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

o%“> %C! > …, -=*2,) “*%L C>%?= , C!% %>@…%L =!A=- 23!/ " !=“) 2…/. “ ) …, . (2=K>. 6) …=A )= 2“ C! "=!,2 >@…= “. A= =!A,!%"=…, K=>%*. g=2 A C!%,ƒ"% ,2“ !=“) 2 C%C ! )…%L =!A=23!/ , %*%…)=2 >@…% ! H=E2“ "%C!%“/, “" ƒ=……/ “ *%…- “2!3,!%"=…, A =!A=23!…/. *=!*=“%" K=>%*.

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4. p`q)eŠ a`knj op“lnrcnk|mncn onoepe)mncn qe)emh“

m` deiqŠbhe onoepe)mni qhk{ Q

4.1. nK?, “" ) …, % !=“ 2 C%C ! …%L =! =23!/ " K= *=.

d> %K “C ) …, C!%)…%“2, K=>%* C% …=*>%……/A “ ) …, A 3 %C%!, + L“2"3E2 …=,K%>@H, C%C ! )…/ “,>/ ˆQˆ, “2=",2“ C%C ! )…= =!A=23!=.bƒ=",“,A%“2, %2 “C%“%K= =!A,!%"=…, %…= A%› 2 "/C%>… 2@“ >,K% " ", .%A32%" , %2%+…32/. “2 !›… L C!, =!A,!%"=…,, " ƒ=…/A, *=!*=“=A,, >,K% 2%>@*% “ C%A%?@E

.%A32%"O C!, =!A,!%"=…,, “"=!…/A, *=!*=“=A,.o!,A … …,

+ Q — поперечная сила в наклонном сечении с длиной проекции С на продольную ось, определяемая от всех внешний сил по одну сторону от рассматриваемого наклонного сечения; Qb — поперечная сила, воспринимаемая бетоном в наклонном сечении; Qsw —поперечная сила, воспринимаемая хомутами (поперечной арматурой); Qb O C%C ! )…% 3“,> …, , "%“C!,…,A= A% K 2%…%A " …=*>%……%A “ ) …,,; Qsw O C%C ! )…% 3“,> …, , "%“C!,…,A=-A% .%A32=A, (C%C ! )…%L =!A=23!%L) (!,“.12, =).

C!,…,A= 2“ … K%> 2,5bh0Rbt , A … 0,5 bh0Rbt .

Qsw = 0,75qswC,

+ h0 ≤ C ≤ 2h0 .

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e“>, %*=› 2“ , )2%

Q ≤ Qb min = 0,5bh0Rbt ,

2% C%C ! )…= =!A=23!= (.%A32/ , %2%+…32= =!A=23!=) “2=" 2“

K%! ,=A 2!= dsw , H=+= S .%A32%", = 2=*› " %C! > …,,

C>%?= , “ ) …, %2%+…32/. “2 !›… L As inc ( “>, C! 3“A%2! …= ,. C%“2=…%"*= " " ƒ=…/. *=!*=“=.).

d> ! H …, .2%L ƒ= =), " K=>*=. C! A%3+%>@…%+% “ ) …, …= > ›,2 "%“C%>@ƒ%"=2@“ “> 3E?,A, -%!A3>=A,

+ h0 < C ≤ 2h0 .

+ q0 O …=,K%> %C=“…= C!% * , …=*>%……%+% “ ) …, (2! - ?,…/), C!,…,A= A%L !="…%L q, …% … K%> 2h0; aswO C>%?= @

C%C ! )…%+% “ ) …, % …%L " 2", .%A32=; CswO ),“>% " 2" L

.%A32%" " C%C ! )…%A “ ) …,, K=>*,; qswO C! >@…% 3“,>, " .%A32=.…= ,…, 3 >,…/ K=>*, " C! >=.…=*>%……%+% “ ) …, ; SO !=““2% …, A › 3 .%A32=A, C% >,… K=>*,; Rsw O !=“) 2…% “%C!%2,"> …, .%A32%"; Rbt O!=“) 2…% “%C!%2,"> …, K 2%…= !=“2 › …,E; Qbw O C! >@…= C%C ! )…= “,>=, "%“C!,…,A= K 2%…%A “›=2%L ƒ%…/ , .%A32=A,; SmaxO …=,K%>@H !=““2% …, A › 3 .%A32=A, " 2 .“>3)= ., *%+ = .%A32/ 2! K3E2“ C% !=“) 23.

