Aps 7° Semestre

8/17/2019 Aps 7° Semestre

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"CÁLCULO ESTRUTURAL DE UMA LAJE, UMA VIGA E UM PILAR DE CONCRETO

ARMADO",

Rogério CR Lobo, RA-A735JG-!


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MEMORIAL DESCRITIVO

VIGAS


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S#

$! INTRODU%&O!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$

'! CARACTER(STICAS DA EDI)ICA%&O!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$

MEMORIAL DE CÁLCULO!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'

$! O*JETIVO!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!3

'! REA%+ES DAS LAJES!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!3

3! PR-DIMENSIONAMENTO DAS ALTURAS DAS VIGAS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!5

! DETERMINA%&O DOS CARREGAMENTOS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!.

!$! P/0o Pr12rio / P/0o 4 A6/4ri4!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!.!'! C4rr/g4#/8o Ui9or#/ 40 Vig40!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!.

5! DETERMINA%&O DAS REA%+ES DAS VIGAS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!7

.! DETERMINA%&O DOS ES)OR%OS DAS VIGAS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!.!$! )or:4 Cor848/!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!.!'! Mo#/8o0 )/8or/0!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$;

7! DIMENSIONAMENTO DAS ARMADURAS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$$7!$! Di#/0io4#/8o < )/=>o!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$$

7!'! Di#/0io4#/8o < )or:4 Cor848/!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$37!3! Co#2o0i:>o 4 Ar#4r4 Logi8i4!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$7!! Di#/0io4#/8o 4 Ar#4r4 / P//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$

?! DETAL@AMENTO DAS ARMADURAS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$5?!$! Co#2o0i:>o 4 Ar#4r4 Logi8i4 Po0i8i64!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$5?!'! Co#2o0i:>o 4 4r#4r4 Logi8i4 /g48i64!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$.?!3! Ar#4r4 Logi8i4 / o#2r/00>o!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$.?!! Di02o0i:>o 40 *4rr40 Logi8i4i0 4 S/:>o Tr406/r04!!!!!!!!!!!!!!!!!!!!!!!!!!!$.

?!!$! Di08ribi:>o 4 4r#4r4 24r4 4 V;.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$7?!!'! Di08ribi:>o 4 4r#4r4 24r4 4 V$'!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$

?!!3! Di08ribi:>o 4 4r#4r4 24r4 4 V$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$! COMPRIMENTO DE ANCORAGEM!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!''

!$! R/0i08Bi4 / A/rBi4!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!''!'! Co#2ri#/8o / Aor4g/# *0io!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!''

$;! DECALAGEM DA ARMADURA LONGITUDINAL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'3

$;!$! D/0o4#/8ol a

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'3

$$! ANCORAGEM NO APOIO!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'3

$$!$! Di#/0>o #i#4 o 42oio!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'3$$!'! E09or:o 4 4or4r 4 4r#4r4!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'3$$!3! Ar#4r4 N//00ri4 o 42oio!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'.

Digi8/ 8/=8oF


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$$!3!$! G4o!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'.$$!! Por84 E08ribo!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'.

ANEHOS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'7

ANEHO A ESUEMA DE VIGAS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'?

ANEHO * REA%+ES!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'

Digi8/ 8/=8oF


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INTRODU%&O

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7/102

O*JETIVO

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DETERMINA%&O DOS CARREGAMENTOS

PESO PR^PRIO E PESO DA ALVENARIA

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DIMENSIONAMENTO DAS ARMADURAS

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16/102

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'' mmd d f

M

! ! d

# # =−×

=−==

AcS orr/02o/ < r/4 / 4:o 4 r/gi>o o#2ri#i4!

Ár/4 8o84 / 4:o / 8r4:>o

2

1 10,8879,772,8092 mm !# ! ! # $%$!L =+=+=

DIMENSIONAMENTO e )OR%A CORTANTE

N4 /8/r#i4:>o o0 /09or:o0 or848/0 o i8/# ., 9or4# ob8io0 o0 64or/0

4r48/r08io0 V / 44 #4 40 8rB0 6ig40, 2oré# 24r4 o i#/0io4#/8o < 9or:4

or848/, /6/-0/ 04r 9or:4 or848/ / 2roK/8o V, ob8io 48r46é0 4 /4:>o

k d & &

×= 4,1

A8/0 o i#/0io4#/8o < 9or:4 or848/ /6/-0/ 94/r 4 6/ri9i4:>o 4

0/gr4:4 o or/8o 4 4#4 o8r4 /0#4g4#/8o,

( ) cd ck

'

d

'

d

& c'd f f

tg ( b

&

( b

sen

&

⋅

−⋅⋅≤+⋅

⋅=

⋅⋅=

250185,07,0cot

cos, θ θ

θ θ σ

o 64or /θ

é 4o84o, 04b/o /

°≥≥°

≤≤

6,2645

2cot1

θ

θ


18/102

d ( 9,0= - 42ro=i#4:>o 2/r#i8i4 2/4 N*R .$$?!

A 84b/4 7 #o08r4 4 6/ri9i4:>o o or/8o 24r4 44 6ig4!

9 Z '; MP4 ;,?59 Z $',$ N[##W CA- 5; 9X Z 35 N[##W o8 j Z $,5

Vig40V

N#

fVf

N#

VR,#iN#

bS/gr4:4 o or/8o

k,V 9' 6/ri9!

;. 5.,$; 7?,5 .$,7 5; ## ;5 ## $; ## 3,;; MP4 7,?' MP4 o

$' $.,'; '',.? 37,; '7; ## '3 ## $; ## $, MP4 7,?' MP4 o

$ 75,3; $;5,' .$,7 5; ## ;5 ## $; ## ,;3 MP4 7,?' MP4 o

T4b/4 7 - V/ri9i4:>o 4 S/gr4:4 o Cor/8o

P4r4 44 6ig4 9oi /8/r#i4o o 64or 4 4r#4r4 8r406/r04 #i#4 //00ri424r4 44 6ig4, 48r46é0 4 /4:>o

'k

ck s'

f

f

s

! 3/2

min

3,02,0=

P4r4 o i#/0io4#/8o o0 /08ribo0, 9oi 8ii4o 4 /4:>o, o0i/r4o '

r4#o0 24r4 o0 /08ribo0

'd

s'

f (

&d

s

!

⋅⋅= θ cot

Ob0 #/0#o 4o 04o CA-.; o0 /08ribo0 9 X 0/r orr/02o/8/ 4o CA-5;,

o 0/K4, 35 MP4!

D/2oi0 9oi 44o o /024:4#/8o #i#o

23

2

300

6,0minmax cd c'd f se

mm

d # ≤

≤ σ

o

23

2

200

3,0minmax cd c'd f se

mm

d # >

≤ σ

P4r4 o id#/8ro o0 /08ribo0 9or4# 4o84o0φ

/ .,3 ##, / 048i094 40

oi:/0

≥

==≤

mm

mmb'

t

5

1410

140

10φ

Ar#4r4 Tr406/r04 Mi#4 ASl[S /08ribo0 A0; 44 ALogi8i4

Vig40 ASl[S#i k,V #4=S Y A0,V

;. $' ##W '[39' 3;; ## '? ##W[## .,3 3$ ##W $; # $35 ##W

$' $' ##W '[39' 3;; ## $ ##W[## .,3 3$ ##W '; # 3 ##W


19/102

$ $' ##W '[39' 3;; ## ;; ##W[## .,3 3$ ##W ? # $?' ##W

T4b/4 ? - Di#/0io4#/8o < 9or:4 or848/

COMPOSI%&O DA ARMADURA LONGITUDINAL

A o#2o0i:>o 4 4r#4r4 ogi8i4 24r4 o b4o 8r4io4o 4 6ig4, 0/ 4 o#

40 0o#40 40 r/40 / 4:o /o8r440!

Vig40 M A0,M A0,V A0,8o84 Ac0

;. $,' N# 555 ##W $35 ##W .; ##W -

$'

.,5? N# 5? ##W

3 ##W

7 ##W -

., N# 57 ##W . ##W -

$$,.' N# $;5 ##W $ ##W -

$

?$,;. N# ?; ##W

$?' ##W

..' ##W -

7,7. N# 37 ##W .$ ##W -

$37,7. N# ??7 ##W $;. ##W 77, ##W

T4b/4 Co#2o0i:>o 4 Ar#4r4 Logi8i4 b4o 8r4io4o

DIMENSIONAMENTO DA ARMADURA DE PELE

A 4r#4r4 / 2// o8ro4 4 4b/r8r4 / 9i00r40 4 4#4 2or 4:>o / r/8r4:>o /

8/#2/r48r4, 4K4 4 r/0i08ir < 9or:4 or848/! Ar#4r4 / 2// é r/o#/6/ 24r46ig40 o# 48r4 #4ior o ig4 4 ;; ##!

