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8/17/2019 Civile 3 Final Deicei
http://slidepdf.com/reader/full/civile-3-final-deicei 1/75
Facultatea de Arhitectura si ConstructiiC.C.I.A. – anul lV
Oradea
PROIECT
LA
CONSTRUCTII CIVILE III
STUDENT: Deicei Viorel
PROFESOR: dr.ing.MARGINEAN SORIN
-2012201!-
1
8/17/2019 Civile 3 Final Deicei
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"ORDEROU
P#r$e %cri%#:
1. Te&# l'cr#rii(
2. Me&ori' $e)nic(
!. No$e de c#lc'l.
P#r$e de%en#$#:
1. Pl#n *#r$er Sc 1:+0
2. Pl#n de di%$ri,'$ie # inc#rc#rilor er$ic#le *e *l#n%e' Sc 1:+0
!. Sec$i'ne $r#n%er%#l# er$ic#l# Sc 1:+0
. De$#li' &on$#n$i Sc 1:+0+. De$#li' &on$#n$i Sc 1:2+
/. De$#li' &on$#n$i Sc 1:2+
2
8/17/2019 Civile 3 Final Deicei
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TEMA PROIECTULUI
S# %e eriice %$r'c$'r# de rei%$en$# # 'nei cl#diri c' di#r#g&e din id#rie %i$'#$# in Or#de#.l#dire# #re regi&'l de in#l$i&e P3.S$r'c$'r# con%$r'c$i# e%$e 'r&#$o#re#:
- 'nd#$ii con$in'e din ,e$on(- *l#n%ee &onoli$e din ,e$on #r&#$4 gr51! c&(- *#rdo%eli din *#rc)e$(- $enc'ieli '&ede din &or$#r #r-ci&en$ l# *ere$i %i $##ne(- $er&oiol#$ie e6$erio#r# din *oli%$iren e6*#nd#$ de 10 c& gro%i&e(- #co*eri%'l e%$e de $i* $er#%# necirc'l#,il# ##nd %$r#$iic#$i#:
1. $enc'i#l# $##n'l'i M2+(2. *l#n%e' din ,e$on #r&#$ &onoli$ 1/20(!. ,#riere de #*ori: 17 c#r$on #%#l$#$ 8A93 17 c#r$on #%#l$#$ *eror#$8AP9(. ,e$on '%or de *#n$# de gro%i&e &edie c& 8de l# ! l# 1! c&9(+. $er&oiol#$ie 1+ c&(
/. %#*# de *ro$ec$ie M100 8! c& gro%i&e9(;. )idroiol#$ie co&*'%# din 142 %$r#$'ri de &e&,r#n# ,i$'&ino#%#4 %#': 17 c#r$on#%#l$#$ *eror#$ 8AP93 27c#r$on 3 ! %$r#$'ri ,i$'&(
. %$r#$ *ie$ri% 8*en$r' le%$#re9 < ! c& gro%i&e.
Aco*eri%'l $i* $er#%# necirc'l#,il# #re 'r&#$o#re# %$r#$iic#$ie:
!
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Meoriu tehnic
1.1 Regi& de in#l$i&e='cr#re# #re c# o,iec$i con%$r'ire#4 condi$iile de #&*#%#&en$4 di&en%ion#re#4 conor&#re# %i%erire# edili$#r# # 'nei cl#diri c' regi& de in#l$i&e P3E.
#$egori# de i&*or$#n$# # con%$r'c$iei e%$e D in conor&i$#$e c' *reederile =egii nr. 101>>+4?GR ;//1>>; %i #le ordin'l'i M=PAT nr.!1N1>>+.l#%# de i&*or$#n$# # cl#dirii e%$e III4 in conor&i$#$e c' Nor&#$i'l P100200.@on# %ei%&ic# de c#lc'l E4 conor& Nor&#$i'l'i de *roiec$#re #n$i%ei%&ic# P100200(#lo#re# *erio#dei de col$ e%re Tc5 0.;%ec. %i #lo#re# coeicien$'l'i %ei%&ic #g50.12g.
1.2 F'nc$i'ni de #r)i$ec$'r#on%$r'ci# *ro*'%B # #e# regi&'l de CnBli&e P3E.In conor&i$#$e c' $e&# de *roiec$#re inr#%$r'c$'r# c#%ei e%$e or&#$# din 'nd#$ii con$in'e din ,e$on %i&*l' %i ele#$ii din ,e$on #r&#$ &onoli$.
S'*r#%$r'c$'r# c#%ei # i or&#$# din *ere$i *or$#n$i din id#rie de c#r#&id# *lin# #r%#8STAS+1+2-/9 c' ,5;.+N&&24&or$#r M+.Pere$ii de id#rie or i conin#$i c' %$#l*i%ori de ,e$on #r&#$ %i cen$'ri de ,e$on #r&#$. Pl#n%eele%i %c#rile %'n$ din ,e$on #r&#$ &onoli$.Aco*eri%'l c#%ei # i re#li#$ %', or&# 'nei $er#%e necirc'l#,ile. Niel'l 0.00 #l *#rdo%elii *#r$er'l'i %e con%ider# niel'l de inc#%$r#re # di#r#g&elor dinid#rie.
1.!. Ele&en$e de rei%$en$# Fundatiile con%$r'c$iei or i con$in'e. F'nd#$iile con$in'e or i re#li#$e din ,e$on #r&#$&onoli$ #r&#$e l# *#r$e# %'*erio#r#.
S$r#$'l *or$#n$ #l 'nd#$iilor con$in'e *en$r' *ere$ii *or$#n$i #i cl#dirii e%$e #lc#$'i$ din #rgil# *r#o#%# ##nd co$e de 'nd#re l# -1.>+ & #$# de niel'l $eren'l'i n#$'r#l.D'*# $er&in#re# %#*#$'rilor %i in#in$e# $'rn#rii ,e$o#nelor in 'nd#$ii %e # c)e&# geo$e)nici#n'l%i *roiec$#n$'l *en$r' eriic#re# %i rece*$ion#re# n#$'rii $eren'l'i %i co$ei de 'nd#re.A*ele %',$er#ne n' #' o%$ in$erce*$#$e *e #d#nci&e# ine%$ig#$#4 ci %'n$ c#n$on#$e inor&#$i'nile *er&e#,ile #le *#nnoni#n'l'i l# #d#nci&i de *e%$e +.00 &.De%i #*ele %',$er#ne n' %'n$ in$erce*$#$e %e in$#lne%c $o$'%i #*e de inil$r#$ie %', or&# de*#ne re#$ice %'%*end#$e c#re *o$ #ec$# %*#$iile con%$r'i$e l# %',%ol. Pen$r' # con$r#c#r# #ce%$ne#'n% %e reco&#nd# con%$r'ire# 'n'i dren gr#i$#$ion#l.Ad#nci&e# de ing)e$ e%$e de 0.0 & conor& STAS /0+;;. Peretii c#%ei or i re#li#$i din c#r#&id# *lin# de #rgil# #r%# %i or #e# 'r&#$o#rele gro%i&i:
-*ere$ii e6$eriori or i de 2+ c& l# c#re %e #d#'g# 10 c& de *oli%$iren(-*ere$ii in$eriori or i de 2+ c&.
Gro%i&ile *ere$ilor #le%e &#i %'% core%*'nd condi$iilor de iol#re $er&ic# %i de ei$#re # or&#riiconden%'l'i de$erin#$e in 'nc$ie de on# cli&#$ic# in c#re %e #l# con%$r'c$i#4 iol#re onic# %i *reenire # incendiilor %i # eec$elor #ce%$or#. Ele&en$ele de id#rie din c#r#&id# *lin# de #rgil#
#r%# or #e# rei%$en$# 'ni$#re l# co&*re%i'ne %$#nd#rdi#$# eg#l# c'
2+.; mm N f b =.
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Rei%$en$# c#r#c$eri%$ic# # id#riei e%$e
2:+.2 mm N f k =. Rei%$en$# c#r#c$eri%$ic# l# orec#re
c' eor$ 'ni$#r de co&*re%i'ne n'l # id#riei e%$e
2
0 20.0 mm N f vk =. Mod'l' de el#%$ici$#$e
longi$'din#l #l id#riei e%$e
22:+01000 mm N f k =⋅
. Zidaria # i in$#ri$# c' %$#l*i%ori de ,e$on #r&#$ &onoli$ c' di&en%i'nile 2+62+ c& de cl#%#121+. S$#l*i%orii #' o%$ di%*'%i in %$r'c$'r# conor& *re%cri*$iilor d#$e de P21>+- Nor&#$i *riind c#lc'l'l %i e6ec'$#re# %$r'c$'rilor din id#rie. M#rc# de &or$#re olo%i$# *en$r' id#rii #i M+-@. #r#&iile cer#&ice $re,'ie %# inde*line#%c# condi$iile *re#'$e in %$#nd#rde. Pen$r''$ili#re# c#r#&iilor cer#&ice l# id#riile *or$#n$e #le cl#dirii $re,'ie %# %e re%*ec$e r#*or$'l de$e%ere l# *'nere in o*er#. ='ngi&e# de %'*r#*'nere # i de cel *'$in H din l'ngi&e# c#r#&iii. Planseele cl#dirii or i re#li#$e din ,e$on #r&#$ &onoli$ %i or #e# o gro%i&e de 1! c& #r#ini%#e. P#rdo%e#l# %',%ol'l'i e%$e #lc#$'i$# din '&#$o#rele %$r#$'ri: $enc'i#l#4 *l#c# de ,e$on#r&#$4 %#*# de niel#re &or$#r %i *#rc)e$ =U. Pl#n%e'l *e%$e #co*eri% e%$e or&#$ din'r&#$o#rele %$r#$'ri:$enc'i#l# $##n4 *l#n%e' de ,e$on #r&#$4 'n %$r#$ de c#r$on #%#l$#$ %i 'n'l dec#r$on #%#l$#$ *eror#$4 ,e$on '%or de *#n$#4 *oli%$iren 12c&4 %#*# de &or$#r M100 !c&4 'n %$r#$de c#r$on #%#l$#$ *eror#$4 do'# de c#r$on #%#l$#$ %i $rei %$r#$'ri de ,i$'&. Alc#$'ire# *l#n%eelor# #%ig'r# re#li#re# 'nei %#i,e orion$#le c#$ &#i rigide *en$r' #%ig'r#re# conl'cr#rii %*#$i#le #ele&en$elor %$r'c$'r#le %', #c$i'ne# %#rcinilor %ei%&ice.Stalpisorii %e *re#d *en$r' %*orire# c#*#ci$#$ii *or$#n$e %i # %$#,ili$#$ii *ere$ilor l# inc#rc#rier$ic#le %i deo*o$ri# *en$r' %*orire# c#*#ci$#$ii *or$#n$e # *ere$ilor %$r'c$'r#li l# #c$i'ne#co&,in#$# # %#rcinilor eric#le %i orion$#le. Di%*'nere# %$#l*i%orilor *en$r' %*orire# c#*#ci$#$ii *or$#n$e %i # %$#,ili$#$ii *ere$ilor l# inc#rc#ri er$ic#le %e #ce in *ere$ii %$r'c$'r#li c' inc#rc#ri&#ri. De#%e&ene# %e di%*'n *en$r' rigidi#re# *ere$ilor in#l$i or&#nd i&*re'n# c' cen$'rilein$er&edi#re o re$e#. S$#l*i%orii con%$r'c$iei or i #lc#$'i$i din ,e$on #r&#$ &onoli$ de cl#%#121+ %i in$#ri$i c' #r&#$'ri longi$'din#le din o$el P +2 c' di#&e$r'l ,#relor de 1/4 i#r
#r&#$'rile $r#ner%#le8e$rierii9 or i din o$el O" !;8
2210 mm N R f a yd ==9 c' di#&en$r'l
,#relor de /. E$rierii or i inde%i$i l# 10 c& in onele de inn#dire # ,#relor longi$'din#le %i l# *#r$e# %'*erio#r# # %$#l*i%orilor %', cen$'r# *e o l'ngi&e de &ini& +0 c&. =# con%$r'c$iile%i$'#$e in on# %ei%&ic# de c#lc'l E inn#dire# ,#relor longi$'din#le in$in%e %e # #ce *rin%'*r#*'nere# *e o l'ngi&e &ini&# de 0 de di#&e$re. "#rele din o$el O" !; or i $er&in#$e c'cioc'ri in &od o,lig#$ori'. =# niel'l *l#n%eelor4 %$#l*i%orii or i leg#$i &onoli$ c' cen$'rile din ,e$on #r&#$.
