RO-Curs 4-A [Compatibility Mode]

7/18/2019 RO-Curs 4-A [Compatibility Mode]

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CONSTRUCŢII MIXTE OŢEL - BETON

Conf.dr.ing Adrian CIUTINA

- CURS 4-a -

Grinzi com!"# $%&

Notele de curs pot fi descărcate de pe pagina de webhttp://www.ct.upt.ro/users/AdrianCiutina/

Uni'#r"i(a(#a )o*i(#+nica Timi,oaraac!*(a(#a d# Con"(r!cii/#ar(am#n(!* d# Con"(r!cii M#(a*ic# ,i M#canica Con"(r!cii*or



Adrian Ci!(ina0 Con"(r!cii mi1(# o#*-2#(on

Arm3(!ri*# (ran"'#r"a*# a*# da*#i din 2#(on (r#2!i# "3 fi#dim#n"iona(# *a "(ar#a *imi(3 !*(im3 a"(f#* nc5( "3 "# r#'in3di"(r!g#r#a $a'ari#r#a& r#ma(!r3 a da*#i din 2#(on a grinzii

com!"#. #nom#n#*# rincia*# car# (r#2!i# mi#dica(# nac#"( caz "!n(6 forf#car#a *ongi(!dina*37 d#"icar#a *ongi(!dina*3.

E!rocod# 4 "(i!*#az3 !n roc#n( minim d# armar#(ran"'#r"a*3 a da*#i din 2#(on0 #n(r! ca ac#a"(a "3 fi# caa2i*3"3 r#ia #for(!ri*# d# forf#car# $*!n#car#& rod!"# d# con#c(ori. 8#rificar#a arm3(!ri*or (ran"'#r"a*# *a forf#car# *ongi(!dina*3

"# fac# rin !rm3(oar#a form!*36

9 :.; Ca*c!*!* con#1i!nii grinzi*or com!"#CALCULUL ARMĂTURILOR TRANSVRSAL

, L Ed Rd v v≤!nd#6 v L,Ed < 'a*oar#a d# ca*c!* a forf#c3rii *ongi(!dina*# # !ni(a(#ad# *!ngim#7

v Rd < r#zi"(#na d# ca*c!* *a forf#car# *ongi(!dina*3 #n(r!

"!rafaa con"id#ra(37




Efor(!* d# ca*c!* v L,Ed (r#2!i# "3 fi# coma(i2i*3 c! ca*c!*!*

con#c(ori*or *a SLU. Efor(!* d# ca*c!* v L,Ed "# d#(#rmin3 din r#zi"(#na con#c(ori*or# grind3 P Rd ,i "# ca*c!*#az3 ca for3 # !ni(a(#a d# *!ngim# agrinzii com!"#0 rin r#*aii*#6

#n(r! grinzi com!"# c! con#c(ori di"!=i # !n "ing!r r5nd6

#n(r! grinzi com!"# c! con#c(ori di"!=i # do!3 r5nd!ri6


, Rd

L Ed f

Pv

h s=

,

2 Rd L Ed

f

Pv

h s=

!a"oarea de ca"cu" a #or#ec$rii "on%itudina"e





S!raf##*# o(#nia*# d#c#dar# rin forf#car# #n(r!

da*# *in#

S!raf##*# o(#nia*# d#c#dar# rin forf#car# #n(r!

da*# n#r'!ra(#

S!raf##*# $"#ci!ni*#& o(#nia*# (iic# d# c#dar# rinforf#car# "!n( indica(# n fig!ri*# d# mai >o"6

re&isten'a de ca"cu" "a #or#ecare




Aria arm3(!ri*or (ran"'#r"a*# d# *a ar(#a "!#rioar3 $ At &

r#"#c(i' inf#rioar# $ Ab& a da*#i din 2#(on 'or fi con"id#ra(# nca*c!*. Abh r#r#zin(3 aria arm3(!ri*or (ran"'#r"a*# nc*ina(# a*#'!(#*or din 2#(on7 Ta2*a c!(a(3 con(in!3 #"(# grinda com!"3 "a! fi1a(3 d#

ac#a"(a rin con#c(ori oa(# fi con"id#ra(3 ca arm3(!r3(ran"'#r"a*3.


