Железобетонные и каменные конструкции. Монолитное железобетонное ребристое перекрытие с балочными плитами. Учебное пособие

3. qŠ`Šh)eqjhi p`q)eŠ h ondanp p`an)ei (opndnk|mni) `pl`Šrp{

b qe)emh“u bŠnpnqŠeoemm{u h ck`bm{u a`knj

3.1. q2=2, “*,L !=“ 2 "2%!%“2 C ……/. K= %*

b2%!%“2 C ……/ K=>*, ! K!,“2%+% C ! *!/2, C% “"% L “2=2,) “*%L “. A " K%>@H,…“2" “>3)= " C! “2="> E2 “%K%L A…%+%C!%> 2…/ … !=ƒ! ƒ…/ K=>*, “ "3A , K%> C!%> 2=A, (“A. !,“. 4). m=+!3ƒ*= …= …,. C ! = 2“ %2 C>,2/, C!,) A C!, C% “) 2 …=+!3ƒ%* … !=ƒ! ƒ…%“2@E C>,2/ C! … K! += A.

e“>, …= C ! *!/2, L“2"3 2 !="…%A !…% !=“C! > ……= …=+!3ƒ*=, 2% …= "2%!%“2 C ……/ K=>*, C!,…,A=E2 2=*› !="…%A !…% !=“C! > ……%L, 2. .C%>=+=E2, )2% “A ›…/ C=… >, C>,2/ ƒ=+!3› …/ C%>…%“2@E.

q >@E 3) 2= 3C!3+%+% ƒ=? A> …, "2%!%“2 C ……/.K=>%* …=

+ lC>O H,!,…= +!3ƒ%"%L C>%?= , C!, !=“) 2 "2%!%“2 C ……%L K=>*, (“A. 2 !,“. 4); g , !O “%%2" 2“2" ……% C%“2% ……= , "! - A ……= …=+!3ƒ*, …= 1 A2 C ! *!/2, , C% “),2=……/ “ 3) 2%A *%.--, , …2%" …= ›…%“2, C% …=+!3ƒ* γf (“A. 2=K>. 1); g“"=

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= (h"2#hC>)b"2 γ›/K γfO “%K“2" ……/L " “ 1 C%+.A "2%!%“2 C ……%L K=>*,, 2=*› C% “),2=……/L “ 3) 2%A *%.--, , …2= γf .

d> C! "=!,2 >@…%+% %C! > …, “%K“2" ……%+% " “= "2%!%- “2 C ……%L K=>*,, *=* 3› %2A )=>%“@, "/“%23 A%›…% C!,… 2@ !="…%L (1/10#1/15)l"2, = H,!,…3O (0,3÷0,5) h"2.

d> !=“) 2= "2%!%“2 C ……/.K=>%* 2! K3 2“ C%“2!%,2@ %+,K=- E?, .CE!/ A%A …2%" , C%C ! )…/. “,>, 2. .…=L2, A=*“,A=>@- …/ , A,…,A=>@…/ ,. ƒ…=) …, " !=“) 2…/. “ ) …, ..

o!, !="…/. C!%> 2=. "2%!%“2 C ……/. K=>%* l"2 ,>, C!, C!%- > 2=., %2>,)=E?,.“ !3+ %2 !3+= … K%> ) A …= 10%, > %C! > …, .CE! l , Q A%›…% "%“C%>@ƒ%"=2@“ +%2%"/A, 2=K>, =A, (C!,>.1).

b“>3)= L“2", …= K=>*3 !="…%A !…% !=“C! > ……%L …=- +!3ƒ*, q"2′ , p"2′ ƒ…=) …, l , Q %C! > E2 C% -%!A3>=A

+ α*, β*, γ*, δ*O 2=K>,)…/ *%.--, , …2/ (C!,>.1). p ƒ3>@2=2/ !=“) 2%" %K/)…% C! “2="> E2 " 2=K>,)…%L -%!A

(2=K>.4 , 5).