Centurile din ,e$on #r&#$ %'n$ re#li#$e in edere# #%ig'r#rii rigidi$#$ii *l#n%eelor in *l#n'l lor4
leg#$'r# *l#n%eelor c' *ere$ii %$r'c$'r#li. en$'rile de ,e$on #r&#$ de l# niel'l *l#n%eelor %e or *reede# o,lig#$ori' in *ere$ii %$r'c$'r#li din id#rie l# niel'l iec#r'i *l#n%e' #l #cl#dirii. Eleor #lc#$'i o re$e# inc)i%# %i con$in'# *e $o#$# %'*r##$# nielelor con%$r'c$iei. en$'rile $re,'ie%# #%ig're $r#n%&i$ere# direc$# # %#rcinilor gr#i$#$ion#le din *l#n%eele c#ldirii l# *ere$ii%$r'c$'r#li %i de l# nielele %'*erio#re l# cele inerio#re4 $r#n%&i$ere# or$elor de iner$ie l# *ere$ii%$r'c$'r#li4 *rel'#re# eor$'rilor de in$indere ce #*#r in *ere$ii %$r'c$'r#li. =#$i&e# cen$'rilor # ieg#l# c' gro%i&e# *ere$el'i %$r'c$'r#l *e c#re il in$#re%$e. Ar&#re# longi$'din#l# # cen$'rilor %e
+
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#ce c' ,#re din o$el P +2. Di#&e$r'l &ini& #l ,#relor ce %e or '$ili# in cen$'ri # i de *en$r' ,#re din P +2 %i 10 *en$r' cele din O" !;. Buiandrugii %e or re#li# *en$r' gol'rile &#ri *re#'$e in *ere$ii %$r'c$'r#li din ,e$on #r&#$$'rn#$i &onoli$. "'i#ndr'gii or #e# %ec$i'ni $r#n%er%#le eg#le c' gro%i&e# *ere$el'i %$r'c$'r#l4i#r in#l$i&e# de &ini&'& 1+ din l'&in# gol'l'i.
Golurile mari din *ere$ii %$rc'$'r#li #' o%$ #&*l#%#$e %i di&en%ion#$e #%$el c# *linirle din$re ele%# %#$i%#c# condi$iile nece%#re de rei%$en$# %i %$#,ili$#$e %', #c$i'ne# inc#rc#rilor er$ic#le.Scarile con%$r'c$iei or i e6ec'$#$e din ,e$on #r&#$ &onoli$. Sc#rile %e or e6ec'$# *rin$'r&#re# *e loc # ,e$on'l'i in cor#4 $'rn#$ od#$# c' *l#c# r#&*ei.
1.. Ele&en$e de ini%#Fini%#ele %'n$ i&*or$#n$e iind *#r$e in$egr#n$# # con%$r'c$iei4 ele&en$e ce con$ri,'ie%c l# %ol'$i##r)i$ec$'r#l# in#l#. A%$el ele&en$ele de ini%# #le cl#dirii in di%c'$ie %'n$ 'r&#$o#rele:-*#rdo%elile or i $i* *#rc)e$ l#&in#$ de c'lo#re inc)i%#(-'gr#elile in$erio#re or i o*%ele l##,ile *e ,## de di%*er%ie4 i#r l# gr'*'rile %#ni$#re8%ionde %c'rgere94 ,'c#$#rie4 onele e6*'%e direc$ '&idi$#$ii %e or olo%i *l#c#ri c' ini%#e cer#&ice
%#' 'gr#eli i&*er&e#,ile4 *#rdo%elile iind de #%e&ene# i&*er&e#,ile(-$enc'ielile e6$erio#re or i $enc'ieli dri%c'i$e gri %i $enc'ieli dri%c'i$e in #l, &#$(-*l#c#ri e6$erio#re c' *l#c# $r#er$in(-*l#c#rile $re*$elor %e or re#li# *rin *l#c#e de le&n &#%i *rin *rindere in di,l'ri # $re*$ei %i *rin or$#re #*oi # con$r#$re*$ei(-$#&*l#rie *en$r' ere%$re %i '%i din *roile de #l'&ini' c' ge#& $er&o*#n %i ,#rier# $er&ic#(-$ro$'#r'l # i *##$ c' *ie$re c',ice %#' d#le c',ice din ,##l$ %#' gr#ni$(-$igl# %oli4 reg$#ng'l#r# de c'lo#re #n$r#ci$.
1.+. Ele&en$e de iol#$iiIol#re# $er&ic# # cl#dirii re*rein$# o i&*or$#n$# e$#*# in *roiec$#re# 'nei con%$r'c$ii4 #r# de
#ce#%$# #& #e# *ierderi de energie $er&ic#. A%$el id'rile e6$erio#re %i #r$ic'l#$iile in$re id#rie%i $#&*l#rie %e or $er&oiol# c' *l#ci $er&oiol#n$e din *oli%$iren e6*#nd#$ i6#$e &ec#nic c'#'$or'l di,l'rilor %*eci#le %#' *rin li*ire in *'nc$e c' #dei #dec#$.=# niel'l %ol'l'i %e or re#li# l'cr#ri de )idroiol#re in onele e6*'%e. Se # '$ili#)idroiol#$i# din &e&,r#ne ,i$'&ino#%e %i l# #co*eri%. ?idroiol#$i# din &e&,r#ne ,i$'&ino#%e$re,'ie *re%#$# in$re do'# ele&en$e rigide de con%$r'c$ie4 inc#rc#rile $r#n%&i%e de con$r'c$ie$re,'ie %# #c$ionee con$in'' %i c#$ &#i 'nior& *e %'*r##$# )idroiol#$iei.S', *#rdo%e#l# %e #*lic# 'n %$r#$ de r'*ere # c#*il#ri$#$ii din *ie$ri%. =# %ocl'ri %e #*lic# o)idroiol#$ie din &e&,r#ne ,i$'&ino#%e.
1./. In%$#l#$ii
In%$#l#$iile %#ni$#re4 elec$rice %i $er&ice or i e6ec'$#$e in 'r&# el#,or#rii 'nor *roiec$e de%*ecili$#$e.Ali&en$#re# c' #*B # clBdirii %e # #ce din ree#'# de #*# *o$#,il# # loc#li$#$ii.O,iec$ele %#ni$#re de #i#nB %'n$ r#cord#$e l# in%$#l#iile de #*B c'ren$#.Energi# $er&icB # clBdirii %e # 'rni# din re$e#'# $er&ic# loc#l#.Ali&en$#re# c' energie elec$ricB # clBdirii %e # re#li# din ree#'# *',licB de o#%B $en%i'ne *rinin$er&edi'l iridei de ,r#n#&en$ *o#$B *e ##d# l#$er#lB.on%$r'ci# # #e# in%$#l#ie elec$ricB *en$r' il'&in#$ i *en$r' '$ili$Bile elec$ro-c#%nice.
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#n#li#re# clBdirii %e # r#cord# l# ree#'# loc#l# de c#n#li#re.Ven$il#i# i il'&in#re# $'$'ror %*#iilor e%$e direc$B i n#$'r#lB *rin in$er&edi'l ge#&'rilore6i%$en$e *e $o#$e ##dele.In #c$ii$#$e# de loc'ire n' e6i%$B o*er#ii gener#$o#re de no6e $o6ice %#' C&,olnBiri *roe%ion#le.