O2"6 L!ngim#a "!raf##i d# forf#car# c-c din fig!ra d# mai "!" (r#2!i#*!a(3 #ga*3 c! $hsc < n3*im#a con#c(or!*!i0 d < diam#(r!* ca!*!i

g!>on!*!i0 st - di"(ana (ran"'#r"a*3 din(r# g!>oan#&6- :hsc ? d n caz!* !n!i "ing!r r5nd d# con#c(ori7- 2hsc + d + 2st n caz!* a do!3 r5nd!ri d# con#c(ori.

re&isten'a de ca"cu" "a #or#ecare





re&isten'a de ca"cu" "a #or#ecare R#zi"(#na d# ca*c!* a (!(!ror "!raf##*or o(#nia*# d#di"(r!g#r# rin forf#car# $n (a*3 "a! n n(3ri(!ri*# c! '!(#& "#

ca*c!*#az3 c! $EN @;;:-@0 .:.4&6 cotsf sk f Rd

f s f

A f v

s h

θ= ⋅

γ

Und# Asf /sf #"(# raor(!* din(r# aria arm3(!ri*or (ran"'#r"a*# =idi"(ana din(r# 2ar#*# d# armar#. 8a*oar#a Asf /sf "# #1(rag# din(a2#*#*# r#z#n(a(# an(#rior0 d!3 caz7

θf #"(# !ng+i!* 2ar#*or comrima(#. n a2"#na !n!ica*c!* rig!ro"0 o( fi !(i*iza(# !rm3(oar#*# 'a*ori6

D #n(r! (3*i comrima(# $ &D #n(r! (3*i n(in"# $ &hf #"(# n3*im#a $com*#(3& a da*#i din 2#(on.

1.0 cot 1.25 f ≤ θ ≤

1.0 cot 2.0 f ≤ θ ≤ 45 26.5 f ≥ θ ≥

45 38.6 f ≥ θ ≥





re&isten'a de ca"cu" "a #or#ecare ( contri)u*iata)"ei pro#i"ate

n caz!* r#z#n#i (a2*#i rofi*a(# iar "!rafaa d# forf#car#(r#c# rin gro"im#a da*#i0 hf (r#2!i# con"id#ra( ca fiindgro"im#a d# d#a"!ra (a2*#i rofi*a(#. /ac3 (a2*a rofi*a(3 ar# di"ozi(i'# d# 2*ocar# m#canic# "a!

d# fr#car#0 iar n#r'!ri*# "!n( #r#ndic!*ar# # grind30con(ri2!ia ac#"(#ia *a r#zi"(#na arm3(!ri*or0 # o "!rafa3 d#(i!* a-a "# fac# con"id#r5nd '#rificar#a6

cot

sf sk pe yp f Ed

f s ap

A f A f hv

s+ >

γ γ θ

(#rm#n!* ia n con"id#rar# con(ri2!ia (a2*#i rofi*a(#. A pe r#r#zin(3 aria #ficac# a (a2*#i rofi*a(# # !ni(a(#a d#*!ngim# a grinzii.

/ pe yp ap A f γ




CRIN+ ,NTRU ARMĂTURIL TRANSVRSAL

n caz!* da*#*or *in# "# r#comand3 o ari# minim3 d# armar#(ran"'#r"a*3 d# 0:F din aria 2#(on!*!i. n caz!* da*#*or n#r'!ra(#0 c! n#r'!ri*# ara*#*# "a!#r#ndic!*ar# # d#"c+id#r#a grinzii0 #"(# n#c#"ar3di"!n#r#a !n#i arii minim# d# armar# (ran"'#r"a*3 d# 0:Fdin aria 2#(on!*!i "i(!a( d#a"!ra ni'#*!*!i da*#i0 con"id#ra(# n

"#n" *ongi(!dina*. )#n(r! r#'#nir#a di"(r!g#rii grinzi*or com!"# rind#"icar#a *ongi(!dina*3 a da*#i din 2#(on n dr#(!* g!>oan#*or0"!n( a*ica(# !n#*# r#'#d#ri "!*im#n(ar# #n(r! (oa(# grinzi*#

com!"# car# r#zin(3 o di"(an3 mai mic3 d# % mm n(r#margin#a *i2#r3 a *3cii din 2#(on ,i a1a c#a mai aroia(3 acon#c(ori*or6

"# di"!n# o arm3(!r3 (ran"'#r"a*3 "!2 form3 d# 2!c*3 car#

ncon>oar3 con#c(orii7

9 :.; Ca*c!*!* con#1i!nii grinzi*or com!"#




n caz!* n car# "# fo*o"#"c con#c(ori d# (i g!>on c! ca0 iardi"(ana d# *a margin#a *3cii d# 2#(on *a a1!* c#*!i mai

aroia( con#c(or #"(# mai mar# d# 6d 0 n car# d #"(#diam#(r!* nomina* a* con#c(or!*!i0 2ar#*# n forma d# 2!c*3'or a'#a !n diam#(r! d# c#* !in 0.5d .

2ar#*# d# armar# "# 'or am*a"a c5( mai >o" c! !(in3a"ig!r5nd!-"# (o(!,i o aco#rir# "!fici#n(3 *a ar(#ainf#rioar3.