6ig4 48r4 b40/ b

V;. 5;; ## $; ##

V$' 3;; ## $; ##

V$ 5;; ## $; ##

T4b/4 $; - S/:>o 40 Vig40

Co#o 2o/ 0/r 6i08o 4 84b/4 $;, 40 6ig40 V;. / V$ //00i84# / 4r#4r4 /

2//, / o#o 40 40 8B# 4 #/0#4 0/:>o 8r406/r04, /6/r>o 8/r 4 #/0#4 r/4 / 4:o,

/ é /8/r#i44 48r46é0 4 /4:>o

'c pele# ! ! ,,100

10,0≥

o/ A, é 4 r/4 4 0/:>o / or/8o!

Logo 4 4r#4r4 / 2// 24r4 40 6ig40 i8440 4i#4,


20/102

22

, 8020454/70140500100

10,0mm facemm ! pele# =×=→=××≥ φ

DETAL@AMENTO DAS ARMADURAS

COMPOSI%&O DA ARMADURA LONGITUDINAL POSITIVA

Ar#4r4 Po0i8i64 r/9/r/-0/ o!

Pri#/ir4#/8/, /6/-0/ /9iir o id#/8ro 40 b4rr40 / 6>o o#2or 40

4r#4r40 ogi8i4i0, 24r4 048i094/r 40 r/40 / 4:o /8/r#i440 o0 i8/0

48/rior/0!

A 84b/4 $$ /#o08r4 #4 #4/ir4 0i#2/0, #40 0/# /64r /# o0i/r4:>o o0

i#i8/0 24r4 4 i02o0i:>o 40 b4rr40, 2o/o oorr/r #4:40 2o08/rior#/8/, 2or848o

/00/ 0/ri4 #4 2ré-o#2o0i:>o 40 b4rr40 24r4 44 6ig4!

Vig40 A0,8o84 84/ Y A0 A0;,8

. .; ##W3 $.,; .;3 ##W

7.; ##W' $;,; $57 ##W

$'7 ##W ' $;,; $57 ##W $57 ##W

. ##W ' $;,; $57 ##W $57 ##W

$

..' ##W ' $.,; ;' ##W 77; ##W3 $',5 3.? ##W

.$ ##W' $.,; ;' ##W

.? ##W' $',5 '5 ##W

T4b/4 $$ - Co#2o0i:>o 4 Ar#4r4 Po0i8i64

COMPOSI%&O DA ARMADURA LONGITUDINAL NEGATIVA

Ar#4r4 N/g48i64 r/9/r/-0/ o!

A 84b/4 $', 400i# o#o 4 84b/4 $$, /#o08r4 #4 #4/ir4 0i#2/0, #40 0/#

/64r /# o0i/r4:>o o0 i#i8/0 24r4 4 i02o0i:>o 40 b4rr40, 2o/o oorr/r

#4:40 2o08/rior#/8/, 2or848o /00/ 0/ri4 #4 2ré-o#2o0i:>o 40 b4rr40 24r4 44

6ig4!

Vig40 A0,8o84 84/ Y A0; A0;,8$' $ ##W ' $;,; $57 ##W $57 ##W

$ $;. ##W3 $.,; .;3 ##W

$; ##W

$',5 $ ##WT4b/4 $' - Co#2o0i:>o 4 Ar#4r4 N/g48i64


21/102

ARMADURA LONGITUDINAL DE COMPRESS&O

So#/8/ 4 V$ 8/# 4r#4r4 24, o 0/K4, //00i84 / 4r#4r4 /

o#2r/00>o, 40 o8r40 40 6ig40 0o#/8/ //00i84# 4 4r#4r4 / 2or84 /08ribo /

/6/ 0/r 2/o #/o0 #4ior / o id#/8ro o /08ribo 4o84o 24r4 4 0/:>o! Logo 24r4 4

V;. / V$' 0/r 04o Y / ? ## / 24r4 4 V$ 84#bé# 0/r 04o Y / ?, o9or#/

ii4o 4 84b/4 $3!

Vig4 Ac0 Y A0; 84/$ 7? ##W ? 5; ##W '

T4b/4 $3 - Ar#4r4 ogi8i4 / o#2r/00>o

DISPOSI%&O DAS *ARRAS LONGITUDINAIS NA SE%&O TRANSVERSAL

N4 i02o0i:>o 40 b4rr40 ogi8i4i0 4 0/:>o 8r406/r04 40 6ig40 /6/-0/

/6i84r 400i#/8ri4 / 4r#4r4, r/02/i84r o obri#/8o 4 4r#4r4 / i08di40 i6r/0

/8r/ 40 b4rr40!

( )

( )

mmb'

mmd

mme

mmd mme

estribomm

cobrimentommc

agregadom)x

l

v

agregadom)x

l

h

t

140

5,12255,05,0

20

30252,12,120

3,6

25

,

,

=

=×=≥

=×=≥

==

φ

φ

φ

N#/ro / b4rr40 24r4 4 4rgr4 4 6ig4 b

( ) ( ) barrasden*meronondeenncb ht ' =−+++≥ :12 φ φ

Di08ribi:>o 4 4r#4r4 24r4 4 V;.

R/0#o 4 48i4/ / b4rr40 24r4 4 V;. $;[5;;

- 4r#4r4 ogi8i4 b4o 8r4io4o 3Y$. ] 'Y$;

- 4r#4r4 8r406/r04 E Y.,3 $ r4#o [ $; #

- 4r#4r4 / 2// Y5- 4r#4r4 ogi8i4 2or84 /08ribo 'Y?


22/102

I08r4:>o $. $Q 8/848i64 i08ribi:>o 40 b4rr40 o b4o 8r4io4o V;.

P/4 i08r4:>o $., 2o/-0/ 2/r/b/r / o /024:4#/8o orio84 é #/or / 3;

##, ogo /6/-0/ #4r 4 b40/ 4 6ig4 o 48/r4r o id#/8ro 4 4r#4r4 ogi8i4

4o844!

Ao84o 24r4 4r#4r4 ogi8i4 'Y'; ] 'Y$;, 4o #4 r/4 / 4:o / 7?5

##W, #4ior / 4 r/4 //00ri4 .; ##W, o /024:4#/8o orio84 /8r/ 40 b4rr40 é

ig4 4 37,. ## m / 3; ## i08r4:>o $7!

I08r4:>o $7 'Q 8/848i64 i08ribi:>o 40 b4rr40 o b4o 8r4io4o V;.

D/9iio 4 i08ribi:>o 4 4r#4r4, 2o/-0/ 44r o o6o 64or / c

( ) ( )

!503,48'

786

8,37991

7923142

3,767923,413142'

%k mmd novo

d novo

←≅=

=×+×

××+××=

P4r4 /8/r#i4r o /024:4#/8o /8r/ o0 /024:4#/8o0 4 4r#4r4 / 2//

mm# pele 8052,775

1,36)353,41(500≈=

−+−=


23/102

I08r4:>o $? - Di08ribi:>o 4 Ar#4r4 4 Vig4 ;.

Di08ribi:>o 4 4r#4r4 24r4 4 V$'

R/0#o 4 48i4/ / b4rr40 24r4 4 V$' $;[3;;

- 4r#4r4 ogi8i4 2o0i8i64 b4o 8r4io4o 'Y$; 24r4 o0 oi0 6>o0

- 4r#4r4 ogi8i4 /g48i64 b4o 8r4io4o 'Y$;

- 4r#4r4 8r406/r04 E Y.,3 $ r4#o [ '; #

- 4r#4r4 ogi8i4 2or84 /08ribo 'Y?


24/102

I08r4:>o $ Di08ribi:>o 4 4r#4r4 4 V$'

4 Ar#4r4 4 0/:>o / #o#/8o 2o0i8i6o

b Ar#4r4 4 0/:>o / #o#/8o /g48i6o

P4r4 /084 6ig4 o o6o c é 37,' ##, 64or #4ior / o 4o84o iii4#/8/, 2oré#

/004 48/r4:>o >o #4 o0 64or/0 40 4r#4r40 /o8r440!

Di08ribi:>o 4 4r#4r4 24r4 4 V$

R/0#o 4 48i4/ / b4rr40 24r4 4 V$ $;[5;;

- 4r#4r4 ogi8i4 2o0i8i64 b4o 8r4io4o 'Y$. ] 3Y$',5 2ri#/iro 6>o /

'Y$. ] 'Y$',5 0/go 6>o

- 4r#4r4 ogi8i4 /g48i64 b4o 8r4io4o 3Y$. ] Y$',5

- 4r#4r4 ogi8i4 /g48i64 b4o o#2ri#io 'Y?