Note de calcul
In#l$i&e# *#r#*e$'l'i ere%$relor # i de >0 c&.Di%$#n$ele din$re #6e or i:- 65!.0 &- J5!.+0 &- 5!.20 &- K5.>0 &
!. Materiale
- ele&en$e *en$r' id#rie: c#r#&ii *line de #rgil# #r%#4
2+4; mm N f b =
- &or$#r M+ 8 R/ 4 *#g !1 4 T#,.!.2 < *en$r' *ereii %$r'c$'r#li l# con%$r'cii deini$ie *en$r'→> 2
10 mm N f b
&ini& M10 4 i#r *en$r'→< 2
10 mm N f b
&ini& &or$#r M+ 9
- rei%$en$# c#r#c$eri%$ic# l# co&*re%i'ne # id#riei
2:+42 mm N f k = 8 idBrie BrB ro%$'ri *#r#lele
c' *l#n'l *ere$el'i 9- rei%$en$# c#r#c$eri%$ic# l# orec#re # id#riei %', eor$ de co&*re%i'ne n'l e%$e
2
04 240 mm N f vk =
- &od'l'l de el#%$ici$#$e longi$'din#l# # id#rie
22:+071000 mm N f E k ==
- &od'l'l de el#%$ici$#$e $r#n%er%#l #l id#riei %e #d&i$e c# e%$e 0L din cel longi$'din#l4 %i
#n'&e:
2110740 mm N E G ==
- *l#n%eele %i cen$'rile or i #lc#$'i$e din ,e$on #r&#$ &onoli$4 c' cl#%# ,e$on'l'i 1/20
- %#&,'rii or #e# ,e$on din cl#%# 121+4 ##nd rei%$en$# de c#lc'l
2+4> mm N f cd =
- o$el'l olo%i$ e%$e S2!+ 8O"!;94 ##nd
2210 mm N f
yd
=
- #r&#re# %$#l*i%orilor din ,e$on #r&#$ %e re#lie## c':L:40&in = p
- rei%$en$# de *roiec$#re l# co&*re%i'ne # id#riei e%$e: !
k d
f m f
γ 7=
4 'nde
;
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→=1 m
coeicien$'l condi$iilor de l'cr'→ ! γ
coeicien$ de %ig'r#n$# reeri$or l# &#$eri#l 8'nc$ie de &#n# de l'cr'9. In c#'l 'n'i con$rol
nor&#l #l e6ec'$iei
242= ! γ
Re'l$#
2!0.1
2.2
:+.270.1 mm N f d ==
". Sta#ilirea incarcarilor $erticale
2.1. Ari# $o$#l# # niel'l'i
0/.1:;2+41072+.1:7 == B " 2m
2.2. Ariile ne$e #le inc#*erilor
=∑=
10
1
4241 7i
ii l l 2
>2.1+!/+479>+42722+.!7++.!78 m=++
2.!. Ariile oc'*#$e de *ere$i
( ) 2/1.2:2+.070+.107/0+.1:7! m # pereti =+=
2.. Vol'&'l id#riei
→= !/:.;:;+.27/1.2: m
*en$r' 'n niel4 d#c# n' $ine& con$ de gol'rile *en$r' '%i %iere%$re
ol'&'l $'$'ror gol'rilor de '%i %i ere%$re4 *en$r' 'n niel(→=−
!:./;20.11/:.;: m
ol'&'l $o$#l #l id#riei *en$r' 'n niel(→= !4!!;+7:./; m
ol'&'l $o$#l #l id#riei *en$r' in$re#g# cl#dire 8+ niel'ri9.
2.+. Gre'$#$e# id#riei
- gre'$#$e# ol'&e$ric# # id#riei %e con%ider#
!+41> mkN
8incl'#nd $enc'i#l#9(
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- gre'$#$e# $o$#l# # id#riei *e 'n niel:kN nivel G id :/41!1+:./;7+41> ==
- gre'$#$e# $o$#l# # id#riei *en$r' in$re#g# cl#dire:kN G id !4/+;>.!!;7+41> ==
2./. Gre'$#$e# *l#n%e'l'i
2./.1. Gre'$#$e# *l#%e'l'i *e 1&
2
- $enc'i#l# in$r#do% 82 c& gro%i&e9:
2!!:.002.071> mkN mmkN =
(
- *l#c# din ,e$on #r&#$ 81! c& gro%i&e9:
2! 2+.!1!.072+ mkN mmkN =
- *#rdo%e#l# 3 %#*# 8242 c& 324 c& gro%i&e 9 :
2!!;/.0+::.01;/.002:.0721022.07: mkN mmkN mmkN =+=+
To$#l:!>. 22 . mkN mkN ≅
O,%er#$ie:
00.11 =Ψ i
*en$r' gr'*#re# %*eci#l# de inc#rc#re.
- inc#rc#re '$il# *e *l#n%e':
2+.1 mkN $ =
8loc'in$#9(
D#r4.02 =Ψ i
*en$r' gr'*#re# %*eci#l#.
Deci4 o& l'cr# c' o inc#rc#re '$il# de c#lc'l 1
2m
de
22/.0.07+0.1 mkN mkN =
⇒ inc#rc#re# $o$#l#1
2m
*l#n%e' e%$e
200.+/.0. mkN =+
2./.2. Gre'$#$e# $o$#l# # *l#n%e'l'i *e 'n niel
kN G #m planseunet ;;000.+7>241+!7 2
==
2.;. Gre'$#$e# $o$#l# # cl#dirii *e 'n niel
;;0:/.1!1+41 +=+= planseu id niv GGG
>
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kN G niv :/.20:+41 =⇒
- inc#rc#re# ec)i#len$## 'n'i niel
21m de %'*r##$#:
=ec%iv$21+.11
0/.1:;
:/.20:+mkN =
2.. Gre'$#$e# $o$#l# # cl#dirii
kN GG niv !.102>+7:/.20:++741 ===
%. Calculul &ortei seisice de 'roiectare
!.1.oeicien$ii de c#lc'l
i9. #c$or'l de i&*or$#n$#:→= 00.1 & γ
cl#diri de $i* c'ren$
ii9. #lo#re# %*ec$r'l'i el#%$ic de *roiec$#re:
98798 ' a' S g e β = g g !!.0;+.2712.0 ==
E6i%$# #c$ori de red'cere # or$ei %ei%&ice4 deo#rece %i &#$eri#l'l #&or$ie## o *#r$e din
#ce#%$#.
→= L:ς
#c$or de red'cere *en$r' idBri# conin#$B
ς η
+=
+
10
:+
10
+=⇒η
→=⇒ ::40η
#c$or de corec$ie ce $ine con$ de #&or$i#reς 98' S e
iii9. #c$or'l de corec$ie *en$r' con$ri,'$i# &od'l'i *ro*ri' 'nd#&en$#l de i,r#$ie::+40=λ
d#c#C ' ' ≤1
%i cl#dire# #re &#i &'l$ de 2 niel'ri.041=λ
in celel#l$e %i$'#$ii.
Perio#d# *ro*rie 'nd#&en$#l# de i,r#re %e de$er&in# %i&*liic#$ #%$el:
10
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!
1 7 ( C ' t =
→= 0+40t C
coeicien$ 'nc$ie de $i*'l %$r'c$'rii
→== mm ( ;+41!;+.27+in#l$i&e# cl#dirii in &e$ri
s' s' C ;.0!+;40;+41!70+.0
!
1 =<==⇒
:+.0=⇒ λ in c#'l no%$r'
1' ' C > i n5+ niel'ri
i9. #c$or'l de co&*or$#re$
F#c$or'l de co&*or$#re$
de*inde de:- $i*'l id#riei(
- #c$or'l de %'*r#rei%$en$#1α
α u
(- reg'l#ri$#$e# %$r'c$'rii.
Pen$r' cl#diri c' %$r'c$'r# din id#rie conin#$#
2+.11
=α
α u
12+.!2+.17+.27+.2 =⇒==⇒ $$ &
u
α
α
!.2. #lc'l'l or$ei $#ie$o#re de ,##
λ γ 77987 m' S F d & b =
Ordon#$# %*ec$r'l'i de r#%*'n% de *roiec$#re core%*'n#$o#re *erio#dei de i,r#$ie 'nd#&en$#le
1'
%e o,$ine c' rel#$i#:$
' a' S
g
d
η β 798798 =
kN g
F b ;+.:!>:+.07!.102>
712+.!
::.07;+.2712.071 ==⇒
11
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!.!. For$ele %ei%&ice de niel orion$#le
For$# %ei%&ic# c#re #c$ione## l# niel'l i4 %e c#lc'le## conor& P1004 c' rel#$i#:
∑−
=n
i
ii
ii
bi
sm
sm F F
1
7
77
4 'nde:
→i F
or$# %ei%&ic# orion$#l# %$#$ic ec)i#len$# de l# niel'l i(→b F
or$# $#ie$o#re de ,## core%*'n#$o#re &od'l'i 'nd#&en$#l(→i s
co&*onen$# or&ei 'nd#&en$#le *e direc$i# gr#d'l'i de li,er$#$e din#&ic# de $r#n%l#$ie l#
niel'l i→nn'&#r'l de niel'ri #l cl#dirii
→im
&#%# de niel.
For&# *ro*rie 'nd#&en$#l# 8T
1
9 *o#$e i #*ro6i&#$# *rin$r-o #ri#$ie lini#r# cre%c#$o#re *ein#l$i&e. In #ce%$ c# or$ele orion$#le de niel %'n$ d#$e de rel#$i#:
∑−
= n
i
ii
iibi
m m F F
1
777
4 'nde:
→i
in#l$i&e# niel'l'i i #$# de %ec$i'ne# de inc#%$r#re.
D#$ iind c# &#%ele de niel %'n$ eg#le *e in#l$i&e# cl#dirii4 or&'l# deine:
∑∑=−
== n
i
i
i
bn
i
ii
ii
bi
F m
m
F F
11
77
7
7
12
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Pen$r' in#l$i&i eg#le de niel rel#$i# deine:
1+7
71+77
1
i F
%
F
F F b
eta)
ibn
i
i
ibi ===
∑=
Deci4 #e&1+
1
b F F = kN >:.++1+
;+.:!>==
1+72
2
b F F = 928>;.111 12 F F kN ==
1+
7!!
b F F =
5
9!8>+.1/; 1! F F kN =
98>!.22!1+
71 F F kN
F F b ===
9+8>2.2;>1+
7+1++ F F kN
F F b ===
!.. #lc'l'l &o&en$'l'i de r#%$'rn#re l# ,## cl#dirii 8co$#0040±
9
1!
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∑=
++++==+
1
+!21 7+7777!772777i
eta)eta)eta)eta)eta)iir % F % F % F % F % F F !
;+.27+7>2.2;>;+.277>!.22!;+.27!7>+.1/;;+.2727>;.111;+.27>:.++ ++++=r !
mkN ! r 7>.:/;=⇒
. Calculul e&orturilor unitare de co'resiune in 'eretii structurali
.1.Inc#rc#ri din gre'$#$e# *l#n%e'l'i %i inc#rc#re# de e6*lo#$#re 8'$il#9
1
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Prin i&*#r$ire# oc)i'rilor de *l#n%e' din$re *ere$ii de rei%$en$#4 d'c#nd'-%e linii l#°+
diniec#re col$4 %-#' o,$in'$ ig'ri geo&e$rice %i&*le 8$r#*e4 $ri'ng)i94 %#' co&,in#$ii din$re#ce%$e#. A& c#lc'l#$ #riile iec#rei *or$i'ni c#re de%c#rc# *e 'n *ere$e4 re%*ec$i gre'$#$ile
1+
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#ce%$or *or$i'ni de *l#n%e'4 i#r *rin i&*#r$ire# l# l'ngi&e# *ere$el'i #eren$ #& o,$in'$inc#rc#re# 'nior&# din gre'$#$e# *l#n%e'l'i *l'% '$il# *e &e$r' lini#r.
