civile 3 final deicei

8/17/2019 Civile 3 Final Deicei

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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



"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



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:

!



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 =.



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

+



#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.

/



#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

;



→=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(



- 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

>



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



!

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



!.!. 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



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!



∑=

++++==+

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



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+



#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/



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

1;



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(

1



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

1>



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 , 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


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

20



A zid= Abrut − Agol=1.9−0.687=1.21m2


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


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 , 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

21



G z=V zid , net ∙ γ z=2.65 ∙19,5=51.67kN


11+q

12+q

5=49.1kN



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 , 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


11+q

10+q

14=60.2 kN


Gbaza=Gtotal∙5=613kN

22



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 , 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


7+2q

11+q

13+q

8=31kN



σ 0=

Gbaza

A zid

=364.6

0.748=487.43

kN

m2

2!



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

E# 1.21 $$.# $4.!" 1#1.%" $"".2" "41."2

E4 %.92 "1.$! 49.1 1%%.!! "%#." "4!.$$

E" 1.## $2.4 $4.!" 122.$ $1# 4$%.9

E$ %."1 41.92 #1 !2.92 #$4.$ 4!.4#

(. )istri#utia &ortei seisice de 'roiectare intre 'eretii acti$i

+.1. #lc'l'l rigidi$#$ii con%olelor er$ic#le 8#le &on$#n$ilor9 < %e neglie## #*or$'l riglelor de c'*l#re. Pere$ii #c$ii ii o& #lege *en$r' c#lc'l n'&#i *e cei $r#n%er%#li.

i p

c

#

(

&

(

E R

7!7!

!

+=

4 'nde:

→ E &od'l'l de el#%$ici$#$e #l id#riei(

→ ( in#l$i&e# $o$#l# # *ere$el'i 8+624051400&9

→ p &

&o&en$'l de iner$ie core%*'n#$or onei #c$ie # *ere$el'i *en$r' c#re %e c#lc'le##rigidi$#$e#

→i # #ri# ini&ii *ere$el'i #c$i

2



2+



Calculul oentelor de inertie

Peretele E!*

2/



( )( )

m #

* # *

i

iiG +!.0

2+.0!:.12+.0!+.>22+.01:.1

>!;+.02+.0!:.112+.02+.0!+.>2+:;+.02+.01:.1=

⋅+⋅+⋅⋅⋅⋅+⋅⋅+⋅⋅⋅

=∑

⋅∑=

G * - di%$#n$# *#n# l# cen$r'l de gre'$#$e #l &on$#n$'l'i 1 *e direc$i# #6ei *rinci*#le 6 < 6(

( )m

#

y # y

i

iiG >2+.

2+.0!:.12+.0!+.>22+.01:.1

;2+.>2+.01:.1>2+.2+.0!:.1>2+.2+.0!+.>12+.02+.01:.1=

⋅+⋅+⋅⋅⋅⋅+⋅⋅+⋅⋅+⋅⋅

=∑

⋅∑=

G y

- di%$#n$# *#n# l# cen$r'l de gre'$#$e #l &on$#n$'l'i 1 *e direc$i# #6ei *rinci*#le J < J(

( ) ( )

2!!

2!

2

!

2

!

2

:2.2+

:0.2+.0/;+.012

2+.0/;+.002+.0!:.1

12

2+.0!:.190.282+.0++.

12

2+.0++.

90.282+.0++.12

2+.0++.:0.2+.0/;+4012

2+.0/;+40

m

dy # & & ii * i

=

⋅⋅+⋅

+⋅⋅+⋅

++⋅⋅+⋅

+

+−⋅⋅+⋅+−⋅⋅+⋅=⋅+∑=

( )

( ) 2!

!2

!2

!

>1.2:.2+.02+.0

12

2+.02+.02

02+.02+.012

2+.02+.0:.2+.02+.0

12

2+.02+.02

12

m

dy #%b

& iib

=

+⋅⋅+

⋅⋅+

+⋅⋅+⋅

+

−⋅⋅+

⋅⋅=

⋅+

⋅∑=

b

bb c

& &

& E & E E

+⋅+⋅

=

• E i E , - &od'lii de el#%$ici$#$e longi$'din#li #i idBriei i ,e$on'l'i(• I i I , - &o&en$ele de inerie #le %eci'nilor de idBrie i de ,e$on4c#lc'l#$e Cn r#*or$ c' #6ele *rinci*#le de inerie #le *ere$el'i.