- 4r#4r4 8r406/r04 E Y.,3 $ r4#o [ ? #

- 4r#4r4 / 2// Y5

O 2ri#/iro 6>o 4 6ig4 $, o 2ri#/iro i#/0io4#/8o, 84#bé# 8/# 3 b4rr40, o

4 o#o 9oi 6i08o 4 V;., >o 4b/# 4 0/:>o 4 6ig4, o 0/K4, o /024:4#/8o

orio84 é #/or / o //00rio! Por848o 4 4r#4r4 ogi8i4 / 4:o 24r4 o

2ri#/iro 6>o 9oi #oi9i4o 24r4 'Y'; ] 'Y$;, ogo /08/ 8r/o 4 6ig4 $ 8/r 0/:>o

0/#/48/ < 4 V;.!

Pri#/iro 6>o


25/102

( ) ( )

!503,48'

786

8,37991

7923142

3,767923,413142'

%k mmd novo

d novo

←≅=

=×+×

××+××=

P4r4 /8/r#i4r o /024:4#/8o /8r/ o0 /024:4#/8o0 4 4r#4r4 / 2//

mm# pele 8052,775

1,36)353,41(500 ≈=−+−=

S/go 6>o

( ) ( )

!503,52'

648

6,33879

12322012

5,7312323,392012'

%k mmd novo

d novo

←≅=

=×+×

××+××=

P4r4 /8/r#i4r o /024:4#/8o /8r/ o0 /024:4#/8o0 4 4r#4r4 / 2//

mm# pele 8008,785

1,36)2,343,39(500≈=

−+−=

I08r4:>o $ Di08ribi:>o 4 4r#4r4 4 V$, 24r4 #o#/8o 2o0i8i6o

4 Ar#4r4 o 2ri#/iro 8r/o / #o#/8o 2o0i8i6o

b Ar#4r4 o 0/go 8r/o / #o#/8o /g48i6o

No 8r/o / #o#/8o /g48i6o 4 6ig4 $, o 2ri#/iro i#/0io4#/8o, 84#bé#

8/# 3 b4rr40, 2or848o 4 4r#4r4 ogi8i4 / 4:o 24r4 o 2ri#/iro 6>o 9oi #oi9i4o

24r4 'Y'; ] Y$',5, !

/8/r#i4o o /024:4#/8o /8r/ o0 /024:4#/8o0 4 4r#4r4 / 2//


26/102

mm# pele 708,705

1,36)5,322,363,41(500≈=

−++−=

I08r4:>o '; Di08ribi:>o 4 4r#4r4 4 V$, 24r4 #o#/8o /g48i6o

( ) ( ) ( )

!603,64'1120

4,72061

123)22(3142

11012325,7712323,413142'

%k mmd novo

d novo

←≅=

=

×++×

××+××+××=

COMPRIMENTO DE ANCORAGEM

RESISTnNCIA DE ADERnNCIA

ctbbd f f ⋅⋅⋅= 321 η η η


27/102

64or / 4o 4 r/0i08Bi4 < 8r4:>o ir/84 o or/8oc

ck ctb

f f

γ

3/22,0=

MPa f ctb 05,14,1

202,0 3/2

≈×

=

−

−

−

=

nervuradasbarras

dentadasbarras

lisasbarras

25,2

4,1

1

1η

−

−=

ader+nciam)

ader+nciaboa

7,0

12η

>→−≤→

=mm

mm

32100

132

321

3φ

φ

φ η

Co#o 40 b4rr40 0>o 8o40 CA-5;, /r6r440 / o# Y 3' ##!

MPa f bd 37,205,11125,2 =×××= r/gi>o / bo4 4/rBi4

MPa f bd 66,105,17,0125,2 =×××=

r/gi>o / # 4/rBi4

COMPRIMENTO DE ANCORAGEM *ÁSICO

9,4537,2

435

4

1

4

1=×=⋅=

bd

d

#

b

f

f l

φ

r/gi>o / bo4 4/rBi4

# φ ? $; $',5 $. ';

bl 3.7, ## 5,' ## 57,; ## 73,7 ## $?, ##

T4b/4 $ Co#2ri#/8o / Aor4g/# *0io r/gi>o / bo4 4/rBi4

6,6566,1

435

4

1

4

1=×=⋅=

bd

d

#

b

f

f l

φ

r/gi>o / # 4/rBi4

# φ

? $; $',5 $. ';


28/102

bl 5',? ## .5.,; ## ?';,; ## $;,. ## $3$',; ##

T4b/4 $5 Co#2ri#/8o / Aor4g/# *0io r/gi>o / # 4/rBi4

DECALAGEM DA ARMADURA LONGITUDINAL

DESLOCAMENTOl a

θ cot..5,0 ( al =

V;. mal 30,05,1405,05,0 =××=

V$' mal 20,05,1243,05,0 =××=

V$. mal 30,05,1405,05,0 =××=

ANCORAGEM NO APOIO

DIMENS&O M(NIMA DO APOIO

≥ mml b

60

8min,

φ

# φ ? $; $',5 $. ';

min,bl . ## ?; ## $;; ## $'? ## $.; ##

T4b/4 $. Di#/0>o #i#4 o 42oio

ES)OR%O A ANCORAR A ARMADURA

θ cot0,5Vdaoios, ⋅=

V. Y$; V Z 5.,$; N V. Y'; V Z 5.,$; N


29/102

==≥

==×=

=

=×

=

=××=

mm

mmlb

l

mml

mm !

mm !

k" R

b

necb

ef #

apoio#

apoio s

100

10

13877,133,0

*3966,39157

4,135

9,45

157

4,135435

109,58

9,585,154,785,0

min,

,

2

,

23

,

,

φ

φ

φ φ

==≥

==×=

=

=×

=

=××=

mm

mmlb

l

mml

mm !

mm !

k" R

b

necb

ef #

apoio#

apoio s

100

10

*27577,133,0

19890,9628

4,135

9,45

628

4,135435

109,58

9,585,154,785,0

min,

,

2

,

23

,

,

φ

φ

φ φ

I08r4:>o '$ D/44g/# V.

V$' Y$; V Z , N

==

≥

==×=

=

=×

=

=××=

mm

mmlb

l

mml

mm !

mm !

k" R

b

necb

ef #

apoio#

apoio s

100

10

*13877,133,0

6663,6157

2,169,45

157

7,22435

1087,9

87,95,116,135,0

min,

,

2

,

23

,

,

φ

φ

φ φ

V$' Y$; V Z $.,' N

==

≥

==×=

=

=×

=

=××=

mm

mmlb

l

mml

mm !

mm !

k" R

b

necb

ef #

apoio#

apoio s

100

10

*13877,133,0

1144,11157

1,399,45

157

1,39435

1017

0,175,168,225,0

min,

,

2

,

23

,

,

φ

φ

φ φ


30/102

I08r4:>o '' D/44g/# V$'

V$ Y$; V Z 3?,; N

==≥

==×=

=

=×

=

=××=

mm

mmlb

l

mml

mm !

mm !

k" R

b

necb

ef #

apoio#

apoio s

100

10

7,13777,133,0

*2688,261577,919,45

157

7,91435

109,39

9,395,12,535,0

min,

,

2

,

23

,

,

φ

φ

φ φ

V$ Y'; V Z 3?,; N

==≥

==×=

=

=×

=

=××=

mm

mmlb

l

mml

mm !

mm !

k" R

b

necb

ef #

apoio#

apoio s

100

10

*27577,133,0

13407,66287,919,45

628

7,91435

109,39

9,395,12,535,0

min,

,

2

,

23

,

,

φ

φ

φ φ

V$ Y$',5 V Z 3.,. N

==≥

==×=

=

=×

=

=××=

mm

mmlb

l

mml

mm !

mm !

k" R

b

necb

ef #

apoio#

apoio s

100

10

17277,133,0

*2076,16245

3,889,45

245

3,88435

1043,38

43,385,124,515,0

min,

,

2

,

23

,

,

φ

φ

φ φ

V$ Y$. V Z 3.,. N

==≥

==×=

=

=×

=

=××=

mm

mmlb

l

mml

mm !

mm !

k" R

b

necb

ef #

apoio#

apoio s

100

10

*22077,133,0

1611,10402

3,889,45

402

3,88435

1043,38

43,385,124,515,0

min,

,

2

,

23

,

,

φ

φ

φ φ

V$ Y$',5 V Z 75,3 N V$ Y'; V Z 75,3 N


31/102

==≥

==×=

=

=×

=

=××=

mm

mmlb

l

mml

mm !

mm !

k" R

b

necb

ef #

apoio#

apoio s

100

10

17277,133,0

*21217491

8,1819,45

491

8,181435

1006,79

06,795,142,1055,0

min,

,

2

,

23

,

,

φ

φ

φ φ

==≥

==×=

=

=×

=

=××=

mm

mmlb

l

mml

mm !

mm !