S1=
C 1
∙C 2
2=
1.78 ∙1.78
2=1.58m
2
S2=(B+b) ∙ h
2=(1.1+4.65)∙1.78
2¿5.12m
2
S3=
C 1
∙C 2
2=
1.63 ∙1.63
2=1.32m
2
S4=(B+b)∙ h
2 =(4.65+1.63)∙1.63
2 ¿5.11m2
S5=(B+b) ∙ h
2=(3.0+1.63)∙1.63
2¿3.77m
2
S6=
C 1
∙ C 2
2=
1.63 ∙2.05
2=1.67m
2
S7=C 1 ∙C 2
2=1.20 ∙1.20
2=0.72m2
S8=
C 1
∙C 2
2=
1.45 ∙1.45
2=1.05m
2
S9=
C 1
∙ C 2
2=
0.70∙0.70
2=0.24m
2
S10=(B+b) ∙h
2=(4.65+1.40) ∙1.63
2¿4.93m
2
S11=
C 1
∙ C 2
2=
1.48∙1.48
2=1.09m
2
1/
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S12=(B+b)∙ h
2=(3.20+1.73) ∙1.48
2¿3.64m
2
S13=C
1
∙C 2
2 =1.45 ∙1.452 =1.03m2
S14=(B+b) ∙ h
2=(4.65+1.70) ∙1.48
2¿4.7m
2
q1=S
1∙ G p=1.58 ∙5=7.9kN
q2=S2∙ G p=5.12 ∙5=25.6 kN
q3=S
3∙ G p=1.32 ∙5=6.6kN
q4=S
4∙ G p=5.11 ∙5=25.55kN
q5=S
5∙ G p=3.77 ∙5=18.85 kN
q6=S6 ∙G p=1.67 ∙5=8.35 kN
q7=S
7∙G p=0.72 ∙5=3.6 kN
q8=S
8∙G p=1.05 ∙5=5.25 kN
q9=S
9∙G p=0.24 ∙5=1.20kN
q10=S
10∙ G p=4.93∙5=24.65 kN
q11=S
11∙ G p=1.09 ∙5=5.45 kN
q12=S
12∙G p=3.64 ∙5=18.2 kN
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q13=S
13∙ G p=1.03 ∙5=5.15 kN
q14=S
14∙ G p=4.7 ∙5=23.5 kN
To$od#$#4 #& c#lc'l#$ gre'$#$e# iec#r'i &on$#n$ *rin c#lc'l'l ol'&'l'i #ce%$or# %i in&'l$ire# c'
gre'$#$e# ol'&ic# &edie # id#riei4 *e c#re #& con%ider#$-o
!+41>
m
kN
.O,%er#$ie: $o#$e d#$ele o,$in'$e %'n$ *en$r' 'n niel de id#rie4 i&*re'n# c' *l#n%e'l
%i inc#rc#re# '$il# #eren$e 8de de#%'*r#9.Ul$erior4 c' re'l$#$ele in%cri%e %i in de%en4 *'$e& in$oc&i 'r&#$or'l $#,el:
No$#: Pen$r' c#lc'l'l gre'$#$ii l# ,## #& in&'l$i$ gre'$#$e# $o$#l# c' + < n'&#r'l de niel'ri #l
cl#dirii. Eor$'l 'ni$#r #6i#l l-#& c#lc'l#$ c' or&'l#: id
baa
#G=0σ
.
idarie #
- #ri# id#riei &on$#n$'l'i i(
idarieG
- gre'$#$e# id#riei core%*'n#$o#re &on$#n$'l'i i(
planseuG
- gre'$#$e# *l#n%e'l'i core%*'nd#$o#re &on$#n$'l'i i(
total G
- gre'$#$e# $o$#l# core%*'n#$o#re &on$#n$'l'i i(
baaG
- gre'$#$e# l# ,## &on$#n$'l'i i l# $o#$e niel'rile(
0τ
- eor$'l 'ni$#r de co&*re%i'ne(
aferent planseu plan seu #$G ⋅=
aferent #
- #ri# *l#n%e'l'i #eren$# &on$#n$'l'i i(
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planseu idarietotal GGG +=
1⋅+⋅= acoperisniveluritotal baa Gnr GG
=nivelurinr
Pen$r' &on$#n$'l E1:
A zid, gol=2 ∙0.90 ∙0.25+0.45 ∙0.25+5 ∙0.25 ∙0.25=0.87
A zid, brut =2∙2.025 ∙0.25+2∙4.65 ∙0.25+1.775 ∙0.25=3.78m2
A zid= Abrut − Agol=3.78−0.87=2.91m2
V zid , brut = A zid. brut ∙ h zid=3.78 ∙2.50=9.45m3
V zid , gol=2 ∙0.90 ∙0.25 ∙1.80+0.45 ∙0.25 ∙2.10+5 ∙0.25 ∙0.25 ∙2.5=1.82m3
V zid , net =V zid, brut −V zid ,gol=9.45−1.82 ¿7.63m3
G z=V zid , net ∙ γ z=7.63 ∙19,5=148.78 kN
G p=q pl ∙ Aaferent =4q1+2q
2=82.8 kN
Gtotal=G z+G p=148.78+82.8=225.58 kN
Gbaza=Gtotal∙5=225.58 ∙5=1127.9 kN
σ 0=
Gbaza
A zid
=1127.9
2.91=387.6
kN
m2
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Pen$r' &on$#n$'l E2:
A zid, gol=2 ∙0.90 ∙0.25+3 ∙0.45∙0.25+3 ∙0.25 ∙0.25=0.974
A zid, brut =3.65 ∙0.25+4.65 ∙0.25+4.075 ∙0.25+0.7 ∙0.25=3.26m2
A zid= Abrut − Agol=3.26−0.974=2.28m2
V zid , brut = A zid. brut ∙ h zid=3.26 ∙2.50=8.15m3
V zid , gol=2 ∙0.90 ∙0.25 ∙1.80+3 ∙0.45 ∙0.25 ∙2.10+3 ∙0.25 ∙0.25 ∙2.5=1.98m3
V zid , net =V zid, brut −V zid ,gol=8.15−1.98 ¿6.17m3
G z=V zid , net ∙ γ z=6.17 ∙19,5=120.31 kN
G p=q pl ∙ Aaferent =3q1+2q
9+2q
6+q
4+q
2+q
3=100.55 kN
Gtotal=G z+G p=220.86 k N
Gbaza=Gtotal∙5=1104.3 kN
σ 0=
Gbaza
A zid
=1104.3
2.28=484.34
kN
m2
Pen$r' &on$#n$'l E!:
A zid, gol=2 ∙0.90 ∙0.25+0.45 ∙0.25+2∙0.25 ∙0.25=0.687
A zid, brut =3.65 ∙0.25+3.95 ∙0.25=1.9m2
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A zid= Abrut − Agol=1.9−0.687=1.21m2
V zid , brut = A zid. brut ∙ h zid=1.9 ∙2.50=4.75m3
V zid , gol=2 ∙0.90 ∙0.25 ∙1.80+0.45 ∙0.25 ∙2.10+2∙0.25 ∙0.25 ∙2.5=1.35m3
V zid , net =V zid, brut −V zid,gol=4.75−1.35¿3.40m3
G z=V zid , net ∙ γ z=3.40 ∙19,5=66.3 kN
G p=q pl ∙ Aaferent =q1+q
10+q
2+q
3=64.75 kN
Gtotal=G z+G p=131.05 kN
Gbaza=Gtotal∙5=655.25 kN
σ 0=
Gbaza
A zid
=655.25
1.21=541.52
kN
m2
Pen$r' &on$#n$'l E: A zid, gol=2 ∙0.90 ∙0.25+0.45 ∙0.25+2∙0.25 ∙0.25=0.687
A zid, brut =3.35 ∙0.25+3.10 ∙0.25=1.61m2
A zid= Abrut − A gol=1.56−0.687=0.92m2
V zid , brut = A zid. brut ∙ h zid=1.61 ∙2.50=4.0m3
V zid , gol=2 ∙0.90 ∙0.25 ∙1.80+0.45 ∙0.25 ∙2.10+2∙0.25 ∙0.25 ∙2.5=1.35m3
V zid , net =V zid, brut −V zid ,gol=4.0−1.35¿2.65m3
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G z=V zid , net ∙ γ z=2.65 ∙19,5=51.67kN
G p=q pl ∙ Aaferent =q3+q
11+q
12+q
5=49.1kN
Gtotal=G z+G p=100.77 kN
Gbaza=Gtotal∙5=503.85 kN
σ 0=
Gbaza
A zid
=503.85
0.92=547.66
kN
m2
Pen$r' &on$#n$'l E+:
A zid, gol=2 ∙0.90 ∙0.25+0.45 ∙0.25+2∙0.25 ∙0.25=0.687
A zid, brut =3.35 ∙0.25+3.95 ∙0.25=1.82m2
A zid= Abrut − Agol=1.82−0.687=1.33m2
V zid , brut = A zid. brut ∙ h zid=1.82 ∙2.50=4.55m3
V zid , gol=2 ∙0.90 ∙0.25 ∙1.80+0.45 ∙0.25 ∙2.10+2∙0.25 ∙0.25 ∙2.5=1.35m3
V zid , net =V zid, brut −V zid ,gol ¿3.2m3
G z=V zid , net ∙ γ z=3.2 ∙19,5=62.4 kN
G p=q pl ∙ Aaferent =q3+q
11+q
10+q
14=60.2 kN
Gtotal=G z+G p=122.6 kN
Gbaza=Gtotal∙5=613kN
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σ 0=
Gbaza
A zid
= 613
1.33=460.9
kN
m2
Pen$r' &on$#n$'l E/:
A zid, gol=4 ∙0.45∙0.25+0.25 ∙0.25=0.512
A zid, brut =1.45 ∙0.25+1.45 ∙0.25+1.475 ∙0.25+0.70 ∙0.25=1.26m2
A zid= Abrut − Agol=1.26−0.512=0.748m2
V zid , brut = A zid. brut ∙ h zid=1.26 ∙2.50=3.15m3
V zid , gol=4 ∙0.45 ∙0.25 ∙2.10+0.25 ∙0.25 ∙2.5=1.01m3
V zid , net =V zid, brut −V zid,gol=3.15−1.01¿2.14 m3
G z=V zid , net ∙ γ z=2.15 ∙19,5=41.92kN
G p=q pl ∙ Aaferent =2q9+2q
7+2q
11+q
13+q
8=31kN
Gtotal=G z+G p=72.92 kN
Gbaza=Gtotal∙5=364.6 kN
σ 0=
Gbaza
A zid
=364.6
0.748=487.43
kN
m2
2!