V#lorile &od'l'l'i de el#%$ici$#$e %ec#n$ de %c'r$B d'r#$B #l idBriei 8E+9

Ti*'l c#lc'l'l'i8%i$'#i# de *roiec$#re9

@idBrie c'ele&en$e din#rgilB #r%B

S$#,ilire# c#r#c$eri%$icilordin#&ice

!,,, & -

Deor&#ii Cn ULS +00

2;



Deor&#ii Cn SLS 8n'&#i *en$r' %i%$e&e %$#$icnede$er&in#$e9

00

Rei%$en# c#r#c$eri%$icB l# co&*re%i'ne 8 Cn N&&29 # idBriilor :

Rei%$en#cBrB&iii &ed

8N&&29

Rei%$en# &edie # &or$#r'l'i8N&&29

M10 M+ M2.+ M110.0 .!0 !.+0 2.+ 2.1+

!.+ 2.0 2.!0 1.;+

;.+ !.+0 ".( 2.!0 1.;+2.0 2.!0 1.+ 1.0

+.0 2./+ 2.1+ 1.;+ 1.!+2.10 1.;0 1.0 1.0+

22 2:+00002:+0:+.210001000 mkN mm N f E k ==⋅==

22 2;0000002;000 mkN mm N E b ==

2N/!4+2>/101>1.2:242+

>1.22;000000:242+2:+0000 m & &

& E & E E b

bb c =+ ⋅+⋅=+ ⋅+⋅=

$ii& c#i p

c

#

(

&

(

E R

7!7!

!

+=

'nde−i #

#ri# ini&ii2/.22+.0:+.> m #i =⋅=

p= z+ b=25.82+2,91=28.73m4

m

kN R 112:+1

/.2

;+41!7!

;!42:7!

;+41!

/!4+2>/101!

=+

=

2



Peretele E"

m #

* # *

i

iiG :.1

2+.0!:.12+.00.12+.00/.+2+.0:0.1

/:+402+.0!:.1!!.22+.00.1+0.12+.00/.+!+.12+.0:0.1=

⋅+⋅+⋅+⋅⋅⋅+⋅⋅+⋅⋅+⋅⋅

=∑

⋅∑=

m #

y # y

i

iiG >0.2

2+.0!:.12+.00.12+.00/.+2+.0:0.1

>2+.2+.0!:.1>2+.2+.00.1;;+.22+.00/.+12+.02+.0:0.1=

⋅+⋅+⋅+⋅⋅⋅+⋅⋅+⋅⋅+⋅⋅

=∑

⋅∑=

2>



( ) ( ) ( )

( )

2!

2!

2!

2!

2!

2

+04;9;+.282+.02+4012

2+.02+.0

90!.282+.0!:.112

2+.0!:.10!.22+.00.1

12

2+.00.1

!:.02+.0++412

2+.0++4;:.22+.0!0.1

12

2+.0!0.1

m

dy # & & ii * i

=−⋅⋅+⋅

+

+−⋅⋅+⋅

++⋅⋅+⋅

+

+−⋅⋅+⋅

+−⋅⋅+⋅

=⋅+∑=

2!

2!

2!

2141

0!.22+.02+.012

2+.02+.0;;.22+.02+.0

12

2+.02+.02

12

m

dy #%b

& iib

=

=⋅⋅+⋅

+

⋅⋅+

⋅⋅=

⋅+

⋅∑=

22 2:+00002:+0:+.210001000 mkN mm N f E k ==⋅==

22 2;0000002;000 mkN mm N E b ==

2:+./20>!/21.1+0.;

21.12;000000+0.;2:+0000mkN

& &

& E & E E

b

bb c =

+⋅+⋅

=+

⋅+⋅=

$ii& c#i p

c

#

(

&

(

E R

7!7!

!

+=

'nde−i #

#ri# ini&ii2

!2.12+.0!0.+ m #i =⋅=

p= z+ b=7.50+1.21=8.71m4

m

kN R ;/1

!241

;+41!7!

;14:7!

;+41!

:+4/20>!/!

=+

=

Peretele E%

!0



m #

* # *

i

iiG

>>402+.0:0.12+.00.!

>0402+.0:0.10+.12+.00.!=

⋅+⋅⋅⋅+⋅⋅

=∑

⋅∑=

m # y # yi

iiG !!.2

2+.0:0.12+.00.!+2+.!2+.0:0.1;0412+.00.! =⋅+⋅ ⋅⋅+⋅⋅=∑ ⋅∑=

( ) ( ) 2!