Š = K > , = 4

m= !,“.9 ,ƒ%K!=› …/ .=!=*2 !…/ %+,K=E?, .CE! ,ƒ+,K=- E?,. A%A …2%" l , C%C ! )…/. “,> Q " C 2,C!%> 2…%L … !=ƒ- ! ƒ…%L K=>* C!, L“2",, …= … !="…%A !…% !=“C! > ……%L …=+!3ƒ*,.

j=* %2A )=>%“@ "/H , “>, ),“>% C!%> 2%" "2%!%“2 C ……%L K=>*, K%>@H C 2,, 2% %…= !=““),2/"= 2“ C% “. A C 2,C!%- > 2…%L K=>*,.

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=)

K)

")

p,“.9.n+,K=E?, .CE!/ l , Q C 2,C!%> 2…%L … !=ƒ! ƒ…%L "2%!%“2 C ……%L K=>*,:

= O !=“) 2…= “. A=; K O .CE!/ l; " O .CE!/ Q

g= !=“) 2…/ A%A …2/ , C%C ! )…/ “,>/ 3 %C%! "2%!%“2 - C ……/.K=>%* …= > ›,2 C!,…,A=2@ ,.ƒ…=) …, C% +!=… A +>="…/. K=>%*, *%2%!/ C!,K>,› ……% A%›…% C% “),2=2@ C% -%!A3>=A:

+ l%“@O A%A …2 …= %“, %C%!/ (C% A% 3>E); Q%“@O …=,K%>@H= C%C ! )…= “,>= “C!="= ,>, “> "= %2 %“, %C%!/; b+> O H,!,…=

! K!= +>="…%L K=>*,.

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j!%A 2%+%, C!=*2,) “*, *!,"%>,… L…3E %+,K=E?3E .CE- !3 Q ƒ=A … E2 C! A%>,… L…%L ( "3A 2! 3+%>@…,*=A, " *=›-

%A C!%> 2 ). o!, .2%A 2%)*, C ! “ ) …, .CE! Qmax , Qmin “ %“@E K=>*, %C! > 2“ C% -%!A3>

o!, C%“2!% …,, %+,K=E?,. .CE! A%A …2%" ƒ…=) …, %!-,…=2 C%“> …,. C% “),2/"=E2 %K/)…% ) ! ƒ 0,1#0,2 C!%> 2= K=>*, (./l"2), = C!, C%“2!% …,, .CE! C%C ! )…/. “,> O “C!="= , “> "= %2 %C%!.

3.2. q2=2, “*,L !=“ 2 > ="…/. K= %*

q2=2,) “*,L !=“) 2 +>="…/. K=>%* A%…%>,2…/. ! K!,“2/. C ! *!/2,L “> %"=>% K/ "/C%>…,2@ “ 3) 2%A ">, …, › “2- *%“2, *%>%……, 2. . *=* !,+ > L !=A…%L *%…“2!3* ,,. n …=*% "“> “2", 2%+%, )2% C%+%……/ › “2*%“2, *%>%……, *=* C!=",>%, ƒ…=),2 >@…% A …@H C%+%……/.› “2*%“2 L +>="…/.K=>%*, C%“> - …, %K/)…% !=““),2/"=E2“ K ƒ 3) 2= ƒ=? A> …, " *%>%……=..

m=+!3ƒ*= …= +>="…3E K=>*3 C ! = 2“ %2 "2%!%“2 C ……/.

K=>%* " ", “%“! %2%) ……/.“,> G+> , p+> " A “2=.C ! “ ) …, K=>%* (“A.!,“.4 , 10).

o%“2% ……= …=+!3ƒ*= G+> “*>= /"= 2“ ,ƒ “%K“2" ……%+% " “= C%>=, C>,2/ C ! *!/2, , "2%!%“2 C ……%L K=>*, , “%K“2" ……%+% " “= 3)=“2*= +>="…%L K=>*, >,…%L, !="…%L lC> (“A.!,“.4):

G"2 = (h"2 O hC>) b"2 γ›/K γf l"2 O 2% › %2 " “= "2%!%“2 C ……%L K=>*,, + γf = 1,1;

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=) 1

K)

")

)

p,“.10.q2=2,) “*,L !=“) 2 +>="…%L K=>*,:

= O *%…“2!3* , K=>%)…%+% C ! *!/2, ; K O !=“) 2…= “. A=; " O

.CE!= l; O .CE!= Q;

1 O +>="…= K=>*=; 2 O "2%!%“2 C ……/ K=>*,

+ pn O …%!A=2,"…= C%> ƒ…= …=+!3ƒ*=, L“2"3E?= …= 1 A2 C - ! *!/2, , + γf = 1,2 (“A.2=K>.1).