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AriaGreutate
aGreutate
aGreutat
eGreutat
eEfortul
GrupZidari
eiZidariei
Planseului
total baza σo
m2 kN kN kN kN kN/m2
E1 2.91 14.! 2. 22"." 112!.9 #!.$
E2 2.2 12%.#1 1%%."" 22%.$ 11%4.# 44.#4
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22.!/+/>210+/40/241
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In concl'ie 4 condi$i# e%$e inde*lini$B #%$el Cnc$
[ ] [ ]ml m * +C >>+.27!.0!;.1 =<=
Deo#rece &on$#n$'l e%$e %i&e$ric 4 %e o,in #cele#i #lori Cn c#'l %c)i&,Brii #ci'nii %ei%&'l'i
Montantul E" 1
1
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[ ]2
24 10.1 m # c =
[ ]2
14 !2+.0 m # =
[ ]2
14 7 m # # sta lpi sor ec%b η =
[ ]2
14
0/2+.07:.+ m #b =⇒
[ ]2
14
!2+.0 m #b =⇒
[ ]2
24 7 m # # sta lpisor ec%b η =
[ ]2
24 0/2+.07:.+ m #b =⇒ [ ]2
24 !2+.0 m #b =⇒
I#r
[ ]2
24 72+.0 m * # =
%$ii& c#
[ ]2
2424141424 m # # # # # bb c +++=
[ ]2
2414142424 m # # # # # bb c −−−=⇒
[ ]2
24 0>.0 m # =⇒
d#r
[ ]m * # 72+.024 =
[ ]m *2+.0
0>.0=⇒
[ ]m * !/.0=⇒
2
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Ae&
[ ]2
1 !2+.0 m # = i
[ ]md y 12+.014 =
[ ]2
2 0>.0 m # = i
[ ]md y !.024 =
[ ]2
! 0/2+.0 m # = i
[ ]md y 12+.0!4 =
[ ]2
0/2+.0 m # = i
[ ]md y 12+.04 =
i
[ ]m #i
d # y
i yi
cG ∑∑=⇒ 4
244
7
[ ]m y cG 0>.0244 =⇒
[ ] [ ]mm #i
d #
*
i *i
cG !;+41
7 4
244 == ∑∑
Tre,'ie Cnde*lini$B condii# c#+C l * 7!0.0<
Unde[ ]ml + !0.+= [ ]ml + +>.17!0.0 =⇒
[ ]m *C !/.02+.0 += [ ]m *C /1.0=⇒
In concl'ie 4 condi$i# e%$e inde*lini$B #%$el Cnc$
[ ] [ ]ml m * +C +>.17!.0/1.0 =<=
Sc)i&,B& %en%'l #ci'nii %ei%&'l'i
Montantul E" 2
!
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[ ]2
24 10.1 m # c =
[ ]2
14 !+.0 m # =
[ ]2
24 !!.0 m # =
[ ]2
!4 0/2+.0 m # =
2
14 7 m # # sta lpi sor ec%b η =
[ ]2
14 0/2+.07:.+ m #b =⇒ 2
14 !2+.0 m #b =⇒
I#r[ ]2
4 72+.0 m * # =
%$ii& c#
[ ]2
4!424141424 m # # # # # # b c ++++=
[ ]2
!4241414244 m # # # # # # b c −−−−=⇒
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[ ]2
4 002.0 m # =⇒
d#r
[ ]m * # 72+.04 =
[ ]m *2+.0
002.0=⇒
[ ]m * 00:.0=⇒
Ae&
[ ]2
1 !+.0 m # = i
[ ]md y !;+.014 =
[ ]2
2 !!.0 m # = i
[ ]md y !;+.024 =
[ ]2
! 0/2+.0 m # = i
[ ]md y 12+.0!4 =
[ ]2
0/2+.0 m # = i
[ ]md y !;+.04 =
[ ]2
+ 002.0 m # = i
[ ]md y +0:.04 =
i
[ ]m #i
d # y
i yi
cG ∑∑=⇒ 4
244
7
[ ]m y cG !+.0244 =⇒
[ ] [ ]mm #i
d # *
i *i
cG :0417 4
244 ==
∑
∑
Tre,'ie Cnde*lini$B condii# c#+C l * 7!0.0<
Unde[ ]ml + !0.+= [ ]ml + +>.17!0.0 =⇒
[ ]m *C 00:.0+.0 += [ ]m *C +0:.0=⇒
In concl'ie 4 condi$i# e%$e inde*lini$B #%$el Cnc$
[ ] [ ]ml m * +C +>.17!.0+0:.0 =<=
Montantul E% 1
+
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[ ]2
!4 +1;.0 m # c =
[ ]2!4 2+.07 m * # c = [ ]m * 2+.0
+1;.0
=⇒
[ ]m * 0/.2=⇒
Tre,'ie Cnde*lini$B condii# c#+C l * 7!0.0<
Unde
[ ]ml + 0.!= [ ]ml + 02.17!0.0 =⇒
I#r [ ]m *C 0/.2=
A%$el condi$i# n' e%$e inde*lini$B deo#rece
[ ] [ ]ml m * +C 02.17!.00/.2 =>=
n concl'ie 4 l# #ce%$ &on$#n$ $re,'ie di%*'% 'n %$l*ior 4 c#re C&*re'nB c' idBri# %# *rei# Cnc#rc#rile d#$or#$e %e%i%&'l'i .
/
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N' c'no#%$e& di&en%i'nile %$l*ior'l'i 4 d#r *en$r' # de$er&in# di&en%i'nile cele &#iecono&ice 4 o& reol# 'r&B$or'l %i%$e& de ec'#ii :
( ) 2
!4 772+.0 ml * # ec% c += η
'nde :
o 6 < re*rein$B o di&en%i'ne # %$#l*ior'l'i de ,e$ono l < re*rein$B o di&en%i'ne # onei co&*ri&#$e de idBrie
Pen$r' o di&en%ion#re econo&ic# con%iderB&+l l * 7!0.0=+
4 c#re in c#'l no%$r' e%$e[ ]ml * 02.1=+
[ ]ml * −=⇒ 02.1
In$rod'ce&
[ ]ml * −= 02.1
Cn
( ) [ ]2
!4 772+.0 ml * # ec% c += η
de 'nde re'l$B
( )[ ] [ ]2
!4 02.1772+.0 ml l # ec% c +−= η
( )[ ] [ ]2
!4 02.17:.+72+.0 ml l # c +−=⇒
( ) [ ]2
!4 2+.002.17!;.1 ml l # c +−=⇒
[ ]2
!4 2+.0!;.1!>;.1 ml l # c +−=⇒
D#r
[ ]2
!4 +1;.0 m # c =
[ ]22+.0!;.1!>;.1+1;.0 ml l +−=⇒
+1;.0!;.112.1 −=⇒ l [ ]ml
12.1
:+;.0=⇒
[ ]ml ;:.0=⇒
Pen$r'
[ ]ml * −= 02.1
i
[ ]ml ;:.0=
[ ]m * 2.0=⇒
N' *'$e& l'# #%$el de di&en%i'ni #le %$l*ior'l'i de 2+62 4 #%$el #lege& 2+62+ di&en%i'ne#%$Bl*ior'l'i 8 Di&eni'ne# &ini&B # 'n'i %$Bl*i%or e%$e de 2+62+ c& 4 i#r %'*r### i&B e%$ede >00 c&2 9
;
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[ ]2
!4 +1;.0 m # c =
[ ]2
14 7 m # # sta lpi sor ec%b η =
[ ]2
14 0/2+.07:.+ m #b =⇒ [ ]2
14 !2+.0 m #b =⇒
I#r
[ ]2
14 72+.0 m * # =
%$ii& c#
2
1414!4 m # # # b c +=
2
14!414 m # # # b c −=⇒
[ ]2
14 1;.0 m # =⇒
d#r
[ ]m * # 72+.014 =
[ ]m *2+.0
1;.0=⇒
[ ]m * />.0=⇒
Ae&
[ ]2
1 0/2+.0 m # = i
[ ]md y 12+.014 =
[ ]2
2 1;.0 m # = i
[ ]md y +>+.024 =
[ ]m #i
d #
y
i yi
cG
∑∑
=⇒ 4
!44
7
[ ]m y cG ;.0244 =⇒
[ ] [ ]mm #i
d # *
i *i
cG 0+417 4
!44 ==∑
∑
Tre,'ie Cnde*lini$B condii# c#+C l * 7!0.0<
Unde
[ ]ml + 0.!= [ ]ml + 02.17!0.0 =⇒
[ ]m *C />.02+.0 += [ ]m *C >.0=⇒
In concl'ie 4 condi$i# e%$e inde*lini$B #%$el Cnc$
[ ] [ ]ml m * +C 02.17!.0>.0 =<=
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Montantul E% 2
[ ]2
!4 +1;.0 m # c =
[ ]2
14 !2+.0 m # =
[ ]2
14 7 m # # sta lpi sor ec%b η =
[ ]2
14 0/2+.07:.+ m #b =⇒ [ ]2
14 !2+.0 m #b =⇒
[ ]2
24 7 m # # sta lpi sor ec%b η =
[ ]2
24 0/2+.07:.+ m #b =⇒ [ ]2
24 !2+.0 m #b =⇒
Se o,%erB cB24241414 cbb # # # # >++
⇒ n' $o#$B %eci'ne# %$Bl*ior'l'i e%$e co&*ri&#$B
>
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2
241424 m # # # # bb c ++=
S$ii& cB
[ ]2972+.072+.0!0.187 m * # ec%ec% c η η ++=
[ ]20.7 m * # c =⇒ [ ]m
# *
c
0.=⇒
[ ]m *0.
+1;40=⇒
[ ]m * 12.0=⇒
Ae&
[ ]2
1 2;.0 m # = i
[ ]md y 10.014 =
[ ]2
! 0/2+.0 m # = i
[ ]md y 10.0!4 =
[ ]2
0/2+.0 m # = i
[ ]md y 10.04 =
[ ]m #i
d # y
i yi
cG ∑∑=⇒ 4
!44
7
[ ]m y cG 10.0244 =⇒
[ ] [ ]mm #i
d # *
i *i
cG >2.07 4
!44 ==∑
∑
Tre,'ie Cnde*lini$B condii# c#
+C l * 7!0.0<
Unde[ ]ml + 0.!= [ ]ml + 02.17!0.0 =⇒
[ ]m *C 12.02+.0 −= [ ]m *C 1!.0=⇒
In concl'ie 4 condi$i# e%$e inde*lini$B #%$el Cnc$
[ ] [ ]ml m * +C 02.17!.01!.0 =<=
Montantul E/ 2
+0
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[ ]2
4 ++.0 m # c =
[ ]2
4 2+.07 m * # c = [ ]m *
2+.0
++.0=⇒
[ ]m * :2.1=⇒
Tre,'ie Cnde*lini$B condii# c#+C l * 7!0.0<
Unde
[ ]ml + >0.2= [ ]ml + :;.07!0.0 =⇒
I#r
[ ]m *C :2.1=
A%$el condi$i# n' e%$e inde*lini$B deo#rece
[ ] [ ]ml m * +C :;.07!.0:2.1 =>=
n concl'ie 4 l# #ce%$ &on$#n$ $re,'ie di%*'% 'n %$l*ior 4 c#re C&*re'nB c' idBri# %# *rei# Cnc#rc#rile d#$or#$e %e%i%&'l'i .