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b

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ef #

apoio#

apoio s

100

10

22077,133,0

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8,1819,45

628

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1006,79

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,

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φ

φ

φ φ

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ARMADURA NECESSÁRIA NO APOIO

G4o

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D CA-5; CA-.;

Y '; ## 5Y .Y

Y p '; ## ?Y -

T4b/4 $7 G4o o0 42oio0

PORTA ESTRI*O

O0 2or84 /08ribo0 /08>o /#o08r4o0 4 2r44 ;5 o /844#/8o 40 6ig40,

400i# o#o 4 i02o0i:>o o0 /08ribo0!


32/102

ANEHOS


33/102

ANEHO A ESUEMA DE VIGAS


34/102

ANEHO * REA%+ES


35/102

MEMORIAL DESCRITIVO

LAJES


36/102


37/102


38/102

$! INTRODU%&O

L4K/0 0>o //#/8o0 /08r8r4i0 bii#/0io4i0 24o0 o# 4rg40

2r/2o/r48/#/8/ or#4i0 4o 0/ 24o! A0 4K/0 8r40#i8/# 40 4rg40 o 2i0o o 40 4rg40 8r40#i8i40 o0, #48/ri4i0 / #é8oo0 4#i4#/8o o #4i0 i9or#/

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)io4i4/ 2rii24#/8/ 48o 4o 2o0iio4#/8o o0 2i4r/0

R/0i08Bi4 48o 4o0 /09or:o0!

'! CARACTER(STICAS DA EDI)ICA%&O

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39/102

R/0i/i4 Mo8/ Mori o4i4o 4 R4 M/ / S, $$;, o *4irro Vi4 No64!

Po00i '? 424r84#/8o0 8/o /# #éi4 r/4 8o84 / $$' #W! G4/ri4 o#/ri4

o#2o084 2or $$ oK40 o#/ri4i0! Ár/4 / 4/r o# 04>o / 9/0840, rr40/ir4 /

24Xgro! Ár/4 / o08r:>o 3$7. #W!

E08/ /i9io é o 8i2o r/0i/i4 / 2o00i 7 246i#/8o0 8i2o! C44 246i#/8o2o00i 424r84#/8o, o# 6ig40 i02o0840 0i#/8ri4#/8/ i6iio o 246i#/8o /# '

24r8/0, 44 #4 o# ' 424r84#/8o0 # 424r84#/8o o# . #W / o o8ro o# .5

#W, r/084o /# 42ro=i#44#/8/ #4 r/4 / $35 #W / 4K/0 >o 0i#é8ri40!

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40/102

M/#ori4 / Co


41/102


42/102

CONDI%+ES DE CONTORNO

P4r4 o9/rir r4bii4/ < /08r8r4 0/r 8ii4o or/8o o# r/0i08Bi4

4r48/r08i4 < o#2r/00>o 9 '; MP4 C';! O o/9ii/8/ / i484:>o 8ér#i4

2o/ 0/r 4#i8io o#o 0/o ig4 4 $;-5

[aC!

P4r4 o 4:o /08r8r4 8ii4r/#o0 o 4:o CA5; 24r4 Y≥

.,3 ## / CA-.; 24r4

Y Z 5 ##!

A #4004 /02/9i4 o or/8o 4r#4o 0/r / ';;; g[#3 / 4 o 4:o 7?5;

g[#3, o# #1o / /408ii4/ ig4 4 '$; GP4! P4r4 o 4:o 8ii4o, o i4gr4#4

8/0>o-/9or#4:>o 4o84o é o #o08r4o 4 )igr4 4 0/gir

)igr4 ' Di4gr4#4 8/0>o = /9or#4:>o

O o/9ii/8/ / Poi00o 4o84o é ig4 4 ;,'!

O 4gr/g4o gr4o 8ii4o 8/# id#/8ro #=i#o / $## bri84 $!

CO*RIMENTO M(NIMOS

S/r>o 0/gi40 40 r/o#/4:/0 4 N*R.$$? 24r4 4 /0o4 4 /02/00r44 4#44 / obri#/8o 4 4r#4r4! A T4b/4 4b4i=o 42r/0/84 o0 obri#/8o0

o#i4i0 obri#/8o #i#o ] 8o/rdi4 / /=/:>o Z $;## 4 0/r/# /=igio0

24r4 i9/r/8/0 8i2o0 / //#/8o0 /08r8r4i0, 6i04o 4 g4r48ir # gr4 4/4o

/ r4bii4/ 24r4 4 /08r8r4!

5


43/102

T4b/4 $ C400/0 / 4gr/00i6i4/ 4#bi/84 24r4 r/obri#/8o #i#o

N/08/ 40o, 4 400/ / 4gr/00i6i4/ 4#bi/84 é 400i9i44 o#o

#o/r44 II 2or 0/r # 4#bi/8/ rb4o, 2oré# 4 or#4 N*R .$$?[';;3 94 #4

r/00464 q2o/-0/ 4#i8ir # #iro-i#4 o# 400/ / 4gr/00i6i4/ # 6/

#4i0 br4o 24r4 4#bi/8/0 i8/ro0 0/o0 0440, or#i81rio0, b4/iro0, oi40

/ r/40 / 0/r6i:o / 424r84#/8o0 r/0i/i4i0 / oK8o0 o#/ri4i0 o

4#bi/8/0 o# or/8o r/6/08io o# 4rg4#4004 / 2i8r4! Por848o 0/r

4#i8i4 400/ I, / /=ig/ # obri#/8o #i#o / '; ## #4i0 #4 8o/rdi424r4 /=/:>o / $; ## 8o84i4o 3; ## / obri#/8o!

VINCULA%&O DAS LAJES

A /8424 0/gi8/ o 2roK/8o 40 4K/0 o0i08/ /# i/8i9i4r o0 8i2o0 /

6o / 040 bor40! E=i08/#, b40i4#/8/, 8rB0 8i2o0

- bor4 i6r/ 4r48/ri4-0/ 2/4 40Bi4 / 42oio, 42r/0/84o, 2or848o,/0o4#/8o0 6/r8i4i0!

- bor4 0i#2/0#/8/ 42oi44 >o /0o4#/8o0 6/r8i4i0!

-bor4 /g40844 >o /0o4#/8o0 6/r8i4i0 / 40 ro84:/0 0>o

i#2/i40, 0>o 4K/0 / 42r/0/84# o8ii4/, 0/o o /g4084#/8o

2ro#o6io 2/4 4K/ 4K4/8/

U#4 i9/r/:4 0igi9i48i64 /8r/ 40 /02/00r40 / 40 4K/0 4K4/8/0 2o/

i#i84r 4 o0i/r4:>o / bor4 /g40844 0o#/8/ 24r4 4 4K/ o# #/or

/02/00r4, 4#i8io-0/ 0i#2/0#/8/ 42oi44 4 4K/ o# #4ior /02/00r4, /6/-0/

.


44/102

4i4 44i04r 4 i9/r/:4 /8r/ o0 #o#/8o0 4848/0 40 bor40 40 4K/0, 4o

o0i/r440 /g408440!

Po/ oorr/r, 2or /=/#2o, #4 bor4 o# #4 24r8/ /g40844 / 4 o8r4

42oi44, o#o #o08r4o 4 )igr4 $! U# ri8ério 42ro=i#4o, 2o006/ 24r4 /08/

40o, é ii4o 4 T4b/4 $!

)igr4 3 C40o /02/9io / 6i4:>o

31

≤

Co0i/r4-0/ 4 bor4 8o84#/8/ 42oi44

3

2

3 1


45/102

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/# 40 ir/:/0 2o/# 0/r 44i0440 8ii4o o #o/o /08io-i/4r!

Iii4#/8/ 40 4K/0 0>o 4440 i0o44#/8/, ob0/r64o-0/ 40

oi:/0 / 42oio / boro /g4084o, o9or#/ 4K4 o8ii4/ o >o /8r/ 40

4K/0! Po08/rior#/8/ é 9/i84 4 o#248ibii4:>o /8r/ o0 #o#/8o0 / boro! O0

64or/0 o0 #o#/8o0 9/8or/0 #=i#o0 o 6>o 2o0i8i6o / / /g4084#/8o

/g48i6o 24r4 40 9or#40 / oi:/0 / 42oio /o8r4#-0/ 84b/4o0, 8ii4r/#o0

24r4 84 4 84b/4 / M4r0

A i9/r/i4:>o /8r/ 40 4K/0 4r#440 /# #4 / 40 ir/:/0 é r/4i44

o#24r4o-0/ 4 r/4:>o /8r/ o0 6>o0 i#/0/0 4 4K/!