2!

2 /2.120.12+.0!0.112

2+.0!0.1/!.02+.00.!

12

2+.00.!mdy # & & ii * i

=−⋅⋅+⋅

+⋅⋅+⋅

=⋅+∑=

( ) 2!

2!

0+/.0/.02+.02+.012

2+.02+.02

12mdy #

%b & iib =

+⋅⋅+

⋅⋅=

⋅+

⋅∑=

22 2:+00002:+0:+.210001000 mkN mm N f E k ==⋅==

22 2;0000002;000 mkN mm N E b ==

!1



22.!/+/>210+/40/241

0+/402;000000/2.12:+0000mkN

& &

& E & E E

b

bb c =

+⋅+⋅

=+

⋅+⋅=

$ii& c#i p

c

#

(

&

(

E R

7!7!

!

+

=

'nde−i #

#ri# ini&ii2>1.02+.0/+.! m #i =⋅=

p= z+ b=1.62+0.056=1.676m4

m

kN R :+./+02

>1.0

;+41!7!

/;/.17!

;+41!

2.!/+/>21!

=

+

=

Peretele E/

cm #

* # *

i

iiG ;2.0

2+.0/+.22+.0!/.1

;+.02+.0/+.2/;+402+.0!/.1=

⋅+⋅⋅⋅+⋅⋅

=∑

⋅∑=

!2



cm #

y # y

i

ii

G 0/.12+.0/+.22+.0+.1

+:.12+.0/+.212+.02+.0!/.1=

⋅+⋅⋅⋅+⋅⋅

=∑

⋅∑=

( ) ( ) 2!

2!

2 ;+.0+1.02+.0/+.212

2+.0/+.2>.02+.0:/40

12

2+.0:/40mdy # & & ii * i

=⋅⋅+⋅

+−⋅⋅+⋅

=⋅+∑=

( ) 2!

2!

112.0>+.02+.02+.012

2+.02+.02

12mdy #

%b & iib =

+⋅⋅+

⋅=

⋅+

⋅∑=

22 2:+00002:+0:+.210001000 mkN mm N f E k ==⋅==

22 2;0000002;000 mkN mm N E b ==

2+>:;:1>11240;+.0

112.02;000000;+.02:+0000mkN

& &

& E & E E

b

bb c =

+⋅+⋅

=+

⋅+⋅=

$ii& c#i p

c

#

(

&

(

E R

7!7!

!

+=

'nde−i #

#ri# ini&ii2;2.02+.0>0.2 m #i =⋅=

p= z+ b=0.75+0.112=0.862m4

m

kN R !0.+/!+

;2.0

;+41!7!

:/2.07!

;+41!

+>:;:1>!

=+

=

Peretele E(

cm #

* # *

i

iiG ;!.0

2+.0!+.12+.00.!

/:.02+.0!+.1;+.02+.00.!=

⋅+⋅⋅⋅+⋅⋅

=∑

⋅∑=

!!



cm #

y # y

i

iiG //.2

2+.0!+.12+.00.!

>;+.!2+.0!+.11+.22+.00.!=

⋅+⋅⋅⋅+⋅⋅

=∑

⋅∑=

( ) ( ) ( ) 2!

2!

20.1!1+.12+.0:+.0

12

2+.0:+.0+1.02+.00.!

12

2+.00.!mdy # & & ii * i

=−⋅⋅+⋅

+−⋅⋅+⋅

=⋅+∑=

( ) 2!

2!

21/.0!1+.12+.02+.012

2+.02+.02

12mdy #

%b & iib =

+⋅⋅+

⋅=

⋅+

⋅∑=

2/0;;>;021/.00.1

21/.02;0000000.12:+0000mkN

& &

& E & E E

b

bb c =

+⋅+⋅

=+

⋅+⋅=

!



$ii& c#i p

c

#

(

&

(

E R

7!7!

!

+=

'nde−i #

#ri# ini&ii2

>1.02+.0/+.! m #i =⋅=

p= z+ b=1.40+0.216=1.61m4

m

kN R >.101+

>1.0

;+41!7!

/1.17!

;+41!

/0;;>;0!