N' c'no#%$e& di&en%i'nile %$l*ior'l'i 4 d#r *en$r' # de$er&in# di&en%i'nile cele &#iecono&ice 4 o& reol# 'r&B$or'l %i%$e& de ec'#ii :
+1
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( ) [ ]2
4 772+.0 ml * # ec% c += η
'nde :
o 6 < re*rein$B o di&en%i'ne # %$#l*ior'l'i de ,e$ono l < re*rein$B o di&en%i'ne # onei co&*ri&#$e de idBrie
Pen$r' o di&en%ion#re econo&ic# con%iderB&+l l * 7!0.0=+
4 c#re in c#'l no%$r' e%$e[ ]ml * :;.0=+
[ ]m *l −=⇒ :;.0
In$rod'ce&
[ ]m *l −= :;.0
Cn
( ) [ ]2
!4 772+.0 ml * # ec% c += η
de 'nde re'l$B
( ) [ ]2
4 :;.0:.+72+.0 m * * # c −+=
[ ]24:;.0:.
2+.0m *
# c +=⇒
[ ]2!4:.:;.0
2+.0m *
# c =−⇒
D#r[ ]2
!4 ++.0 m # c =
[ ]2:.:;.02+.0
++.0m *=−⇒
*:.:;.0:2.1 =−⇒ [ ]m *
:.
:;.0=⇒
[ ]m * 21.0=⇒
Pen$r'
[ ]m *l −= :;.0
i
[ ]m * 21.0=
[ ]ml //.0=⇒
Se i# di&ne%ni'ne# %$l*ior'l'i de 2+62+4 i#r %'*r### i&B e%$e de >00 c&2
[ ]2
4 ++.0 m # c =
+2
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2
14 7 m # # sta lpi sor ec%b η =
[ ]2
14 0/2+.07:.+ m #b =⇒ 2
14 !2+.0 m #b =⇒
I#r
[ ]2
14 72+.0 m * # =
%$ii& c#
2
14144 m # # # b c +=
2
14414 m # # # b c −=⇒
[ ]2
14 112+.0 m # =⇒
d#r
[ ]m * # 72+.014 =
[ ]m *2+.0
112+.0=⇒
[ ]m * +.0=⇒
Ae&
[ ]2
1 0/2+.0 m # = i
[ ]md y 12+.014 =
[ ]2
2 112+.0 m # = i
[ ]md y ;+.024 =
[ ]m #i
d # y
i yi
cG ∑∑=⇒ 4
44
7
[ ]m y cG 10.0244 =⇒
[ ] [ ]mm #id # *
i *i
cG ;+.07 4
44 ==∑∑
Tre,'ie Cnde*lini$B condii# c#+C l * 7!0.0<
Unde
[ ]ml + >0.2= [ ]ml + :;.07!0.0 =⇒
[ ]m *C +.02+.0 += [ ]m *C ;0.0=⇒
In concl'ie 4 condi$i# e%$e inde*lini$B #%$el Cnc$
[ ] [ ]ml m * +C :;.07!.0;0.0 =<=
Montantul E/1
+!
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[ ]2
4 ++.0 m # c =
[ ]2
14 :;+.0 m #
=
2
14 7 m # # sta lpi sor ec%b η =
[ ]2
14 0/2+.07:.+ m #b =⇒ [ ]2
14 !2+.0 m #b =⇒
2
24 7 m # # sta lpi sor ec%b η =
[ ]2
14 0/2+.07:.+ m #b =⇒ 2
14 !2+.0 m #b =⇒
Se o,%erB cB
++.0/+.0 !4241414 =>=++ c b # # # #
⇒ n' $o#$B $#l*# &on$#n$'l'i e%$e co&*ri&#$B
+
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S$ii& cB
[ ]2
4 972+.072+.0:;+.087 m * # ec%ec% c η η ++=
[ ]2
4 /1+4!7 m * # c =⇒ [ ]m
# *
c
/14!
4=⇒
[ ]m */1.!
++.0=⇒ [ ]m * 12/.0=⇒
Ae&
[ ]2
1 102.0 m # = i
[ ]md y 0/.014 =
[ ]2
2 0!1.0 m # = i
[ ]md y 0/.024 =
[ ]2
! 01.0 m # = i
[ ]md y 0/.0!4 =
[ ]2
01.0 m # = i
[ ]md y 0/.04 =
[ ]m #i
d # y
i yi
cG ∑∑=⇒ 4
44
7
[ ]m y cG 0/.0244 =⇒
[ ] [ ]mm #i
d # *
i *i
cG /:.07 4
44 ==
∑∑
Tre,'ie Cnde*lini$B condii# c#+C l * 7!0.0<
Unde[ ]ml + >0.2= [ ]ml + :;.07!0.0 =⇒
[ ]m *C 12/.02+.0 −= [ ]m *C 12.0=⇒
In concl'ie 4 condi$i# e%$e inde*lini$B #%$el Cnc$
[ ] [ ]ml m * +C :;.07!.0!;/.0 =<=
Montantul E( 2
++
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[ ]2
+4 +12.0 m # c =
[ ]2
14 21.0 m # =
[ ]2
14 70/2+.0 m # ec%b η =
[ ]2
14 !2+.0 m #b =⇒
[ ]224 70/2+.0 m # ec%b η =
[ ]2
24 !2+.0 m #b =⇒
[ ]2
24 21/.0 m #
=
Se o,%erB cB #ri# $#l*ii din on# co&*ri&#$#
[ ]2
+424241414 +12.01+41 m # # # # # cb b =>=+++
⇒ n' $o#$B %eci'ne# $#l*ii e%$e co&*ri&#$B
+/
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S$ii& cB
[ ]2+4 972+.072+.0:2+.087 m * # ec%ec% c η η ++=
[ ]2
+4 +/4!7 m * # c =⇒ [ ]m
# *
c
+/4!
+4=⇒
[ ]m *+/4!
+12.0=⇒
[ ]m * 1.0=⇒
Ae&
[ ]21 11>.0 m # =
i
[ ]md y 0;.014 =
[ ]2
! 0!+.0 m # = i
[ ]md y 0;.0!4 =
[ ]2
0!+.0 m # = i
[ ]md y 0;.04 =
[ ]m #id # y i yi
cG ∑∑=⇒ 4+44
7[ ]m y cG 0;.0244 =⇒
[ ] [ ]mm #i
d # *
i *i
cG /:.07 4
+44 ==∑
∑
Tre,'ie Cnde*lini$B condii# c#+C l * 7!0.0<
Unde[ ]ml + /+.!= [ ]ml + 0>+.17!0.0 =⇒
[ ]m *C 1.0=
Inconcl'ie4condi$i# e%$e inde*lini$B #%$el Cnc$
[ ] [ ]ml m * +C 0>.17!.011.01.02+.0 =<=−=
Montantul E( 1
+;
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[ ]2
+4 +12.0 m # c =
[ ]2
+4 2+.07 m * # c = [ ]m *
2+.0
+12.0=⇒
[ ]m * 042=⇒
Tre,'ie Cnde*lini$B condii# c#+C l * 7!0.0<
Unde
[ ]ml + /+.!= [ ]ml + 0>+.17!0.0 =⇒
I#r
[ ]m *C 042=
A%$el condi$i# n' e%$e inde*lini$B deo#rece
[ ] [ ]ml m * +C 0>+.17!.0042 =>=
n concl'ie 4 l# #ce%$ &on$#n$ $re,'ie di%*'% 'n %$l*ior 4 c#re C&*re'nB c' idBri# %# *rei# Cnc#rc#rile d#$or#$e %e%i%&'l'i .
+
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N' c'no#%$e& di&en%i'nile %$l*ior'l'i 4 d#r *en$r' # de$er&in# di&en%i'nile cele &#iecono&ice 4 o& reol# 'r&B$or'l %i%$e& de ec'#ii :
( ) 2
+4 772+.0 ml * # ec% c += η
'nde :o 6 < re*rein$B o di&en%i'ne # %$#l*ior'l'i de ,e$ono l < re*rein$B o di&en%i'ne # onei co&*ri&#$e de idBrie
Pen$r' o di&en%ion#re econo&ic# con%iderB&+l l * 7!0.0=+
4 c#re in c#'l no%$r' e%$e[ ]ml * 0>+.1=+
[ ]ml * −=⇒ 0>+.1
In$rod'ce&[ ]ml * −= 0>+.1
Cn( )
2
+4 772+.0 ml * # ec% c += η de 'nde re'l$B
( )[ ] 2
+4 0>+.1772+.0 ml l # ec% c +−= η
( )[ ] [ ]2
+4 0>+.17:.+72+.0 ml l # c +−=⇒
( ) [ ]2
+4 2+.00>+.17!;.1 ml l # c +−=⇒
[ ]2
+4 2+.0!;.1+0.1 ml l # c +−=⇒
D#r
[ ]2
+4 +12.0 m # c =
[ ]22+.0!;.1+0.1+12.0 ml l +−=⇒
+12.0+.112.1 −=⇒ l [ ]ml
12.1
>::.0=⇒
[ ]ml ::.0=⇒
Pen$r'
[ ]ml * −= 0>+.1
i
[ ]ml ::.0=
[ ]m * 21+.0=⇒
N' *'$e& l'# #%$el de di&en%i'ni #le %$l*ior'l'i de 2+622 4 #%$el #lege& 2+62+di&en%i'ne# %$Bl*ior'l'i 8 Di&eni'ne# &ini&B # 'n'i %$Bl*i%or e%$e de 2+62+ c& 4 i#r %'*r###i&B e%$e de >00 c&2 9
+>
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[ ]2
+4 +12.0 m # c =
[ ]2
14 7 m # # sta lpi sor ec%b η =
[ ]2
14 0/2+.07:.+ m #b =⇒ [ ]2
14 !2+.0 m #b =⇒
I#r
[ ]2
14 72+.0 m * # =
%$ii& c#
[ ]2
1414/4 m # # # b c +=
[ ]2
14+414 m # # # b c −=⇒
[ ]2
14 1/>.0 m # =⇒
d#r
[ ]m * # 72+.014 =
[ ]m *2+.0
1/>.0=⇒
[ ]m * /;.0=⇒
Ae&
[ ]2
1 1/>.0 m # = i
[ ]md y +:+.014 =
[ ]2
2 0/2+.0 m # = i
[ ]md y 12+.024 =
[ ]m #i
d # y i yi cG ∑∑=⇒ 4+44
7
[ ]m y cG /.0244 =⇒
[ ] [ ]mm #i
d # *
i *i
cG ;+.07 4
+44 ==∑
∑
Tre,'ie Cnde*lini$B condii# c#+C l * 7!0.0<
Unde[ ]ml + /+4!= [ ]ml + 0>+.17!0.0 =⇒
[ ]m *C /;.02+.0 += [ ]m *C >2.0=⇒
/0
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In concl'ie 4 condi$i# e%$e inde*lini$B #%$el Cnc$
[ ] [ ]ml m * +C 0>+.17!.0>2.0 =<=
Montantul E0 1
[ ]2
/4 !+/.0 m # c =
[ ]2
/4 2+.07 m * # c = [ ]m *
2+.0
!+/.0=⇒
[ ]m * 241=⇒
Tre,'ie Cnde*lini$B condii# c#+C l * 7!0.0<
Unde
[ ]ml + +0.1= [ ]ml + +.07!0.0 =⇒
/1
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I#r
[ ]m *C 241=
A%$el condi$i# n' e%$e inde*lini$B deo#rece
[ ] [ ]ml m * +C +.07!.0241 =>=
n concl'ie 4 l# #ce%$ &on$#n$ $re,'ie di%*'% 'n %$l*ior 4 c#re C&*re'nB c' idBri# %# *rei# Cnc#rc#rile d#$or#$e %e%i%&'l'i .