L4K/0 4r#440 /# r

L4K/0 4r#440 #4 01 ir/:>o

?


46/102

PR-DIMENSIONAMENTO DAS ALTURAS DAS LAJES

D/ 4oro o# o i8/# 4 $3!'!!$ 4 N*R .$$?[';;3, 40 4K/0 #4i:40 /6/#0/r r/02/i84r i#i8/0 #i#o0, /# 40o / 4K/0 / 2i0o0 o / ob/r8r4 /# b44:o

40 /02/00r40 40 4K/0 /6/# r/02/i84r o i#i8/ #i#o / 7 #!

P4r4 4K/0 o# bor40 42oi440 o /g408440, 4 48r4 8i 2o/ 0/r

/08i#44 2or #/io 4 0/gi8/ /=2r/00>o

( ) *1,05,2 ⋅⋅−= nd

O/

ℓ* /# #/8ro0

d Z 4gr4 8i, /# /8#/8ro0

n Z #/ro / bor40 /g408440

≤

x

7,0*

0/o , m ,x

c Z 3,; # o9or#/ i8/# '!$

)igr4 S/:>o 8r406/r04 4 4K/

P4r4 4K/0 o# bor40 i6r/0, o#o 40 4K/0 /# b44:o, /6/ 0/r 8ii4o

o8ro 2ro/00o!

ALTURA DAS LAJES

A /02/00r4 40 4K/0 2o/ 0/r ob8i4 o# 4 /=2r/00>o )igr4 3

cd h ++= 2φ

= 48r4 8i 4 4K/


47/102

Y = id#/8ro 40 b4rr40

= obri#/8o o#i4 4 4r#4r4

L4K/Di#/0/0 Pré-i#/0io4#/8o

= X \

;$ 3,3; # ,$; # ' ',?7 # .,.; # ,.; #

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;. ','; # ,5 # 3 ','; # ,? # 7,? #

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; ;,5 # ','; # 3 ;,5 # ',; # 5,; #

$; ',; # 3,5; # ' ',5 # 5,. # ?,. #$$ 3,3; # ,$; # ' ',?7 # .,.; # ,.; #

$' ',35 # 3,3; # 3 ',3$ # 5,;? # ?,;? #

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$5 $,75 # ','; # ' $,5 # 3,5 # .,5 #

T4b/4 3 6/ri9i4:>o 4 48r4 40 4K/0

A8r4 4o844 24r4 i#/0io4#/8o 40 4K/0 é / $; # /084o

/8ro o0 24r/0 4 or#4 / 0/o #4ior / 40 48r40 //00ri40 24r4 44

4K/ o /i9io!

DETERMINA%&O DOS CARREGAMENTOS

P4r4 0/ ob8/r o0 4rr/g4#/8o0 40 4K/0 o 2roK/8o, 9or4# /64o0 /# o84

o 2/0o 2r12rio 4 4K/, o 2/0o o r/6/08i#/8o / orr/02o/ 4 2i0o /rd#io,

4rg4#4004 / i#/8o / 4r/i4 24r4 400/84#/8o, 4rg4#4004 / 4r/i4 / 4 24r4

r/boo o 8/8o / 40 4:/0 64ri6/i0!

CARGAS PERMANENTES

C44 4#44 8/6/ 04 /02/00r4 /02/i9i44, / / 2o00/ o 2/0o

/02/9io / 44 #4 /40, ob8i6/#o0 o 4rr/g4#/8o!

P/0o0 /02/9io0 o0i/r4o0

- Pi0o $? N[#3

- Arg4#4004 / i#/8o / 4r/i4 - '$ N[#3

- Arg4#4004 / 4r/i4 / 4 $ N[#3

$;


48/102

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γ 4#44

g; P/0o 2r12rio '5 N[#` ;,$;; # ',5; N[#W

g$ Arg4#4004 / r/g4ri4:>o 02/rior '$ N[#` ;,;; # ;,? N[#W

g' Arg4#4004 / r/g4ri4:>o i9/rior $ N[#` ;,;'; # ;,3? N[#W

g3 Pi0o /rd#io $? N[#` ;,;;? # ;,$ N[#W

g Z 3,?. N[#W

T4b/4 4rg40 2/r#4/8/0

P4r4 4K/0 / 2o004# 24r//0, 9or4# 8ii4o0 8iKoo0 / #/i4 6/ / 9oi

o0i/r44 #4 42ro=i#4:>o / i08ribi 40 4rg40 o/8r440 /ri6440 446/4ri4 /# 4rg40 i08rib40 2or 8o4 4 4K/!

P/0o0 / 24r//

- P4r// / u 6/ P24r Z '!' N[#'

4rg40 24r//0[4rg40 2/r#4/8/0

2é ir/i8o Z ',; # P24r// Z ','; N[#W

4K/0 =\X Co#2! P4r! A24r// g g8o84

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;. ,7 #W ',$; # .,; #W $,37 N[#W 5,'3 N[#W

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$; $;,$5 #W 3,5; # $;,$5 #W ','; N[#W .,;. N[#W

$$ $3,53 #W 3,55 # $;,3; #W $,.7 N[#W 5,5 N[#W$' 7,7. #W ;,;; # - - 3,?. N[#W

$3 7,?' #W ;,;; # - - 3,?. N[#W

$ $;,7 #W ;,;; # - - 3,?. N[#W

$5 3,?5 #W ','; # .,3? #W 3,.5 N[#W 7,5$ N[#W

T4b/4 5 4rg40 2/r#4/8/0, o0i/r4o 40 24r//0

SO*RECARGA

A0 4:/0 64ri6/i0 0obr/4rg4 9or4# o0i/r440 / 4oro o# o 0o 4

/i9i4:>o, 0/go 84b/4 ' 4 N*R .$';[$?;!

$$


49/102

Ei9iio0

r/0i/i4i0or#!, 044, o24, o! / b4/iro $,5 N[#W

/02/04, 4!0! / 464/ri4 ',; N[#W

T4b/4 . V4or/0 #i#o0 40 4rg40 6/r8i4i0

CARREGAMENTO TOTAL

4K/0 g8o84 g8o84 ]

;$ 5,5 N[#W $,5 N[#W 7,; N[#W

;' 3,?. N[#W $,5 N[#W 5,3. N[#W

;3 3,?. N[#W $,5 N[#W 5,3. N[#W

; 3,?. N[#W ',; N[#W 5,?. N[#W

;5 .,'3 N[#W $,5 N[#W 7,73 N[#W

;. 5,'3 N[#W $,5 N[#W .,73 N[#W

;7 ?,7. N[#W $,5 N[#W $;,'. N[#W

;? .,'3 N[#W $,5 N[#W 7,73 N[#W; .,7. N[#W $,5 N[#W ?,'. N[#W

$; .,;. N[#W $,5 N[#W 7,5. N[#W

$$ 5,5 N[#W $,5 N[#W 7,; N[#W

$' 3,?. N[#W $,5 N[#W 5,3. N[#W

$3 3,?. N[#W $,5 N[#W 5,3. N[#W

$ 3,?. N[#W ',; N[#W 5,?. N[#W

$5 7,5$ N[#W ',; N[#W ,5$ N[#W

T4b/4 7 4rg40 8o84i0 40 4K/0

CÁLCULO E VERI)ICA%&O DAS )LEC@AS

P4r4 0/ 48/084r 4 /9iiBi4 4 /08r8r4 4 4K/, é //00ri4 4 6/ri9i4:>o 40

9/40 2ro6o440 2/o0 /09or:o0 4848/0!

E# 4g#40 4K/0 o 2roK/8o, 4 o#24r4:>o 4 9/4 ob8i4 o# 4 9/4

i#i8/ 2/r#i8/ i#iir o 4#/84r 4 /02/00r4 4 #/0#4!

)LEC@AS LIMITES

No i8/# $3!3 4 N*R .$$?, 84b/4 $3!', é /=2r/00o i#i8/0 24r4 9/40 /#

4K/0 0/go 4/i84bii4/ 0/0ori4

250

x

- D/0o4#/8o 8o84

350

x

- D/0o4#/8o /6io 4 4rg40 4i/84i0!

$'


50/102

)LEC@AS ELÁSTICAS

D/ 4oro o# 4 9or#4:>o / C/rX

-csh

x.a

a ⋅⋅

⋅=

3

4

α

O/

Ecs = 0,85 Eci

fck -ci 5600=(MPa)

)LEC@AS DI)ERIDAS NO TEMPO

S/go o i8/# $7!3!'!$!' 4 N*R .$$? ';;3, 4 9/4 4iio4 i9/ri4,

/orr/8/ 40 4rg40 / og4 r4:>o, /# 9:>o 4 9Bi4, 2o/ 0/r 444

/ #4/ir4 42ro=i#44 2/4 #8i2i4:>o 4 9/4 i#/i484 2/o 948or v9 4o 2or

'501 ρ

ξ α

+

∆= f

d b

s !

