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Por se tratar de um exemplo didtico faremos o exemplo para um painel macio unidirecional. Para outros tipos de lajes (outras geometrias), consulte bibliografia com informaes de procedimentos e/ou tabelas prticas. Ser fornecido um arquivo em Microsoft Excel com as formulaes para determinao dos esforos e deslocamentos. B (#&11  Clculo manual Tipo de laje = Painel Macio Unidirecional Vo longitudinal = 5,0 metros Vo transversal = 10,0 metros Revestimento = 30 Kgf/m2 , Contra Piso = 50 Kgf/m2 Sobrecarga de utilizao = 300 Kgf/m2N  $ )!&11  Clculo manualGeometria da laje:Z*$&11  Clculo manual +%&11  Clculo manualEsforo Cortante:,&&11  Clculo manualClculo da flecha/'&11  Clculo ManualMdulo de elasticidade do concreto funo da resistncia compresso do concreto. No caso ser utilizado o mdulo de elasticidade secante para anlises de deformaes:  2)&11  Clculo Manual 3(11 - Clculo ManualVariveis importantes:4*&11  Clculo Manual5Inrcia Equivalente Ie = 60% x 14289 cm4 = 8573 cm4B!)   7+&11  Clculo ManualCombinaes para flechas finais Cargas permanentes + acidentais = longa durao x (flecha permanente) + redutor acidental x flecha acidental B ZoZZ%L:-p   0` 33` Sf3f` 33g` f` www3PP` ZXdbmo` \ғ3y`Ӣ` 3f3ff` 3f3FKf` hk]wwwfܹ` ff>>\`Y{ff` R>&- {p_/̴>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> (    60  `}  `,Clique para editar o estilo do ttulo mestre- -(  08  `  dClique para editar os estilos do texto mestre Segundo nvel Terceiro nvel Quarto nvel Quinto nvel.   e  00 ^ `  >*  04 ^   @*  0  ^ `  @*P  s *޽h ?"` 3380___PPT10.w Design padro 0 *(    N tt B    n*  p88pp  N؋ tt  wB   p*  p88ppd  c $ ?pU   F  N tt  K   dClique para editar os estilos do texto mestre Segundo nvel Terceiro nvel Quarto nvel Quinto nvel.   e   TX tt .    n*  p88pp   T䱝 tt  w.   p*  p88ppH  0rllC ? 3380___PPT10.ǙO ((    Ntt B   \* p88pp  Ntt  wB  ^* p88pp  TXtt .   \* p88pp  Ttt  w.  ^* p88ppH  0rllC ? 3380___PPT10.q^}  0 $(  r  S ܀  `}   r  S  9   H  0޽h ? 33___PPT10i.Ǚt+D=' = @B +  0 A(  x  c $ 'gt   x  c $ 'g    :  3 A'%   0    15 2  0  @  210 2  0    40,15 2H  0޽h ? 33___PPT10i.Ǚt+D=' = @B +  0 1) (  r  S  'g   r  S   `}   ?  0   T  Peso da laje por metro quadrado: h x 1,0 m x 1,0 m x peso concreto = = 0,19 m x 1,0 m x 1,0 m x 2500 Kg/m3 = 475 Kg/m2B!at   *  0   T VPeso da laje por intereixo ou largura da vigota: 475 Kg/m2 x 0,25 m = 118,75 Kg/m61&>  =H  3 A"`%  H  3 A"`) ?:  3 A% 3 :  3 A)m AH  0޽h ? 33___PPT10i.ٙ0d ++D=' = @B +   0   3(  r  S x%  `}     0&  Tm "Peso Total: Peso prprio + Revestimento + ContraPiso + Acidental 475 + 30 + 50 + 300 = 855 Kgf/m2 Por intereixo = 855 x 0,25 = 213,75 Kgf/m 6 j 2,/ =   0*  2 Momento Fletor: , :  3 AC :  3 ApCs   04  @ 8Momento Fletor: M = 213,75 x 5,112 / 8 = 698 Kgf.m 89!  +H  3 A"`qF~  0,<   @  Vo terico = apoio + vo livre + apoio = 0,075 m + 5,0 m + 0,075 m = 5,15 Vo terico = 0,3 x h + vo livre + 0,3 x h = 0,057 m + 5,0 m + 0,057 m = 5,11 m Vo terico = o menor dos dois obtidos acima ,    68c"`  ,$D  0H  0޽h ? 33___PPT10.ۙ0+k=GD|' = @B D7' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* +  0 0;(  r  S G  `}   r  S H  `   :  3 Am;  0J  P u7Esforo Cortante: V = 213,75 x 5,11 / 2 = 546 Kgf "87   00    @Reao de apoio:  0dP  6   h o esforo cortante em uma faixa de um metro Reao de apoio = 546 Kgf x 4 vigotas/m = 2186 Kgf/m "ih :  3 A w H  0޽h ? 33___PPT10i.ݙ`l+D=' = @B +u  0 @(  r  S _  `}   r  S `  `   :  3 A m 3   0Xb    Nflecha em metros p = carregamento em Kgf/m vao = vo terico em metros 100000 = coeficiente adimensional E = mdulo de elasticidade do concreto em MPa I = momento de inrcia equivalente em cm4 8  ,+e1H  0޽h ? 33___PPT10i.ޙ'+D=' = @B +  0 P q(  r  S 8u  `}   r  S u  `"   ^  6}}j  S A  ??"?Ca    0w     #Para fck = 20 MPa = 21287 MPa "$# > ^  6H  0޽h ? 33___PPT10i.ߙD+D=' = @B +  0 p .(  x  c $l  `}     0  'g JMomento de inrcia: funo da geometria da seo. Quanto maior a altura, maior ser o momento de inrcia. H tabelas e mtodos para clculo de momento de inrcia de sees transversais diversas. Para nosso caso, a formulao para o clculo do momento de inrcia :  ^  6j   S A! ??"?w    0  Cu  i7Sendo b a largura e h a altura da seo transversal 88  0(    _-No nosso caso temos b = 25 cm e h = 19 cm ..^  6j   S A& -??"?f 5  -:  3 A% % :  3 A%V JSH  0޽h ? 33___PPT10i.ߙD+D=' = @B +  0 `f(  r  S 䡔  `}   r  S   `   :  3 A$H  0޽h ? 33___PPT10i.0_+D=' = @B +  0 ,$ (  r  S   `}   r  S \  `     0d  `e  YFlecha para cargas acidentais  ^  6^  6j  S A" l??"?#  l:  3 A ~ Z'  0ܰ     ]Flecha para cargas permanentes (peso prprio + rev+contra-piso) (475 + 30 + 50 = 555),@@ /,^  6j   S A n??"? Q n  68c"`z ] ,$D  0  68c"`vY,$D  0H  0޽h ? 33F > ___PPT10 ._G+D ' = @B D ' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*+d  0   (  :  3 A*t r  S ”  `}   r  S Ô 'gP   f  0"` 0  0lŔ   v |"2,0 x (0,7) + 0,3 x (0,4) = 1,5cm >#Z   68c"` G,$D  0l =i =i,$D  0`B  0DԔ= B  T?DԔ?"0?@NNN?Nil 0   0 ,$D  0`B B 0DԔ0  B  T?DԔ?"0?@NNN?N] m H  0޽h ? 33___PPT10.ӈ+͆D' = @B DS' = @BA?%,( < +O%,( < +D' =%(DF' =%(D' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* +R 0 ia(    6ܔ   `} :&11  Clculo Manual  0ޔ  'g/ w%Verificao em planilhas tipo Excel 6$ZZ#:  3 A+x#H  0޽h ? 33___PPT10i.g0-~+D=' = @B +xp^RЀ3ÿ lHb@ 000A$R )Yqã` | ,aP`peE E^ ,`fsL`i7dvTw>yn`) 9 $ى C>@2ݑĐEB@A^XAӠlfOA`?ȭr4`y#"Z[L-\ŁofrQ~q~ZkaibIf~P%. 8z _,7f] d@+b` &E!&322sq1 52032pY B \Lm L LM:@Mr` "̼@jNchf` ?X?(RYz;AUAQS eY+,ypT?,ܐ ]kxp^RЀ3ÿ lHb@00B$ G@;b bW< ]P^bRi7j:&!jUX0 tQfp1 h!hբEEQC}T- hsRgrw=wιw^zg{Ȣ`@*] n[µPV45X*: 1V@~ٮ UÚ]/$e~i[Fap^:dg+u^%h{0ED39DTPzp#&O8ո&3*D MT7*$ɗ/7vxÕZKK4g`R=^{EƄ6\`07w$(\'=MpALǹ9/d|}O{b! 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