oor sspecculaate aboout) whhat happpenns aas ffailluree liimitts aare appproaacheed.