⋅= '

' ρ

Ac0 é 4 4r#4r4 / o#2r/00>o, o 40o / 4r#4r4 24

( ) ( )0t t ξ ξ ξ −=∆

w é # o/9ii/8/ /# 9:>o o 8/#2o, 44o 2/4 /=2r/00>o 0/gi8/ o

ob8io ir/84#/8/ 4 T4b/4 ' 84b/4 $7!$ 4 N*R .$$?[';;3!

( ) ( ) 32,0996,068,0 t t t ⋅=ξ 24r4 8 7; #/0/0

( ) 2=t ξ 24r4 8 m 7; #/0/0

t é o 8/#2o, /# #/0/0, 4o 0/ /0/K4 o 64or 4 9/4 i9/ri4

t 0 é 4 i4/, /# #/0/0, r/48i64 < 42i4:>o 4 4rg4 / og4 r4:>o!

Por848o, 4 9/4 i9/ri4 49 é 44 2or

$3


51/102

i f f aa ⋅= α

T4b/4 ? - V4or/0 / w / 9:>o o 8/#2o

)LEC@A TOTAL

A 9/4 8o84 48 2o/ 0/r ob8i4 2or #8i2i4r 4 9/4 i#/i484 2or f α +1

f it

aa α +⋅= 1

)LEC@AS LIMITES

A0 9/40 ob8i40 o9or#/ o0 i8/0 48/rior/0 >o /6/# 8r424004r o0

/0o4#/8o0 i#i8/0 /084b//io0 4 T4b/4 $? 4 N*R .$$?[';;3, 4 4

6ri40 0i84:/0 4 44i04r!

U#4 /40, / 2o/ 0/r 4 0i84:>o r8i4, orr/02o/ 4o i#i8/ 24r4 o

/0o4#/8o 8o84, r/48i6o < 4/i84bii4/ 6i04 o0 0rio0, 4o 2or

250lim

xa

=

L4K/0 4'i# P$ 4 P' 4g 49 48o84 6/ri9!

;$ $3,'; ## .,$ N[#W $,'$ ## 5,5 N[#W $,; ## $, ## ',.. ## o

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$; $$,.; ## .,.. N[#W ;,57 ## .,;. N[#W ;,5' ## ;,.? ## $,'5 ## o

$$ $3,'; ## .,$ N[#W $,'$ ## 5,5 N[#W $,; ## $, ## ',.. ## o

$' ,; ## ,. N[#W ;,$? ## 3,?. N[#W ;,$5 ## ;,'; ## ;,3? ## o

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$ $;,'; ## ,.. N[#W ;,5 ## 3,?. N[#W ;,37 ## ;, ## ;,5 ## o

$5 7,;; ## ?,3$ N[#W ;,$; ## 7,5$ N[#W ;,; ## ;,$' ## ;,'$ ## o

T4b/4 V/ri9i4:>o 4 9/4

$


52/102

CÁLCULO DOS MOMENTOS )LETORES

O #é8oo 8ii4o o 2r/0/8/ 8r4b4o 9oi o o 2or #/io / 84b/40 /

o / #o#/8o0! C44 4K/ 2o00i 04 24r8i4ri4/ 48o 4o /g4084#/8o!P4r4 0/ 8ii4r 40 84b/40 0>o //00ri40, 4é# 4 04 oi:>o / 42oio, 40

i#/0/0 4 4K/ /# /08>o! Co# i00o, ob8B#-0/ o0 64or/0 r/9/r/8/0 o / M4r0!

D/ 2o00/ /00/0 64or/0, é 2o006/ 44r o0 #o#/8o0 2o0i8i6o0 /

/g48i6o0, 40 40 ir/:/0 4 4K/!

L4K/ lxl =W

#Wg8o84 ] N[#W

#=N#[#

#XN#[#

==N#[#

=XN#[#

;$ $,' $;,? 7,; 3,;? ','3 -.,; -5,

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;3 $,$$ 7,;' 5,3. $,$' ;,?' -',55 -',$3

; ',;; ,.' 5,?. $,5 ;,.7 -3,'3 -',''

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63/102

60B 1% 5 5 6" 6%5

60B 1# 5 5 6" 6%5

60B 1" 5 $ $!" #0%

60B 0 5 1$ $!" !5$%

60B 1 5 ! $! 5616

60B 5 1" $0! 5%%6

60B $ 5 1$ $!" !5$%

60B ! 5 1! $1! !$"6

60B 5 5 1! $1! !$"6

60B 6 5 11 !!" !"$"

60B % 5 1 5! 5!

60B # 5 1! !!" 6#6

60B " 5 " $" 151

AÇO POSBIT(m

m)QUANT

COMPRIMENTO

UNIT(cm) TOTAL(cm)

ARMADURAS SUPERIORES

60B $0 5 $$ 1!! !%5

60B $1 5 16 1$6 1%6

60B $ 5 1# 1$6 !!#

60B $$ 5 1# 10$ 1#5!

60B $! 5 1 10$ 1$6

60B $5 5 1 10$ 1$660B $6 5 1 10$ 1$6

60B $% 5 " 1" 1161

60B $# 5 1$ 1" 16%%

60B $" 5 $$ 1!! !%5

60B !0 5 16 1$6 1%6

60B !1 5 1 1$6 #56

60B ! 5 1 10$ 1$6

60B !$ 5 !6 1%! #00!

60B !! 5 1$ 10# 1!0!

60B !5 5 1! 10 16#060B !6 5 6 1"! 50!!

60B !% 5 $ 151 !#$

60B !# 5 1 101 11

60B !" 5 !6 1%! #00!

60B 50 5 5 56 #0

60B 51 5 10 6!0

60B 5 5 1$ 101 1$1$

AÇO POSBIT(m

m)QUANT

COMPRIMENTOUNIT(cm) TOTAL(cm)

ARMADURA DE CANTO

'.


64/102

60B 5$ 5 15 #$ 1!5

60B 5! 5 15 #$ 1!5

60B 55 5 15 #$ 1!5

60B 56 5 15 #$ 1!5

RESUMO DE AÇO

AÇOBIT(m

m)COMPRIMENTO(

m)PESO (&')

60B 5 %1 $50

ANEHOS

'7


65/102

ANEHO A VINCULA%&O DAS LAJES

'?


66/102

MEMORIAL DESCRITIVO

PILARES

'


67/102

S#rio

Y$! INTRODU%&O!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$

'! CARACTER(STICAS DA EDI)ICA%&O!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$

MEMORIAL DE CÁLCULO!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'

$! O*JETIVO!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!3

'! PR-CARREGAMENTO DOS PILARES!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!3'!$! P/0o Pr12rio o0 Pi4r/0!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!3'!'! C4rr/g4#/8o o $a P46i#/8o Ti2o!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

'!'!$! Pi4r P.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'!'!'! Pi4r P!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!5

'!'!3! Pi4r P'$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!5

3! PR-DIMENSIONAMENTO DOS PILARES!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!.

! CORRE%&O DOS CARREGAMENTOS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!?!$! Pi4r P.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!?!'! Pi4r P!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!?!3! Pi4r P'$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

5! MOMENTO DE ENGASTAMENTO!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!5!$! Pi4r P.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$;

5!'! Pi4r P!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$$5!3! Pi4r P'$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$'

.! VERI)ICA%+ES PARA DIMENSIONAMENTO!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$3.!$! V/ri9i4:>o 4 E0b/8/!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$3

.!$!$! Pi4r P.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$

.!$!'! Pi4r P!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$5

.!$!3! Pi4r P'$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$5

.!'! V/ri9i4:>o 4 )or:4 Nor#4 R/i4ν

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$.

7! DIMENSIONAMENTO DAS ARMADURAS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$.7!$! Pi4r P.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$77!'! Pi4r P!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$?7!3! Pi4r P'$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$?

?! DISTRI*UI%&O DAS ARMADURAS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$?!$! Ar#4r4 Logi8i4i0!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$

?!$!$! Did#/8ro #i#o / 84=4 / 4r#4r4!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$?!$!'! Di08ribi:>o 8r406/r04!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$

?!'! Ar#4r4 8r406/r4!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!';?!3! Co#2ri#/8o / Tr402400/!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!';

! DETAL@AMENTO DA SE%&O TRANSVERSAL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'$!$!$! Di08ribi:>o 4 4r#4r4 24r4 4 P.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'$!$!'! Di08ribi:>o 4 4r#4r4 24r4 4 P!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'$


68/102

!$!3! Di08ribi:>o 4 4r#4r4 24r4 4 P'$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!''