CRIN+ ,NTRU ARMĂTURIL TRANSVRSAL

9 :.; Ca*c!*!* con#1i!nii grinzi*or com!"#



Adrian Ci!(ina0 Como"i(# S(##*-Concr#(# S(r!c(!r#"

Ca*c!*!* d#formaii*or #"(# imor(an( #n(r! r#'#nir#afi"!r3rii "a! a d#form3rii #*#m#n(#*or d# ar(iionar# =i nc+id#r#0 "a! #n(r! a #'i(a d#formaii*# 'izi2i*# a*# *an=##*or

"a! (a'an#*or. 8#rificar#a 'i2raii*or *an=##*or d#'in# imor(an(3 n caz!*a*icaii*or c! d#"c+id#ri mari. Caz!ri*# d# nc3rcar# "!n( carac(#ri"(ic# com2inaii*or SLS.

9 :.@ Ca*c!*!* *a S(ar#a Limi(3 d# S#r'ici!

)rincia*#*# c#rin# a*# grinzi*or com!"# #n(r! "(ar#a *imi(3

d# "#r'ici! "# r#f#r3 *a6 calculul deformațiilor;

controlul fisurilor în beton;

vibrații.




Grinzi*# com!"# (r#2!i# ca*c!*a(# a"(f#* nc5( "3g#i*#ac#"(ora "3 fi# n *imi(#*# agr#a(# d# c*i#n(0 roi#c(an( =ia!(ori(3i*# com#(#n(#0 n concordan3 c! !(i*izar#a

in(#niona(3 a c*3dirii =i r#"#c(i' carac(#ri"(ici*# nc3rc3rii. 8a*ori*# *imi(3 !z!a*# #n(r! "3g#i*# '#r(ica*# "!n( da(# n(a2#*!* d# mai >o"6

9 :.@ Ca*c!*!* *a S(ar#a Limi(3 d# S#r'ici!CALCULUL SĂ-ILOR

Element typeLimit

wmax w2 Roofs – general L/200 L/250

Roofs – carrying personnel other than maintenance L/250 L/300

Floors – general L/250 L/300Floors and roofs supporting brittle finishing elements L/250 L/350

Floors supporting columns (unless deflection is notconsidered in the global analysis)

L/400 L/500

L-span of the beam; L = twice the cantilever span





n conformi(a(# c! EN @;;0 "3g#a(a (o(a*3 a !n#i grinzi "#ca*c!*#az3 c! r#*aia6

!nd#6 w max este săgeata în faza finală, față de linia reazemelor;

w 1 este variaţ ia săgeţ ii grinzii pentru faza de turnare a betonului (G) -faza 1;

w 2 este variația săgeții datorată încărcărilor permanente de lungă durată;

w 3 este variația săgeții datorată acțiunilor variabile (Q) – faza 2;

w c este curbura (contrasăgeata) iniţ ială pe grinda neîncărcată – faza 0;

w tot este săgeata totală a grinzii ca sumă de w 1, w 2 și w 3 .

max 1 2 3 cw w w w w= + + −





Ca*c!*!* "3g#i*or grinzi*or com!"# "# 2az#az3 #carac(#ri"(ici*# #*a"(ic#. n caz!* grinzi*or com!"# "# fac# di"(inci# n(r# "i(!aii*#grinzi*or com!"# r#z#ma(# r#"#c(i' n#r#z#ma(# #n(r! fazad# (!rnar# a 2#(on!*!i.

Con"id#r5nd c3 r#z#m3ri*# "!n( nd#3r(a(# doar d!3 c#2#(on!* #"(# n(3ri(0 d#forma(a (o(a*3 $w tot & #n(r! caz!*grinzi*or r#z#ma(# "# ca*c!*#az3 # 2aza carac(#ri"(ici*or#*#m#n(#*or com!"# $mom#n(#*# d# in#ri#&.

-rin&i"e re&eate

-rin&i"e nere&eate )#n(r! grinzi*# n#r#z#ma(#0 ordin#a d# con"(r!ci# (r#2!i#con"id#ra(3 n ca*c!*!* "3g#ii (o(a*#.





-rin&i"e nere&eate n ac#"( caz0 'ariaia iniia*3 a "3g#ii grinzii da(ori(3 nc3rc3ri*or #rman#n(# $w 1& (r#2!i# "3 fi# con"id#ra(3 ca fiind

"!ma6 'a*orii w 110 car# r#r#zin(3 "3g#a(a da(ora(3 (!rn3rii2#(on!*!i $faza @ d# con"(r!ci#&. Ac#a"(3 'a*oar# (r#2!i#ca*c!*a(3 # 2aza mom#n(!*!i d# in#ri# a* #*#m#n(!*!im#(a*ic "im*! $Ia& =i 'a*oar#a w 120 car# r#r#zin(3 "3g#a(a da(ora(3 a*(or nc3rc3ri #rman#n(# n c#a d#-a do!a faz3 a con"(r!ci#i

$"(ra(!ri "!or(0 fini"a>#&. 8a*oar#a w 12 #"(# 2aza(3 #mom#n(#*# d# in#ri# a*# "#ci!nii com!"# $I 1 =i I 2&.

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RO-Curs 4-A [Compatibility Mode]