N' c'no#%$e& di&en%i'nile %$l*ior'l'i 4 d#r *en$r' # de$er&in# di&en%i'nile cele &#iecono&ice 4 o& reol# 'r&B$or'l %i%$e& de ec'#ii :
( ) 2
+4 772+.0 ml * # ec% c += η
'nde :
o 6 < re*rein$B o di&en%i'ne # %$#l*ior'l'i de ,e$on
o l < re*rein$B o di&en%i'ne # onei co&*ri&#$e de idBrie
Pen$r' o di&en%ion#re econo&ic# con%iderB&+l l * 7!0.0=+
4 c#re in c#'l no%$r' e%$e[ ]ml * +.0=+
[ ]ml * −=⇒ +.0
In$rod'ce&
[ ]ml * −= +.0
Cn
( ) 2
/4 772+.0 ml * # ec% c += η
de 'nde re'l$B
( ) 2
/4 772+.0 ml * # ec% c += η
( )[ ] [ ]2
/4 +.07:.+72+.0 ml l # c +−=⇒
( ) [ ]2
/4 2+.0+.07!;.1 ml l # c +−=⇒
[ ]2
/4 2+.0!;.1/1.0 ml l # c +−=⇒
D#r [ ]2
/4 !+/.0 m # c =
[ ]22+.0!;41/140!+/.0 ml l −⋅−=⇒
l l 2+.0!;.1!+/.0/1.0 −=−⇒ [ ]ml
12.1
2+.0=⇒
/2
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[ ]ml 22.0=⇒
Pen$r'
[ ]ml * −= +.0
i
[ ]ml 22.0=
[ ]m * 2!.0=⇒
='#& di&en%i'ne# %$l*ior'l'i de 2+62+
[ ]2
/4 !+/.0 m # c =
[ ]2
14 7 m # # sta lpi sor ec%b η =
[ ]2
14 0/2+.07:.+ m #b =⇒ [ ]2
14 !2+.0 m #b =⇒
I#r
[ ]2
14 72+.0 m * # =
%$ii& c#[ ]
21414/4 m # # # b c +=
[ ]
214/414 m # # # b c −=⇒
[ ]2
14 01!.0 m # =⇒
d#r
[ ]m * # 72+.014 =
[ ]m *2+.0
01!.0=⇒
[ ]m * 0+2.0=⇒
Ae&[ ]
21 01!.0 m # =
i[ ]md y 2;/.014 =
[ ]2
2 0/2+.0 m # = i
[ ]md y 12+.024 =
[ ]m #i
d # y
i yi
cG ∑∑=⇒ 4
/44
7
[ ]m y cG 1+1.0244 =⇒
[ ] [ ]mm
#i
d # *
i *i
cG :;+.07 4
/44 ==
∑
∑
Tre,'ie Cnde*lini$B condii# c#+C l * 7!0.0<
/!
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Unde
[ ]ml + +0.1= [ ]ml + +.07!0.0 =⇒
[ ]m *C 0+2.02+.0 += [ ]m *C !02.0=⇒
In concl'ie 4 condi$i# e%$e inde*lini$B #%$el Cnc$
[ ] [ ]ml m * +C +.07!.0!02.0 =<=
Montantul E0 2
[ ]2
/4 !+/.0 m # c =
[ ]2
14 1:;.0 m # =2
14 70/2+.0 m # ec%b η =
[ ]2
14 !2+.0 m #b =⇒
[ ]2
24 2!1.0 m # =
[ ]2
!4 0/2+.0 m #
=
I#r[ ]2
4 72+.0 m * # =
S$ii& c#
[ ]24!4241414/4 m # # # # # # b c ++++=
[ ]2
!4241414/44 m # # # # # # b c −−−−=⇒
[ ]2
4 >.0 m # =
Se o,%erB cB
24!4241414 c b # # # # # >+++
⇒ n' $o#$B %eci'ne# %$Bl*ior'l'i e%$e co&*ri&#$B
S$ii& cB
[ ]2
/4 92+.0>2+.072+.0;+.087 m * # ec% c +++= η
[ ]2
/4 2>.!7 m * # c =⇒ [ ]m
# *
c
2>4!
/4=⇒
/
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[ ]m *2>4!
!+/.0=⇒
[ ]m * 10:.0=⇒
Ae&[ ]
21 1:;.0 m # = i
[ ]md y !;+.014 =
[ ]2
2 0/2+.0 m # = i
[ ]md y !;+.024 =
[ ]2
! 2!.0 m # = i
[ ]md y !;+40!4 =
[ ]2
0/2+.0 m # = i
[ ]md y 12+.04 =
[ ]2+ 10:.0 m # =
i
[ ]md y ++.0+4 =
[ ]m #i
d # y
i yi
cG ∑∑=⇒ 4
/44
7
[ ]m y cG !:.0244 =⇒
[ ] [ ]mm #i
d # *
i *i
cG >!.07 4
/44 ==∑
∑
Tre,'ie Cnde*lini$B condii# c#+C l * 7!0.0<
Tre,'ie %# di%*'ne& 'n %$#l*i%or de 2+6+0
Element
A i n i m a
l* σo NEd A z ( +
,(
+ -z(
d
0zna)i
m2 m kN/m2 kN m2 m m kNm
E1 2.4$# 9."4%."
$11%.!
#%.$#!
1.#!"
4.#!"
"1$".!2
E2 1.## ".#%"1!.!
41144.2
%"%.2
%."% 2.#%
2$#1.$$
E# %.91 #.$""#1.
#$22.24
1%."#2
%.94 1.$$1%#2.9
1E4 %.!2" 2.9% "#.1 4!#."! %.1!" %.#! 1.#4 $#4."
/+
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" 2 $
E" %.91 #.$""%2.4
4"#2."
$%.#!4
" %.14 1.$ 94.!4
E$ %.#!" 1."%2$.!
9192.14
9%."!%
%.#" %.2% #.42
Element
A i n i m a
l* σo NEd A z ( 3
,(
3 -z(
d
0zna)i
m2
m kN/m2
kN m2
mm mm kNm
E1 2.4$#9.
"4%."
$11%.!
#%.$#!
1.#!"
4.#!"
"1$".!2
E2 1.##".#
%"1!.!
41144.2
%"%."4
%.$1 2."$2929.1
$
E# %.91#.$
""#1.
#$22.24
1%.2#"
%.94 1.#" 4%.%"
E4 %.!2"2.9
%"#.1
"4!#."!
2%.#!"
%.124 %.# 1!9.9"
E" %.91#.$
""%2.4
4"#2."
$%.2#
%.92 1.#$ !24.#%
E$ %.#!"1."
%2$.!
9192.14
9 %.%!"%.#%
# %.$% 11".2
Undeinima #
- #ri# ini&ii
+l
- l'ngi&e# ini&ii
id
baa
#
G=0σ
'ndenivtotal baa nr GG 7=
4 i#r id #
-#ri# &on$#n$ilor 4 incl'%i # $#l*ilor
0
7σ total Ed
# N =- or# #6i#lB de *roiec$#re
2!107!0.1
mkN f d =
- rei%$en# 'ni$#rB de *roiec$#re l# co&*re%i'ne # id#riei
C *
- l'ngi&e# de &on$#n$ 4 din on# co&*ri&#$#
//
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ZC ,
- di%$#n# de l# cen$r#l %eci'nii 4 *nB l# cen$r'l de gre'$#$e #l onei co&*ri&#$e . Sec#lc'le#B *en$r' iec#re %en% #l #ci'nii orei %ei%&ice .
ZC Ed i na Rd , N ! 7948 =- &o&en$'l de *roiec$#re #l %eci'nii ide#le de idBrie
#lc'l'l #lorilor d)0As9 %i d
Grupls As f d d)As
m m2 kN/m2 kN m
E1 9.$%12"."
2
E2 4.% 912.!$
E# #.4%$.1$
∙10−4
#%.!1%# $4$."4
E4 2.$" "%#.92
E" #.4% $4$."4
E$ 1.%% 19%.1"
Unde sl
- di%$#n# de l# cen$rele de gre'$#$e #le %$l*iorilor de l# e6$re&i$Bi
s #
- ce# &#i &icB din$re #riile de #r&#re #le celor 2 %$l*iori
2!
107;.!0:m
kN f yd =
- rei%$en# de *roiec$#re # #r&B$'rii din cei 2 %$l*i%ori 8S!++9
yd s s #s Rd f #l ! 774 =- re%i%$en# de *roiec$#re l# incooiere core%*'nB$o#re #r&B$'rilor
din %$l*iorii de l# e6$re&i$B$i
d)As d0zna)i d
Grup
kN m kNm kNm
E1 12"."2 "1$".!2 $991.24
E2 912.!$ 2$#1.$$ #"44.42
E# $4$."4 4%.%" 14$."9
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E4 "%#.92 1!9.9" $#.!