ANEHOS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'3

ANEHO A MOMENTO DE ENGASTAMENTO NO PILAR P.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!' ANEHO * DETAL@AMENTO P.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'.

ANEHO C DETAL@AMENTO P!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'7

ANEHO D DETAL@AMENTO P'$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'?

ANEHO E UANTITATIVO DE MATERIAL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'


69/102

3! INTRODU%&O

E08/ #/#ori4 8/# o#o obK/8i6o /0r/6/r o0 2ro/00o0 / i#/0io4#/8o /

/844#/8o o0 2i4r/0 P., P / P'$ o 246i#/8o 8i2o o /i9io r/0i/i4 /#

/08o oio 400i# 4 0/g4 /8424 o 2roK/8o /08r8r4 24ri4 / #4

/i9i4:>o, o0i08io 4 o/2:>o 4 /08r8r4 o 246i#/8o 8i2o / # /i9io /

#8i2o0 44r/0, o# /844#/8o / 4K/0 / 6ig40 2ri#/ir4 /8424, / 2i4r/0

0/g4 /8424!

D/0/6o6io 24r4 4 i0i2i4 Co08r:/0 /# Cor/8o II, 4 Q 4r84 0éri/

o r0o / gr44:>o Eg/4ri4 Ci6i 4 Ui6/r0i4/ E0844 / Lori4 UEL,

#ii08r44 2/o 2ro9/00or J/r / A00i0 Gr400io88o!

S/r 42r/0/84o /08/ #/#ori4

- U#4 2484 / 9r#40 9i4 o 246i#/8o 8i2o, o# 4ré0i#o 40 i#/0/0

o0 2i4r/0 o 246i#/8o 8érr/o!

- D/0/o0 o# o /844#/8o / 4r#4r40 o0 3 2i4r/0 P., P / P'$

! CARACTER(STICAS DA EDI)ICA%&O

R/0i/i4 Mo8/ Mori o4i4o 4 R4 M/ / S, $$;, o *4irro Vi4 No64!Po00i '? 424r84#/8o0 8/o /# #éi4 r/4 8o84 / $$' #W! G4/ri4 o#/ri4

o#2o084 2or $$ oK40 o#/ri4i0! A#24 r/4 / 4/r o# 04>o / 9/0840,

rr40/ir4 / 24Xgro! Ár/4 / o08r:>o 3$7. #W!

E08/ /i9io é o 8i2o r/0i/i4 / 2o00i 7 246i#/8o0 8i2o! C44 246i#/8o

2o00i 424r84#/8o0 2oré# 040 6ig40 /08>o i02o0840 0i#/8ri4#/8/ i6iio o

246i#/8o /# ' 24r8/0, 44 #4 o# ' 424r84#/8o0 # 424r84#/8o o# . #W /

o o8ro o# .5 #W, r/084o /# 42ro=i#44#/8/ #4 r/4 / $35 #W / 4K/0 >o

0i#é8ri40!

# 2roK/8o 4ri8/8io o 246i#/8o 8i2o, o# i#/0/0 /# 2484 / # or8/

/0/#8io #o08r4o 4 48r4 o 2é-ir/i8o 0/ /o8r4 40 2r440 ;$A / ;$*!

$


70/102

M/#ori4 / Co


71/102


72/102

Ob0/r64:>o o 2/0o 2r12rio 0/r r/44o /2oi0 / 9i=4o 4 0/:>o

8r406/r04 24r4 44 # o0 2i4r/0 / /08>o 0/o i#/0io4o0!

CARREGAMENTO NO $a PAVIMENTO TIPO

P4r4 /8/r#i4r o 4rr/g4#/8o N0 o0 2i4r/0, /6/-0/ o//r 40

r/4:/0 40 6ig40 / /08>o 42oi440 //0, /# 0/gi4 44r 4 0/gi8/

/4:>o

( ) ( )∑ ⋅++⋅= .-.-)( pavn Ppcobertura pavnvigasdasreações " sd

Ob0/r64:>o o#o 40 r/4:/0 40 6ig40 9or4# ob8i40 48r46é0 o0

4rr/g4#/8o0 / 2roK/8o0 , >o 0/r //00rio #4Kor4r o 4rr/g4#/8o!

Pi4r P.

A /8/r#i4:>o o0 4rr/g4#/8o0 o0 2i4r/0 / /84/0 0/gi8/0 9or4#

9/i8o0 o# 4=io / 2rogr4#40 / o#284or 98oo, 48o CAD 24r4 94ii84r 4

/=/:>o o0 2ro/00o0!

O Pi4r . r//b/ 4rg4 40 6ig40 V3 / V$7, o9or#/ ii4o 40 9igr40

I08r4:>o ' - R/4:>o 4 V3 o P.

I08r4:>o '5 - R/4:>o 4 V$7 o P.


73/102

Logo o 4rr/g4#/8o o P. é( ) k" " sd 97,14370,735,460,77,145,170 =×+×+=

Pi4r P

O Pi4r r//b/ 4rg4 40 6ig40 V. / V$, o9or#/ ii4o 40 9igr40

I08r4:>o '. - R/4:>o 4 V. o P

I08r4:>o '7 - R/4:>o 4 V$ o P

Logo o 4rr/g4#/8o o P é( ) k" " sd 69,15870,735,460,78,1481,56 =×+×+=

Pi4r P'$

O Pi4r '$ r//b/ 4rg4 40 6ig40 V$3 / V$, o9or#/ ii4o 40 9igr40

I08r4:>o '? - R/4:>o 4 V$3 o P'$

5


74/102

I08r4:>o ' - R/4:>o 4 V$ o P'$

Logo o 4rr/g4#/8o o P'$ é

( ) k" " sd 49,4700,735,460,76,363,21 =×+×+=

PR-DIMENSIONAMENTO DOS PILARES

No 2ré-i#/0io4#/8o, /6/r 0/r /8/r#i44 4 0/:>o / 44 2i4r, 24r4

r/0i08ir 4o 4rr/g4#/8o ob8io o i8/# '!', r/9/r/8/ 4 44 2i4r!

P4r4 / i00o 0/K4 2o006/ 4o8o iii4#/8/ 4g0 24rd#/8ro0, /

/6/r>o 0/r 6/ri9i4o0 2o08/rior#/8/

4 E=/8rii4/ 2or i#/0>o h "

M

h

e

#d

#d

⋅=

, / or#4#/8/ 8/#

64ri4:>o /8r/ ;,;5 / ;,$;, ogo é #/or 4o84r # 64or / /08/K4 /8ro /084

64ri4:>o, o0 40o0 /08/ 8r4b4o 9oi 4o84o

075,0=h

e

!

b Ao84-0/ 4 9or:4 or#4 r/i4 o#o 0/o7,0≥ν 24r4 / 2o004

0/r 42i4o o #é8oo 0i#2i9i4o, o 0/K4, 2o/-0/ 8r409or#4r 4 9/=o-o#2r/00>o

or#4 /# #4 o#2r/00>o /8r44 /i64/8/, 04b/o /cd

#d

f hb

"

⋅⋅=ν

,

0/go o i8/# $7!'!5!$ 4 NR* .$$?[';;3!

.


75/102

P4r4 o o/9ii/8/β

8/# 64ri4:>o 2/r8o / 3 / , ogo 24r4 o0 2i4r/0

0/r 4o84o iii4#/8/

3=β

!

A 84=4 g/o#é8ri4 4 4r#4r4 ogi8i4 / o#2r/00>o tot s,

ρ

8/#

#4 94i=4 04 /8r/ $y 4 3y, 0/o #4i0 04 / $y 4 'y, ogo 24r4 /08/0

8r4b4o 9oi 4o84o

2, =tot s ρ !

/ S/go o i8/# $3!'!3 4 N*R .$$?[';;3, 4 0/:>o >o 2o/

42r/0/84r i#/0>o #/or / $ #, >o 2/r#i8io 2i4r o# 0/:>o 8r406/r04/ r/4 i9/rior 4 3.; #W, 9oi 4o84oi 24r4 4 #/or i#/0>o o0 2i4r/0 '; #!

A 24r8ir o0 24rd#/8ro0 4o84o0 é 2o006/ /8/r#i4r 4 0/:>o o0 2i4r/0

48r46é0 40 /4:/0

4 )or:4 or#4 0oii848/ /i64/8/

⋅+⋅=

h

e " " #d e.#d β 1,

b Ao i0o4r 4 r/4 / or/8o / !

4 /4:>o 4 Nor#4 0oii848/ /

o / 94/o 40 /6i40 0b08i8i:/0, 8/#-0/ 4 0/gi8/ /4:>o

(

( )

( )[ ]cd d tot # cd / #d tot # / tot #

cd d tot # / cd #d

d tot # tot # / cd #d

f f f ! "

! !

f f ! ! f "

f ! ! ! f "

85,085,0

85,085,0

85,0

,

,,

,

,,

−⋅+⋅⋅=

⋅=

−⋅+⋅⋅=

⋅+−⋅⋅=

ρ

ρ

ogo,

( )cd d tot # cd

e.#d

/ f f f

" !