=+

=

Peretele E0

cm #

* # *

i

iiG >2.0

2+.0;+.02+.0>2+.02+.0+0.1

!;+.02+.0;+.0/.12+.0>2+.0:;+.02+.0+0.1=

⋅+⋅+⋅⋅⋅+⋅⋅+⋅⋅

=∑

⋅∑=

cm # y # yi

iiG

>+.02+.0;+.02+.0>2+.02+.0+0.1

+;.12+.0;+.0+;.12+.0>2+.01>.12+.0+0.1 =⋅+⋅+⋅

⋅⋅+⋅⋅+⋅⋅=∑

⋅∑=

!+



( ) ( ) ( )

( ) 2!

2!

2!

2!

2

0>.02+.02+.02+.012

2+.02+.091;+.082+.0;+.0

12

2+.0;+.0

1;+.02+.0>2+4012

2+.0>2+40+.02+.000.1

12

2+.000.1

m

dy # & & ii * i

=+⋅⋅+⋅

+−⋅⋅+⋅

+

++⋅⋅+⋅

+−⋅⋅+⋅

=⋅+∑=

( ) 2!

2!

002.01;+.02+.02+.012

2+.02+.0

12mdy #

%b & iib =−⋅⋅+⋅=

⋅+⋅∑=

2!!;+000002400>.0

002402;0000000>.02:+0000mkN

& &

& E & E E

b

bb c =

+⋅+⋅

=+

⋅+⋅=

$ii& c#i p

c

#

(

&

(

E R

7!

7!

!

+=

'nde−i #

#ri# ini&ii2!;+.02+.0+0.1 m #i =⋅=

p= z+ b=0.09+0.002=0.092m4

m

kN R 1:.!+

!;+40

;+41!7!

0>2.07!

;+41!

!!;+000!

=+

=

D#$ori$# %i&e$riei4 rigidi$#$ile %'n$ #cele#%i c' cele c#lc'l#$e %i *en$r' &on$#n$ii ;-12.

mkN R R 112:+1121 ==

mkN R R ;/1112 ==

mkN R R :+./+0210! ==

mkN R R !.+/!+> ==

mkN R R >.101+;+ ==

mkN R R 1:.!+:/ ==

!/



Re*#r$i#& or$# %ei%&ic# de ,## c#lc'l#$# iec#r'i &on$#n$:

kN F b +>.>!+=(

∑=

=12

1

4 7

ii

i

bib

R

R F F

(m

kN

Rii /.!//!>

12

1 =∑=

kN F F bb 1!.2::/.!//!>

112:+17+>.>!+12414 ===

kN F F bb 1;.121/.!//!>

;/17+>.>!+11424 ===

kN F F bb /0.1//.!//!>

:+./+027+>.>!+104!4 ===

kN F F bb !:.1/.!//!>

!.+/!+7+>.>!+>44 ===

kN F F bb

+>.2//.!//!>

>.101+7+>.>!+

;4+4 ===

kN F F bb >0.0/.!//!>

1:.!+7+>.>!+;4/4 ===

Re*#ri#& %i &o&en$'l de r#%$'rn#re iec#r'i &on$#n$ 4 #%$el :

mkN ! r 72:.>!=

∑=

= 12

1

4 7

i

i

ir ir

R

R ! !

kNm ! ! r r !.2>0+/.!//!>

112:+172:.>!12414 ===

kNm ! ! r r >2.1121/.!//!>

;/172:.>!11424 ===

kNm ! ! r r 2.1/;/.!//!>

:+./+0272:.>!104!4 ===

kNm ! ! r r 0:.1+/.!//!>

!.+/!+72:.>!>44 ===

!;



kNm ! ! r r 1+.2/:/.!//!>

>.101+72:.>!;4+4 ===

kNm ! ! r r 11.>/.!//!>

1:.!+72:.>!:4/4 ===

Rigidi$#$e

#R &i

For$# ,##

F ,4Mi

Mo&. deMr 4Mi

Gr'* R Mi F ,r#%'cire

Mr

N& N& N N N 7 & N 7 &

E1 112+1 2.1! 2>0+.!E2 ;/1 121.1; 1121.>2E! /+02.+ 1/./0 1/;.2

E +/!+.!!//!>./

>!+.+> 1.! >!.2 1+.0

E+ 101+.> 2/.+> 2/.1+E/ !+.1 0.>0 >.11

0.Calculul oentelor inco$oietoare ca'a#ile ale 'eretilor acti$i

MRd 5 MRd8n#4i9 3 MRd 8A%9

ci Ed Rd y N i na ! =948

- &o&en$'l Cncooie$or de *roiec$#re #l %eci'nii ide#le de idBrie(

•

d

Ed

ci f

N

# 7:.0= - #ri# %eci'nii ide#le de idBrie co&*ri&#$B 8Aci9

( ) yd s s s Rd f #l # ! =- rei%$en# de *roiec$#re l# Cncooiere d#$B de #r&B$'rile %$l*iorilor4 c':

• l% - di%$#n# Cn$re cen$rele de gre'$#$e #le celor doi %$l*iori de l# e6$re&i$Bi(

• A% < ce# &#i &icB din$re #riile de #r&#re #le celor doi %$l*iori(

• Jd < rei%$en# de c#lc'l # #r&B$'rii din %$l*iori.