E" $4$."4 !24.#% 1#!%.4
E$ 19%.1" #.42 22."!
Unde9484 i na Rd #s Rd Rd ! ! ! += - rei%$en# de *roiec$#re l# Cncooiere
ZC Ed i na Rd , N ! 7948 =- rei%$enei de *roiec$#re l# Cncooiere # %eci'nii ide#le de idBrie
ne#r&#$B
yd s s #s Rd f #l ! 774 =- re%i%$. de *roiec$#re l# incooiere core%*'nB$o#re #r&B$'rilor din
%$l*iorii de l# e6$re&i$B$i
3. CALULCUL FOR4ELOR TAIETOARE CAPA5ILE 6 Rd -
7
;.1 S?EMA DE A=U=
Rei%$en# de *roiec$#re l# orB $#ie$o#re Rd -
# *ereilor de idBrie conin#$B %e # c#lc'l#c' rel#i# :
21 Rd Rd Rd - - - +=
cvd Rd l t f - 771 =
Undevd f
re*rein$B rei%$en# 'ni$#rB de *roiec$#re l# orec#re # idBriei
!
vk vd
f m f
γ 7=
c'2.2= ! γ
coeicien$ de %ig'r#nB *en$r' &#$eri#l 8 con$rol nor&#l 9
00.1= m
coeicien$'l condiiilor de l'cr'
i#r vk f
%e *o#$e l'# din T#,el'l .# 4 *#gin# 0 R/
'ndevk f
re*rein$B rei%$en# de *roiec$#re # idBriei l# orec#re Cn ro%$ orion$#l
/
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!>+.0=⇒ vk f
*en$r'
2+.;mm
N f b =
%i
20.1mm
N d =σ
S#' ++=
d b
d vk vk
f f f
σ σ 71.070!.0
7.0&in 0
0vk f
5rei%$en$# 'ni$#r# c#r#c$eri%$ic# l# orec#re %', eor$ de co&*re%i'ne n'l # id#riei
Unde
20 200m
kN f vk =
$#,el'l .! din R/
2!107+.;
mkN f b =
27:.0mm
N f d d =σ
4 c'
2!
107!041m
kN f d =
2!107!.17:.0
mkN
d =⇒σ
2!1070!.1
mkN
d =⇒ σ
De 'nde
+
+=
!!
!
1070!.171.0107+.;70!.0
1070!.17.0200&invk f
[ ]22.!>>
/12&in
mkN f vk
=⇒
22.!>>m
kN f vk =⇒
%#'
2!>>2.0mm
N f vk =
I#rt e%$e gro%i&e# ini&ii *ere$el'i
cl
e%$e l'ngi&e# onei co&*ri&#$e # ini&ii *ere$el'i
21 Rd Rd Rd - - - +=- rei%$en# de *riec$#re l# orB $Bie$o#re # *ereilor din idBrie conin#$B
/>
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cvd Rd l t f - 771 =- rei%$en# de *riec$#re l# orB $Bie$o#re # *ereilor din idBrie ne#r&#$B
yd asc Rd f #- 772.02 =
- re%i%$en# de *riec$#re l# orec#re # #r&B$'rii er$ic#le din %$l*i%or'lco&*ri&#$
Undeasc #
- #ri# #r&B$'rii din %$l*ior'l de l# e6$re&i$#$e# co&*ri&#$B
yd f
- rei%$en# de *roiec$#re # #r&B$'rii din %$l*ior'l co&*ri&#$
De 'nde re'l$B *en$r' #&,ele %en%'ri #le #c$i'nii orei %ei%&ice
Grup+
Az( f 5d 671%.#6
71
As f d672 67
m2 kN/m2 kN kN m2
$.1$
∙10−4
kN/m2kN kN
E1 %.$#! 11"." #4.$! !$.%$ 11%.!#
E2 %.2 14.! 44.$4 #.%# 2.$!
E# %."#2 9$."#2.9"
#%.!1%# !$.%$
1%".%1
E4 %.1!" 11.4" #1.!" 9."2 #.%# 4!.""
E" %.#!4" $!.9" 2%.# !$.%$ 9$.44
E$ %."!% 1%#.42 #1.%2 #.%# $9.%"
Grup3
Az( f 5d 671%.#6
71
As f d672 67
m2 kN/m2 kN kN m2
$.1$
∙10−4
kN/m2
kN kN
E1 %.$#! 11"."#4.$! !$.%$ 11%.!#
E2 %."4 9!.9 29.#9 #.%# $!.42
E# %.2#" 42.$412.!9
#%.!1%# #.%# "%.2
E4 %.#!" 11.4" $.%4 2%.41 !$.%$ 9$.4!
E" %.2# 41.!# 12."2 #.%# "%.""
E$ %.%!" 1#.$% 4.% #.%# 42.11
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. VERIFIAREA SIGURANEI 8 =A PARTER 9
.1 Sig'r#n# Cn r#*or$ c' %olici$#re# l# Cncooiere c' orB #6i#lB
M#i *'in *en$r' &on$#n$'l E1 din #n%#&,l'l %$r'c$'rii 4 Cn %eci'ne# de Cnc#%$r#re n'
e%$e %#$i%#c'$B rel#i# Ed Rd ! $ ! 7≥
din P100-1200/
Gruped 8 8 Ed d
kN m
kN m kNm
E1 2>0+.!
#.12"
9%!9.4! :$991.
24
E2 1121.>2 #"%$.%% ;#"44.
42
E# 1/;.2 "2#.19 ;14$.
"9
E4 1+.0 4"#.# ;$#.
!
E" 2/.1+ #!.9! ;1#!%.
4
E$ >.11 2.4! ;22."
!
F#c$or'l de co&*or$#re$
de*inde de:
- $i*'l id#riei(
- #c$or'l de %'*r#rei%$en$#1α
α u
(- reg'l#ri$#$e# %$r'c$'rii.
Pen$r' cl#diri c' %$r'c$'r# din id#rie conin#$#
2+.1
1
=α
α u
12+.!2+.17+.27+.2 =⇒==⇒ $$ &
u
α
α
# 'r&#re 4 *en$r' &on$#n$'l E1 #& %*ori$ #r&B$'r# l#11/ φ φ +
c'[ ]21072.1 m # s
−=
;1
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Re'l$B c# *en$r' &on$#n$'l E1:
[ ]mkN ! #s Rd 7107;.!0:71072.17/0.> !
4
−−=
[ ]mkN ! #s Rd 70+.2204 =⇒
[ ]mkN ! ! ! na Rd #s Rd Rd 7984 +=
[ ]mkN ! Rd 7;2.+1/+0+.220 +=
[ ]mkN ! Rd 7;;.>!:+=⇒
[ ]mkN ! $ ! Ed Rd
7;4>0;>7;;.>!:+ =>=⇒
Grupls As f d d)As
m1%4
m2 kN/m2 kN m
E1 9.$%14.2
4
#%.! 1%#
422%.%"
E2 4.%
$.14
912.!$
E# #.4% $4$."4
E4 2.$" "%#.92
E" #.4% $4$."4
E$ 1.%% 19%.1"
d)As d0zna)i d
Grup
kN m kNm kNm
E1 422%.%" "1$".!2 9#".!!E2 912.!$ 2$#1.$$ #"44.42
E# $4$."4 4%.%" 14$."9
E4 "%#.92 1!9.9" $#.!
E" $4$."4 !24.#% 1#!%.4
E$ 19%.1" #.42 22."!
;2
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GrupEd 8 8 Ed d
kN
m
kN m kNm
E12!%9.
4
#.12"
9%!9.4! ;9#".!
$
E2922.
##"%$.%% ;
#"44.42
E#1"%.9
""2#.19 ;
14$."9
E4 9.1 4"#.# ; $#.!
E"1%.#
"#!.9! ;
1#!%.4
E$ 1"%." 2.4! ; 22."!
.2 Sig'r#n# Cn r#*or$ c' %olici$#re# l# orB $Bie$o#re
M#i *'$in in *ri&ii &on$#nii E14 E24E+ 4 Cn %eci'ne# de Cnc#%$r#re 4 n' e%$e %#$i%Bc'$B
rel#i# 4 deo#rece Ed Rd - $- 7<
A& #le%&in4 Rd -
*en$r' iec#re &on$#n$ *en$r' iec#re direc$ie # %ei%&'l'i
Grup 8
6ed 0&b 8 6Ed 67)min
kN kN kN
E1
#.12"
2.1#
1#.1" :11%.!
#
E2121.1
!#!.$$ : $!.42
E# 1$.$% "1. ; "2.2
E4 14.# 44.94 ; 4!.""
E" 2$."9 #.%9 : "%.""
E$ %.9% 2.1 ; 42.11
Se *ro*'ne #r&#re# Cn ro%$'ri c':2φ
S2++ l# $rei #%ie
Rei%$en# de *roiec$#re l# orB $Bie$o#re %e c#lc'l#B c' rel#i# :
;!
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ysd
s+
+ Rd f s
#l - 777:.0! =
Unde
+l
- l'ngi&e# *ere$el'i
[ ]2107;>.0 m # s+
−= - #ri# #r&B$'rii din ro%$'l orion$#l 4 *en$r' *rel'#re# orei $#ie$o#re
[ ]m s 2.0= - di%$#n# *e er$ic#lB Cn$re 2 rnd'ri %'cce%%ie de #r&B$'ri
2!
107210m
kN f ysd =
- rei%$en# de *roiec$#re # #r&B$'rii din ro%$'ri < S2++
Mon$#n$'l E1 :
ysd
s+
+ Rd f s
#
l - 777:.0! = [ ]kN - Rd !
! 107210720.0
107;>.0
7:+.>7:.0
−
=⇒
[ ]kN - Rd /.;+!! =⇒
Mon$#n$'l E2 :
ysd s+
+ Rd f s
#l - 777:.0! = [ ]kN - Rd
!
! 107210720.0
107;>.07!0.+7:.0
−
=⇒
[ ]kN - Rd ;0.!+1! =⇒
Mon$#n$'l E+ :
ysd s+
+ Rd f s
#l - 777:.0! = [ ]kN - Rd
!
! 107210720.0
107;>.07/+.!7:.0
−
=⇒
[ ]kN - Rd 21.22! =⇒
Grup
%.#
671<672
67# 6d 8 6Ed
kN kN kN kN
E1 11%.!# !"#.$4 $4.#! : 1#.1"
E2 $!.42 #"1.!% 419.12 : #!.$$
E# "2.2 %.%% "2.2 : "1.
E4 4!."" %.%% 4!."" : 44.94
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E" "%."" 242.21 292.!$ : #.%9
E$ 42.11 %.%% 42.11 : 2.1