l%A …2/ , C ! ! ƒ/"=E?, “,>/ " !=“) 2…/. “ ) …, . %C! ->,A C% -%!A3>=A:

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+ α*,β*, γ*,δ* …=.% ,A C% 2=K>, (C!,>. 2)

e“>, ),“>% “%“! %2%) ……/.“,> G+> , p+> " C!%> 2 +>="…%L

%C! >,2@,.ƒ…=) …, " 2%)*=.C!,>%› …, +!3ƒ%" , …= %C%!=A,. o% “) 2 ƒ…=) …,L %! ,…=2 %+,K=E?,..CE! l , Q ! *%A … 3 2“ C!%,ƒ"% ,2@ " 2=K>,)…%L -%!A (“A.2=K>. 4 , 5).

p=“) 2…/A, A%A …2=A, " C!%> 2=.“),2=E2“ A=*“,A=>@…/ C%>%›,2 >@…/ A%A …2/, = …= %C%!=.O A=*“,A=>@…/ %2!, =- 2 >@…/ A%A …2/ 3 +!=… L *%>%……, %C! > A/ C% -%!A3>

bk M+!= ˆM%“@ˆ#ˆQˆ 2 ,

+ b* O H,!,…= *%>%……/; ˆQˆ …=,A …@H= C%C ! )…= “,>= “C!="= ,>, “> "= %2 %C%!/.

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m= !,“. 10 ,ƒ%K!=› …/ %+,K=E?, .CE!/ l , Q +>="…%L K=>*, C!, L“2",, …= … “%“! %2%) ……/. “,> G , p, = …= !,“. 9O ", %+,K=E?,. .CE! M , Q C!, L“2",, …= … !=“- C! > ……%L …=+!3ƒ*, q+> , p+>.

3.3. nC! ) …, C %?=), “ …, C!%)% ?…%L =! =23!/

o%“> "/C%>… …, “2=2,) “*%+% !=“) 2= C!,“23C=E2 * 32%)- … …,E !=ƒA !%" C%C ! )…%+% “ ) …, "2%!%“2 C ……%L , +>="…%L K=>%*.o!, .2%A “> 3 2 ƒ=A 2,2@, )2% …= 3)=“2*=.C%>%›,2 >@…/. A%A …2%" C>,2= C ! *!/2, …=.% ,2“ " “›=2%L ƒ%… , "A “2 “ ! K!%A %K!=ƒ3 2 2="!%"% “ ) …, (!,“.11,=).

m= 3)=“2*=. › %2!, =2 >@…/. A%A …2%" C>,2= C%C= = 2 " !=“2 …323E ƒ%…3, , ƒ “@ K=>*= " !=“) 2=. C!,…,A= 2“ C! A%-

x

p,“.11.o%C ! )…/ “ ) …, "2%!%“2 C ……%L , +>="…%L K=>%* A%…%>,2…%+% ! K!,“2%+% C ! *!/2,

b “%%2" 2“2",, “ ! *%A … = , A, …%!A [1, 2] !=“) 2…= H,!,…= C%>*, b′ %+!=…,),"= 2“ … *%2%!/A, C! >=A,. d> 2="!%"/. K=>%* " “%“2=" A%…%>,2…/. ! K!,“2/. C ! *!/2,L b′ C!,…,A= 2“ !="…%L:

h′

1) “>, h ≥ 0,1, 2% "/K,!= 2“ : > +>="…%L K=>*, b′ ≤ 1/3 l+>;> "2%!%“2 C ……%L K=>*, b′ ≤ lC> ,>, b′ ≤ 1/3 l"2;

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2) “>, hh′ < 0,1, 2% b′ ≤ 12h′ + b.

o%> ƒ…3E "/“%23 K=>*,, !=““A=2!,"= *=* C! A%3+%>@- …3E, A%›…% %C! >,2@ C% -%!A3> :

+ l O …=,K%>@H,L (C% =K“%>E2…%L " >,),… ) !=“) 2…/L C!%> 2…/L A%A …2 ,>, A%A …2 3 +!=…, %C%!/; b O H,!,…= ! - K!= K=>*,; A0 O 2=K>,)…/L *%.--, , …2, ƒ=",“ ?,L %2 *>=““= K 2%…=, *>=““= “2=>, , C!% …2= =!A,!%"=…, K ! 2“ ,ƒ 2=K>.1