140 7 ! Ed # N σ =- or$# #6i#lB de *roiec$#re

22

7 >+00+4>m

kN

mm

N f cd ==

- ,e$on'l din %$#l*i%ori de cl#%# 121+

!



22 1!00!0.1

2.2

:+.271

MQ

7

&d

m

kN

mm

N ====

1!00

>+007;+40;+.0

7

==d

cd ec%

f

f n

:.+=⇒ ec%n

ec%n

5coeicien$ de ec)i#len$#

Efortul Aria &orta a'iala Aria zidariei

Grup σo montantilor de proie(t NEd ideale Az()i

kN/m2 m2 kN m2

E1 4%."$ 2.9 11%.!# 1.1#"

E2 "1!.!4 2.21 1144.2%" 1.1%%

E# "#1.# 1.1! $22.241 %."1!

E4 "#.1" %. 4!#."!2 %.4""

E" "%2.44 1.%$ "#2."$ %."12

E$ 2$.!9 %.$! 192.149 %.#"$

Montantul ! 1

!>



[ ]2

14 1!+.1 m # c =

[ ]2

14 1/:;.02+40/;+40 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

2424141414 m # # # # # bb c +++=

[ ]2

2414141424 m # # # # # bb c −−−=⇒

[ ]2

24 2:1!.0 m # =⇒

0



d#r

[ ]m * # 72+.024 =

[ ]m *2+.0

2:1!.0=⇒

[ ]m * 12.1=⇒

Ae&

[ ]2

1 1/:;.0 m # = i

[ ]md y 12+.014 =

[ ]2

2 2:.0 m # = i

[ ]md y :1.024 =

[ ]2

! 0/2+.0 m # = i

[ ]md y 12+.0!4 =

[ ]2

0/2+.0 m # = i

[ ]md y 12+.04 =

[ ]m #i

d # y

i yi

cG ∑∑=⇒ 4

144

7

[ ]m y cG ++40144 =⇒

[ ] [ ]mm #i

d # *

i *i

cG 20.07 4

144 ==∑

∑

Tre,'ie Cnde*lini$B condii# c#

+C l * 7!0.0<

Unde

[ ]ml + :+.>= [ ]ml + >>+.27!0.0 =⇒

[ ]m *C 12.12+.0 += [ ]m *C !;41=⇒

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



[ ]2

24 10.1 m # c =

[ ]2

14 !2+.0 m # =

[ ]2


[ ]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



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=⇒


[ ] [ ]ml m * +C +>.17!.0/1.0 =<=

Sc)i&,B& %en%'l #ci'nii %ei%&'l'i

Montantul E" 2

!



[ ]2

24 10.1 m # c =

[ ]2

14 !+.0 m # =

[ ]2

24 !!.0 m # =

[ ]2

!4 0/2+.0 m # =

2


[ ]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 −−−−=⇒



[ ]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 ==

∑

∑


Unde[ ]ml + !0.+= [ ]ml + +>.17!0.0 =⇒

[ ]m *C 00:.0+.0 += [ ]m *C +0:.0=⇒


[ ] [ ]ml m * +C +>.17!.0+0:.0 =<=

Montantul E% 1

+



[ ]2

!4 +1;.0 m # c =

[ ]2!4 2+.07 m * # c = [ ]m * 2+.0

+1;.0

=⇒

[ ]m * 0/.2=⇒


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 .