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m=,K%> %C=“…= C!% * , …=*>%……%L 2! ?,…/ %C! > -2“ C% K%!%A C!, !=ƒ>,)…/. ƒ…=) …, . q C% -%!A3> (24).

o!," A %“…%"…/ 3*=ƒ=…, …%!A [1, 2] > !=“) 2= C%- C ! )…%L =!A=23!/ " ,ƒ+,K= A/. .> A …2=..

1.d,=A 2! .%A32%" " " ƒ=…/.*=!*=“=.,ƒ+,K= A/..> A …2%" ! *%A … 3 2“ C!,…,A=2@ … A … 5AA (=!A=23!…= C!%"%>%*= *>=““= bI) C!, "/“%2 K=>*, % 80“A, = " K=>*=. K%>@H L "/“%- 2/O … A … 8AA (“2 !›… "= =!A=23!= *>=““= `I).

2. d,=A 2! .%A32%" " “"=!…/. *=!*=“=. C!,…,A= 2“ " ƒ=",-

“,A%“2, %2 ,=A 2!= C!% %>@…/. ds !=K%),. “2 !›… L.

dsw ≥ (1/3#1/4) ds, …% … A … 6 AA " “%%2" 2“2",, “ …%!A=- 2,"…/A, %*3A …2=A, ,ƒ 3“>%",L “"=!*,.

3. b “C>%H…/. C>,2=., = 2=*› " A…%+%C3“2%2…/. , )=- “2%! K!,“2/. C>,2=. "/“%2%L A … 300 AA , K=>*=. (! K!=.) "/“%2%L A … 150 AA …= 3)=“2* .> A …2=, + C%C ! )…= “,>= C% !=“) 23 "%“C!,…,A= 2“ 2%>@*% K 2%…%A, C%C ! )…3E =!A=23- !3 A%›…% … 3“2=…=">,"=2@. b K=>*=. , ! K!=. "/“%2%L 150 AA , K%> , = 2=*› " )=“2%! K!,“2/. C>,2=. "/“%2%L 300 AA , K%- > , …= 3)=“2*=. .> A …2=, + C%C ! )…= “,>= C% !=“) 23 "%“- C!,…,A= 2“ 2%>@*% K 2%…%A, “> 3 2 C! 3“A%2! 2@ 3“2=…%"*3 C%C ! )…%L =!A=23!/ “ H=+%A … K%> 0,75h0 , … K%> 500 AA.

4.o!, %2“32“2",, %2+,K%" , C!, “%K>E …,, 3“>%", (21), !=““2% …, A › 3 C%C ! )…/A, “2 !›… A, (.%A32=A,) “> 3 2 C!,…,A=2@ " “%%2" 2“2",, “ !,“.12.b% "“ . “>3)= . !=““2% …, A › 3 C%C ! )…/A, “2 !›… A, (.%A32=A,) … %>›…% C! "/- H=2@ Smax, %C! > A% C% -%!A3> (23).

4.2. p=“ 2 C%C ! …%L =! =23!/

C!, =! ,!%"=…,, K= %* “"=!…/ , *=!*=“= ,

c>="…/ , "2%!%“2 C ……/ K=>*, A%…%>,2…%+% ! K!,“2%+% C ! *!/2, =!A,!3E2“ %K/)…% “"=!…/A, *=!*=“=A,, *%2%!/ “%“2% 2 ,ƒ !=K%),.“2 !›… L C!% %>@…%L =!A=23!/ As, C%C ! )…/.

“2 !›… L-.%A32%" Asw , A%…2=›…/.C!% %>@…/.“2 !›… L As.const,,=A 2!/ *%2%!/.…=ƒ…=)=E2“ ,ƒ *%…“2!3*2,"…/.“%%K!=› …,L

ds.const ≥ dsw+ 2 AA,

+ ds.const O ,=A 2! A%…2=›…%+% “2 !›… ; dsw O ,=A 2! .%A32=.