(C!,>. 4) C% C=!=A 2!3 ξ = μ% Rs , + μ%=(1,5...2,0) % 100 Rb

r),2/"= "3.! …% !=“C%>%› …, !=K%) L =!A=23!/ " C%- C ! )…%A “ ) …,, K=>*,, ƒ=?,2…/L “>%L = C!,…,A=E2 !="…/A 50#60 AA, 2%+ = C%>…= "/“%2= K=>*, K3 2 !="…= h = h0 + =. o%>3) ……3E "/“%23 %*!3+> E2 % 5 “A " A …@H3E “2%!%…3.

m=L ……= "/“%2= K=>*, %>›…= K/2@ K%>@H H,!,…/ ! K!= " 2÷2,5 !=ƒ=.e“>, .2% 3“>%", … 3 %"> 2"%! 2“ , … %K.% ,A% ƒ=-=2@“ !3+,A ƒ…=) …, A b , "…%"@ …=L2, h.

hƒ 3“>%", C!%)…%“2, …=*>%……%L C%>%“/ A › 3 …=*>%……/A, 2! ?,…=A, “%+>=“…% qm,o 52#01#2003 [2] %>›…% "/C%>… 2@“ 3“>%",

+ Q O C%C ! )…= “,>= " …%!A=>@…%A “ ) …,, %2 !=“) 2…/. …=+!3ƒ%*.

r2%)…," + %A 2!,) “*, !=ƒA !/ C%C ! )…%+% “ ) …, K=- >%*, C!,“23C=E2 * %C! > …,E C>%?= , “ ) …, C!% %>@- …%L =!A=23!/.m= 3)=“2*=. %2!, =2 >@…/. ,ƒ+,K=E?,. A%A …2%" (3 %C%!), + C>,2= C%C= = 2 " !=“2 …323E ƒ%…3, C>%?= @ =!- A=23!/ %C! > 2“ *=* " C! A%3+%>@…%A “ ) …,, (“A. C. 2.2).

o% ,ƒ" “2…/A b, h0 , l C% “),2/"=E2 C=!=A 2! A0:

A0 = M ≤ A0R . bh02Rb

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m= 3)=“2*=. › C%>%›,2 >@…/. A%A …2%" (" C!%> 2=.), + C>,2= C%C= = 2 " “›=23E ƒ%…3, C>%?= @ =!A=23!/ %C! > 2“ 2=* › , *=* " K=>*=. 2="!%"%+% “ ) …, .

o! › "“ +% "/K,!= 2“ !=“) 2…= H,!,…= C%>*, " “%%2" 2- “2",, “ ! *%A … = , A, C% %+!=…,) …,E b′ “-%!A3>,!%"=……/A, "/H , = ƒ=2 A 3“2=…=">,"= 2“ C%>%› …, … L2!=>@…%L %“,.

.% ,2@ " ! K! K=>*, , “ ) …, %>›…% !=““),2/"=2@“ *=* 2="!%- "% (“A.!,“.11, =).b.2%A “>3)= !=“) 2…/L A%A …2 C! “2="> 2“

" ", “3AA/ "3. A%A …2%": l = l“"+l!, + l“" O A%A …2, "%“C!,…,A= A/L “" “=A, C%>*,, l!O A%A …2, "%“C!,…,A= A/L

! K!%A K=>*,.

o% l! C% “),2= A A0 = M p . bh02Rb

d=> , *=* C%*=ƒ=…% "/H , %C! >,A C% 2=K>.1 (C!,>.4) η , C>%?= @ =!A=23!/ Asp, “%%2" 2“2"3E? L A%A …23 l!

Asp = ηM p . . h0 Rs

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o%>…3E C>%?= @ =!A=23!/ A%›…% …=L2, ,ƒ ƒ=",“,A%“2,

bh0

*%2%!/L … %>› … C! "/H=2@ μ %max.

p=“) 2 C!% %>@…%L =!A=23!/ "/C%>… E2 " 2=K>,)…%L -%!A (2=K>. 6).

Š = K > , = 6

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