/



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%$e de 2+62+ c& 4 i#r %'*r### &#6i&B e%$ede >00 c&2 9

;



[ ]2

!4 +1;.0 m # c =

[ ]2


[ ]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 ==∑

∑


Unde

[ ]ml + 0.!= [ ]ml + 02.17!0.0 =⇒

[ ]m *C />.02+.0 += [ ]m *C >.0=⇒


[ ] [ ]ml m * +C 02.17!.0>.0 =<=



Montantul E% 2

[ ]2

!4 +1;.0 m # c =

[ ]2

14 !2+.0 m # =

[ ]2


[ ]2

14 0/2+.07:.+ m #b =⇒ [ ]2

14 !2+.0 m #b =⇒

[ ]2


[ ]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

>



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=⇒


[ ] [ ]ml m * +C 02.17!.01!.0 =<=

Montantul E/ 2

+0



[ ]2

4 ++.0 m # c =

[ ]2

4 2+.07 m * # c = [ ]m *

2+.0

++.0=⇒

[ ]m * :2.1=⇒


Unde

[ ]ml + >0.2= [ ]ml + :;.07!0.0 =⇒

I#r

[ ]m *C :2.1=


[ ] [ ]ml m * +C :;.07!.0:2.1 =>=



+1



( ) [ ]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


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# %$l*ior'l'i de 2+62+4 i#r %'*r### &#6i&B e%$e de >00 c&2

[ ]2

4 ++.0 m # c =

+2



2


[ ]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 ==∑∑


Unde

[ ]ml + >0.2= [ ]ml + :;.07!0.0 =⇒

[ ]m *C +.02+.0 += [ ]m *C ;0.0=⇒


[ ] [ ]ml m * +C :;.07!.0;0.0 =<=

Montantul E/1

+!



[ ]2

4 ++.0 m # c =

[ ]2

14 :;+.0 m #

=

2


[ ]2

14 0/2+.07:.+ m #b =⇒ [ ]2

14 !2+.0 m #b =⇒

2


[ ]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

+



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 ==

∑∑


Unde[ ]ml + >0.2= [ ]ml + :;.07!0.0 =⇒

[ ]m *C 12/.02+.0 −= [ ]m *C 12.0=⇒


[ ] [ ]ml m * +C :;.07!.0!;/.0 =<=

Montantul E( 2

++



[ ]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

+/



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 ==∑

∑


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

+;



[ ]2

+4 +12.0 m # c =

[ ]2

+4 2+.07 m * # c = [ ]m *

2+.0

+12.0=⇒

[ ]m * 042=⇒


Unde

[ ]ml + /+.!= [ ]ml + 0>+.17!0.0 =⇒

I#r

[ ]m *C 042=


[ ] [ ]ml m * +C 0>+.17!.0042 =>=


+




( ) 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


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%$e de 2+62+ c& 4 i#r %'*r###&#6i&B e%$e de >00 c&2 9

+>



[ ]2

+4 +12.0 m # c =

[ ]2


[ ]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 ==∑

∑


Unde[ ]ml + /+4!= [ ]ml + 0>+.17!0.0 =⇒

[ ]m *C /;.02+.0 += [ ]m *C >2.0=⇒

/0




[ ] [ ]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=⇒


Unde

[ ]ml + +0.1= [ ]ml + +.07!0.0 =⇒

/1



I#r

[ ]m *C 241=


[ ] [ ]ml m * +C +.07!.0241 =>=



( ) 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


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



[ ]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


[ ]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 ==

∑

∑


/!



Unde

[ ]ml + +0.1= [ ]ml + +.07!0.0 =⇒

[ ]m *C 0+2.02+.0 += [ ]m *C !02.0=⇒


[ ] [ ]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=⇒

/



[ ]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 %# 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."

/+



" 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&#$#

//



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

/;



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

/



!>+.0=⇒ vk f

*en$r'

2+.;mm

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%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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- re%i%$en# de *riec$#re l# orec#re # #r&B$'rii er$ic#le din %$l*i%or'lco&*ri&#$

Undeasc #

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yd f

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m2 kN/m2 kN kN m2

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e%$e %#$i%#c'$B rel#i# Ed Rd ! $ ! 7≥

din P100-1200/

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de*inde de:

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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

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4

−−=

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[ ]mkN ! Rd 7;2.+1/+0+.220 +=

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m2 kN/m2 kN m

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;!



ysd

s+

+ Rd f s

#l - 777:.0! =

Unde

+l

- l'ngi&e# *ere$el'i

[ ]2107;>.0 m # s+

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2!

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ysd

s+

+ Rd f s

#

l - 777:.0! = [ ]kN - Rd !

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−

=⇒

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Mon$#n$'l E2 :

ysd s+

+ Rd f s

#l - 777:.0! = [ ]kN - Rd

!

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−

=⇒

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Mon$#n$'l E+ :

ysd s+

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!

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−

=⇒

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Grup

%.#

671<672

67# 6d 8 6Ed

kN kN kN kN

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civile 3 final deicei

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