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nC! >,A ,=A 2! , H=+ .%A32%" " “> 3E? L C%“> %"=- 2 >@…%“2,.

1. hƒ “2=2,) “*%+% !=“) 2= … !=ƒ! ƒ…%L K=>*, (“A. 2=K>. 5) %C! >,A …=,K%>@H3E C% A% 3>E " >,),…3 C%C ! )…%L “,>/

“C!="= ,>, “> "= %2 %C%!/ ˆQˆ.e“>, %*=› 2“ , )2% Q ≤ 0,5Rbtbh0, 2% …= .2%A !=“) 2 …= L“2", C%C ! )…%L “,>/ ƒ=*=…),"= 2“ ,

= ,=A 2! , H=+ .%A32%" …=ƒ…=)=E2“ ,ƒ *%…“2!3*2,"…/. “%%K- !=› …,L " “%%2" 2“2",, “ ƒ=A )=…, A, C.4.1

2.e“>, Q > 0,5Rbt bh0, 2% !=“) 2 C!% %>›= 2“ =>@H . 3.o% -%!A3> (23)

bh2R

Smax = 0 bt ,

Q

C% “),2= A A=*“,A=>@…% %C3“2,A/L H=+ .%A32%" …= 3)=“2* “ …=,K%>@H,A ƒ…=) …, A ˆQˆ (" …=H A “>3)= .2% "2%!= %C%!=). hƒ !,“.12 " “%%2" 2“2",, “ ! *%A … = , A, …%!A 32%)…,A H=+ .%A32%" 3 %C%! S1 , " C!%> 2 S2 " ƒ=",“,A%“2, %2 "/“%2/

K=>*, h.n*%…)=2 >@…% C!,…,A= 2“ A …@H,L ,ƒ Smax , S1 H=+

.%A32%" …= C!,%C%!…/. 3)=“2*=..

o% "“ L >,… … !=ƒ! ƒ…%L K=>*, C ! *!/2, .%A32/ 3“2=- …=">,"=E2“ “ 3) 2%A ", = .CE!/ C%C ! )…/. “,> (!,“. 9," , !,“.10, ).

Š=* *=* C!, =!A,!%"=…,, C>%“*,A, “"=!…/A, *=!*=“=A, %2%+…32/ “2 !›…,, *=* C!=",>%, … >=E2, 2%, “> %"=2 >@- …%, "“ C%C ! )…= “,>= %>›…= K/2@ "%“C!,… 2= C%C ! )…/- A, “2 !›… A, (.%A32=A,) , K 2%…%A “›=2%L ƒ%…/.j%>,) “2"% C>%“*,. “"=!…/. *=!*=“%", = ƒ…=),2, , ),“>% C%C ! )…/. “2 !›- … L (.%A32%") "C%C ! )…%A “ ) …,, K=>*,, ƒ=",“,2 %2 ),“>= “2 !›… L C!% %>@…%L =!A=23!/ " !=“) 2…%A “ ) …,,, = 2=*› %2 H,!,…/ K=>*, b.

p *%A … 3 A% ),“>% C>%“*,. *=!*=“%" " ƒ=",“,A%“2, %2 H,!,…/ K=>*, C!," …% …= !,“.13.

35

q

=)

Qb

S S S S

RswAsw

Rsw Asw

AsincRsw

AsRs

Q AswRsw

C0

qsw

C

K)

p,“.12.p=“) 2…= “. A= > C!%" !*, C!%)…%“2, K=>*, C% …=*>%……%A3 “ ) …,E (=); !=“C%>%› …, .%A32%"

(C%C ! )…%L =!A=23!/) C% >,… K=>*, (K)

q O >,…= C!% * ,, …=*>%……%+% “ ) …, ; q0 O >,…= C!% * ,, …=*>%……%L 2! ?,…/ C!,…,A= A%L !="…%L q0 = q, …% … K%> q0 ≤ 2h0

p,“.13.p=“C%>%› …, C>%“*,. “"=!…/. *=!*=“%" " C%C ! )…%A “ ) …,, K=>*,

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Š C !@, ƒ…= ,=A 2! C!% %>@…%L =!A=23!/ ds, A%›…% ƒ=-=2@“ ,=A 2!%A .%A32%" dsw (C.4.1).

Š=*,A %K!=ƒ%A, …=ƒ…=)," *%>,) “2"% C%C ! )…/. “2 !›… L (.%A32%") " “ ) …,, Csw, ,=A 2! .%A32%" dsw , H=+ .%A32%" S1 >=E2 C!%" !*3 C!%)…%“2, K=>*, C% …=*>%……/A “ ) …, A " A “2=.“ A=*“,A=>@…/A, ƒ…=) …, A, C%C ! )…%L “,>/ Q “ ,“- C%>@ƒ%"=…, A ƒ=",“,A%“2 L (22) , (24)

4.3. n“…%"…/ C!=", = =! ,!%"=…, K= %* “"=!…/ , *=!*=“= ,

d> %K “C ) …, C!%)…%L, >,2 >@…%L , …= ›…%L !=K%2/ >EK%L › > ƒ%K 2%……%L *%…“2!3* ,, … %K.% ,A% … 2%>@*% C!=- ",>@…% %C! >,2@ C!% %>@…3E , C%C ! )…3E =!A=23!3, …% 2=*› +!=A%2…%, " “%%2" 2“2",, “ 2! K%"=…, A, …%!A C!% *2,!%"=…, "/C%>…,2@ =!A,!%"=…, , 2. . C!=",>@…% !=“C%>%›,2@ =!A=- 23!3 " !=“) 2…/. “ ) …, . .> A …2%". b .2%L +>=" !=““A%2!,A %“%K ……%“2, =!A,!%"=…, “"=!…/A, *=!*=“=A, A…%+%C!%> 2…/. … !=ƒ! ƒ…/. K=>%*, ".% ?,. " “%“2=" A%…%>,2…/. › > ƒ%K - 2%……/. C ! *!/2,L.

1. b “%%2" 2“2",, “ =……/A, 2=K>. 6 …=ƒ…=)=E2“ ,=A 2!/ ds , ),“>% !=K%),. “2 !›… L =!A=23!/ ns " !=“) 2…/. “ ) …, . K=>%*, C!, .2%A ! *%A … 3 2“ " *=› %A C!%> 2…%A “ ) …,, “%.!=…,2@ % ,…=*%"% *%>,) “2"% “2 !›… L (ns = 2, 4, 6 ,>, 8). d,=A 2!/ !=K%) L =!A=23!/ …=ƒ…=) …, %2 12 % 40AA, ),“>% !=ƒ…/. ,=A 2!%" … %>›…% K/2@ K%>@H 2! ..

37

2.r“2=…%"," ),“>% “2 !›… L !=K%) L C!%> 2…%L =!A=23!/

ns , ,. !=ƒA ? …, " C%C ! )…%A “ ) …,, K=>*, (" % ,… ,>,"= ! =), …=ƒ…=)=E2 ),“>% C>%“*,. “"=!…/. *=!*=“%", )2% “%-

%2" 2“2"3 2 ),“>3 C%C ! )…/. “2 !›… L (.%A32%") " !=“) 2…%A

“ ) …,, (!,“. 13) (…=C!,A !, ns = 6, 2%+ = nsw= 3).

3. Š C !@, ƒ…= ),“>% .%A32%" nsw, ,. ,=A 2! dsw, H=+ S1 , S2 (C. 4.1), = 2=*› ,=A 2!/ !=K%) L , A%…2=›…%L (*%…“2!3*2,"-

…%L) =!A=23!/, A%›…% C! “2=",2@ “. A3 =!A,!%"=…, … !=ƒ! ƒ- …%L K=>*, “ 3) 2%A A “2 %K!/"= C!% %>@…/. “2 !›… L =!A=23!/ C% .CE! A=2 !,=>%" (!,“. 14).

4. p=ƒ!=K=2/"=E2 “. A3 =!A,!%"=…, %C%!…%+% 3ƒ>= A › 3"3A “%“ …,A, C!%> 2=A, K=>*, , *%>%……%L.

nK!/" “2 !›… L …=ƒ…=)= 2“ " “%%2" 2“2",, “ .CE!=A, ,ƒ- +,K=E?,. A%A …2%". d> .2%+% …= =!A=23!…%A ) !2 › K=>*, “2!%,2“ 2=* …=ƒ/"= A= .CE!= A=2 !,=>%", C! “2="> E?= “%K%L .CE!3 C! >@…/. A%A …2%" ls, *%2%!/ A%› 2 "%“C!,- … 2@ K=>*= “ ,A E?,A“ " !=““A=2!,"= A%A “ ) …,, C!%+%…= *%>,) “2"%A =!A=23!/.

d> C%“2!% …, .CE!/ A=2 !,=>%" A%›…% "%“C%>@ƒ%"=2@“

d> C%“2!% …, .CE!/ A=2 !,=>%" C% -=*2,) “*%L C>%?= , =!A=23!/ " “ ! ,… C!%> 2= , …= %C%! (3 +!=…,) (“A. 2=K>.6) C% -%!A3> (26) %C! > E2 A%A …2, "%“C!,…,A= A/L =!A=23!%L ls. g=2 A " A=“H2=K , C!,… 2%A > C%“2!% …, .CE!/ ,ƒ+,- K=E?,. A%A …2%" (!,“. 14), C!%"% 2 +%!,ƒ%…2=>@…3E >,…,E, “%%2" 2“2"3E?3E ls.

}2= +%!,ƒ%…2=>@…= >,…, %>›…= K/2@ !=“C%>%› …= … - “*%>@*% =>@H .CE!/ ,ƒ+,K=E?,. A%A …2%", )2% C%*=ƒ/"= 2, …=“*%>@*% -=*2,) “*= =!A=23!= As-=*2 C! "/H= 2 !=“) 2…3E

As!=“). e“>, +%!,ƒ%…2=>@…= >,…, C ! “ *= 2 .CE!3 ,ƒ+,K=E?,. A%A …2%", 2% .2% +%"%!,2 % 2%A, )2% =!A=23!/ As-=*2 C%“2="> …% … %“2=2%)…%.

g=2 A C% “),2/"=E2 A%A …2 Ms > A …@H +% *%>,) “2"= “2 !›… L, )2% K3 2 “%%2" 2“2"%"=2@ %K!/"3 “2 !›… L " “ ) …, . “ A …@H,A A%A …2%A. nK/)…% %K!/"=E2 “!=ƒ3 C% "= “2 !›…

38

, …=),…=E2 C!, .2%A %K!/" “ =!A=23!/, !=“C%>%› ……%L "% "2%!%A ! 3. o!, "/C%>… …,, %K!/"%" “2 !›… L … %K.% ,A% “%K>E =2@ C!,… ,C “,AA 2!,, !=“C%>%› …, “2 !›… L " C%- C ! )…%A “ ) …,, C!%+%…=.

p,“.14.}CE!= A=2 !,=>%" , “. A= =!A,!%"=…, +>="…%L K=>*, “"=!…/A, *=!*=“=A, ("=!,=…2 1):

1 O C>%“*, “"=!…/ *=!*=“/;

2 O …= %C%!…= “"=!…= “ 2*=

g…= …%"% ƒ…=) …, Ms, “…%"= C!%"% 2 +%!,ƒ%…2=>@…3E >,- …,E …= .CE! A%A …2%".Š%)*= C ! “ ) …, .2%L >,…,, “ .CE!%L A%A …2%" , K3 2 2%)*%L 2 %! 2,) “*%+% %K!/"=.Š=*,A › %K!=- ƒ%A C%“23C=E2 , C!, %C! > …,, A “2 %K!/"= !3+,. “2 !›… L. o!, C%“2!% …,, .CE!/ A=2 !,=>%" “),2=E2, )2% %K!/"= A/L “2 !› …@ … %K.% ,A% ƒ=" “2, ƒ= 2%)*3 2 %! 2,) “*%+% %K!/"=, + %… 3› … …3› … C% !=“) 23, …= !=““2% …, … A … w , …

A … 20ds.

39

+ QŠ.Š.n O C%C ! )…= “,>= " A “2 2 %! 2,) “*%+% %K!/"= c2 !›… , " >EK%A “>3)= W ≥ (15 20)ds .

hƒ 2%) * 2 %! 2,) “*%+% %K!/"= (2.2.%.) C!%"% 2 C !C … ,- *3> !…/ >,…,, % C ! “ ) …, ,. “ +%!,ƒ%…2=>@…/A, >,…, A, Ms , %*%…)=2 >@…% “2!% 2 .CE!3 A=2 !,=>%", *%2%!= ,A 2 “23C …)=2/L ", (“A. !,“. 14).

g=2 A ,ƒ 2%)*, 2 %! 2,) “*%+% %K!/"= C% +%!,ƒ%…2=>, %2- *>= /"=E2 >,…3 =…* !%"*, w , 3“2=…=">,"=E2 A “2% -=*2,- ) “*%+% %K!/"= “2 !›… .

q"=!…/ *=!*=“/, *=* C!=",>%, “%“2% 2 ,ƒ C! A/. C!% %>@- …/. !=K%),. , A%…2=›…/. “2 !›… L, = 2=*› C !C … ,*3> !- …/. * …,A C%C ! )…/. “2 !›… L (.%A32%"); ,ƒ 3“>%", “"=!*, , K 2%…,!%"=…, ! *%A … 3 2“ C!,A … 2@ “"=!…/ *=!*=“/ “ % …%“2%!%……,A !=“C%>%› …, A C!% %>@…/. “2 !›… L.

e“>, " C!%> 2…/. “ ) …, . C% !=“) 23 2! K3 2“ C%“2=",2@ K%> "3. *=!*=“%", 2% "= *!=L…,. *=!*=“= …= > ›,2 %" “2,% +!=…, 2%! %" C!%+%…=, = %“2=>@…/ " > . .*%…%A,, A 2=>>= ! *%A … 3 2“ “2=",2@ A …@H L >,…/ ,>, › C! 3“A%2! 2@ %K!/" )=“2, !=K%),. “2 !›… L (!,“. 15) C% .CE! A=2 !,=>%".

q. A= =!A,!%"=…, %C%!…%+% 3ƒ>= A%› 2 K/2@ "/C%>… …=

"… “*%>@*,. "=!,=…2=..

1.m= %C%! 3“2=…=">,"= 2“ … “*%>@*% %C%>…,2 >@…/. C>%“*,. =!A=23!…/. *=!*=“%" “ !=K%),A, C!% %>@…/A, “2 !›- … A, " " !.… L !=“2 …32%L ƒ%… K=>*,. }2%2 "=!,=…2 2! K3 2%“2=2%)…%L H,!,…/ K=>*, > !=ƒA ? …, %C%>…,2 >@…/. *=!*=“%" (“A. !,“. 15 “ ) …, 2#2).

2.m= %C%! “"=!,"=E2 A › 3 “%K%L *%…“2!3*2,"…/ (" !.- …, ) “2 !›…, "3. “%“ …,. *=!*=“%" (,ƒ “%“ …,. C!%> 2%").

nC! > E2 … %“2=E?3E C>%?= @ %C%!…%L =!A=23!/ (As-=*2# As const), ,ƒ *%2%!%L ,ƒ+%2%"> E2 C>%“*, =!A=23!…/ “ 2*, , 3“2=…=">,"=E2 ,. " +%!,ƒ%…2=>@…%A …=C!="> …,, …= %C%!

C%" !. *=!*=“%" “ “%K>E …, A ƒ=?,2…%+% “>% (“A. !,“. 14). nK!/" “2 !›… L %C%!…%L =!A=23!/ "/C%>… 2“ C% .CE!

A=2 !,=>%" " “%%2" 2“2",, “ C!=",>=A, ,ƒ>%› ……/A, "/H .

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