85,085,0 ,

,

−⋅+= ρ

)4/o 40 0b08i8i:/0 o0 24rd#/8ro0 #/io4o0 o iiio /08/ i8/# 3,

2o/-0/ ob8/r

( ) #d #d e.#d " " " ⋅=×+×= 225,1075,031,, / 04b/o /

MPa f

f k

d 43515,1

500===

γ

7


76/102

14,124,1

2085,085,085,0 ≈==

c

ck

cd

f f

γ

L/64o /# o0i/r4:>o 40 i4/0, 4 r/4 4 0/:>o /# ##'

0/r

( ) #d / #d #d

/ " ! " "

! ⋅=∴⋅×

=−⋅+

⋅⋅= 466,59

60,20

10225,1

14,1243502,014,12

10225,1 33

Pi4r/0 NS AC,44o b 44o 4o84o AC,/9/8i6o

P. $37,7 N ?55$;,35 ##W ';; ## '7,. ## 5; ## ;; #W

P $5?7,. N $3,.; ##W ';; ## 7',$ ## 5;; ## $;;; #W

P'$ 7;, N '77?,$7 ##W ';; ## $3, ## ';; ## ;; #W

T4b/4 $? - S/:>o Tr406/r04 o0 Pi4r/0 P., P / P'$

CORRE%&O DOS CARREGAMENTOS

Co#o o i8/# ', 9oi 04o #4 0/:>o 9i8i4 24r4 o o o 4rr/g4#/8o,

/08/ i8/# 0/r 6/ri9i4o 0/ o# 4 0/:>o /8/r#i44 24r4 44 2i4r ir 46/r

#i840 #4:40 40 4rg40 / 0/ i00o 49/84r / 4g#4 #4/ir4 o

i#/0io4#/8o!

Logo, 24r4 o0 o0 / 0/g/# 4 24r8ir o i#/0io4#/8o, 0/r>o

8ii4o0 o0 4rr/g4#/8o0 / 0/r>o /9iio0 /08/ i8/#!

Co9or#/ K 6i08o, o 2/0o 2r12rio 0/ 4 2/o 2ro8o 4 0/:>o 8r406/r04 o#

4 48r4 o 2i4r / o 2/0o /02/9io o or/8o, o9or#/ #o08r4 4 /4:>o

concretoel hb Pp λ ⋅⋅⋅=

E 24r4 /8/r#i4:>o o 4rr/g4#/8o N0 o0 2i4r/0, /6/-0/ o//r 40

r/4:/0 40 6ig40 / /08>o 42oi440 //0, /# 0/gi4 44r 4 0/gi8/

/4:>o

( ) ( )∑ ⋅++⋅= .-.-)( pavn Ppcobertura pavnvigasdasreações " sd

PILAR P.

A 0/:>o 8r406/r04 o 2i4r P. é ;,'; #×

;,5 #, ogo o 2/0o 2r12rio é

?


77/102

k" Pp 525,62590,245,020,0 =×××= 24r4 44 246i#/8o!

Logo o 4rr/g4#/8o o P. é

( ) k" " sd 195,14530,7525,660,77,145,170 =×+×+=

- V/ri9i4:>o 4 0/:>o 8r406/r04

!4501,432200

72,86415

72,86415195,1453466,59466,59 2

ok mmhb

!ch

mm " !

adotado

#d /

=o 8r406/r04 o 2i4r P. é ;,'; #×

;,5; #, ogo o 2/0o 2r12rio é

k" Pp 25,72590,250,020,0 =×××= 24r4 44 246i#/8o!

Logo o 4rr/g4#/8o o P é

( ) k" " sd 99,16070,725,760,78,1481,56 =×+×+=

- V/ri9i4:>o 4 0/:>o 8r406/r04

!5001,478200

76,95620

76,9562099,1607466,59466,59 2

ok mmhb

!ch

mm " !

adotado

#d /

=o 4 0/:>o 8r406/r04

!2009,136200

59,27374

59,2737434,460466,59466,59 2

ok mmhb

!ch

mm " !

adotado

#d /

=


78/102

MOMENTO DE ENGASTAMENTO

A8/0 / 2ro00/gir o# o i#/0io4#/8o, /6/-0/ 6/ri9i4r o0 #o#/8o0

/ /g4084#/8o g/r4o0 2/40 6ig40, /08/0 /2//# 4 rigi/ o 2i4r, 4 rigi/4 6ig4!

12

2

,

l . M k & eng =

, o/ é o 4rr/g4#/8o i08ribo 4 6ig4!

Rigi/ o 2i4r p

p

p pl

0 r r == in ,s,

, 24r4 0/:>o r/84g4r12

3hb 0

⋅=

Rigi/ 4 6ig4v

vv

l

0 r =

Mo#/8o 4 b40/ o 2i4r∑

⋅=r

r M M p

& eng p

in ,

,in ,

, /08/ #o#/8o /6/ 0/r

#4Kor4o /# 5;y 24r4 8/4 # #o#/8o 9i4 o# i9Bi4 o0 /#4i0 44r/0

o /i9io! A0 i#2/r9/i:/0 o4i0 2o/# 0/r o0i/r440 o0 2i4r/0, 0/ 40 0/:/0

8r406/r04i0 o0 2i4r/0 r/0i08ir/# 4o #o#/8o #i#o / $Q or/#, ogo /6/-0/

6/ri9i4r /08/ #o#/8o #i#o / 2ri#/ir4 or/#, / 4 0/:>o o 2i4r /6/ r/0i08ir,

o9or#/ i8/# $$!3!3!!3 4 N*R .$$?, o/ é 4 48r4 8o84 4 0/:>o 8r406/r04

4 ir/:>o o0i/r44, /# #/8ro0!

( )h " M #d d 03,0015,0min,1 +=

PILAR P.

$;


79/102

I08r4:>o 3; - Po0i:>o o Pi4r P.

NS Z $53,$5 N

,V$7 Z $3,5 N[#

I08r4:>o 3$ - S/:>o o Pi4r P.

I08r4:>o 3' -Mo#/8o /

/g4084#/8o P.

- Mo#/8o #i#o / $Q or/#

( ) k"m M d 52,3020,003,0015,0195,1453min,1 =×+=

- Rigi/ o 2i4r

3

3

in ,s, 10448,1032900

12

200450

×=

×

== p p r r

- Rigi/ 4 6ig4

3

3

10181,143

2200

12

300140

×=

×

=vr

- Mo#/8o / /g4084#/8o

k"m M & eng 46,512

2,254,13 2

, =×

=

- Mo#/8o 4 b40/ o 2i4r

( ) k"m M p 61,1

10181,143448,1032

10448,10346,5

3

3

in , =×+×

××=

- Mo#/8o 4 b40/ o 2i4r o# i9Bi4 o0 o8ro0

246i#/8o0

k"m M p 42,261,15,1in , =×=

Ob0/r64:>o O #o#/8o / /g4084#/8o 9oi /9iio 48r46é0

o 2rogr4#4 98oo, 24r4 #o8i6o / o#24r4:>o, 6/r A/=o A!

Co#o

k"m M M M 1#d !#d p 42,2,1,1in , =−==

k"m M d 52,30min,1 =, 4

4r#4r4 ogi8i4 o 2i4r /6/r 0/r i#/0io44 / #oo

$$


80/102

/ 04 r/0i08Bi4 48/4 o0 /09or:o0 #i#o0 44o0

r48/ 4 6/ri9i4:>o o #o#/8o / $Q or/#!

PILAR P

I08r4:>o 33 - Po0i:>o o Pi4r P

NS Z $.;7, N

,V. Z ',$5 N[#

I08r4:>o 3 - S/:>o o Pi4r P

$'


81/102

I08r4:>o 35 - Mo#/8o/ /g4084#/8o P

- Mo#/8o #i#o / $Q or/#

( ) k"m M d 06,5360,003,0015,099,1607min,1 =×+=

- Rigi/ o 2i4r

3

3

in ,s, 10390,7182900

12

500200

×=×

== p p r r

- Rigi/ 4 6ig4

3

3

10742,674650

12

300140

×=

×

=vr

- Mo#/8o / /g4084#/8o

k"m M & eng 52,4312

65,415,24 2

, =×

=

- Mo#/8o 4 b40/ o 2i4r

( ) k"m M p 78,20

10742,67390,7182

10390,71852,43

3

3

in , =×+×

××=


246i#/8o0

k"m M p 17,3178,205,1in , =×=

Co#o

k"m M M M 1#d !#d p 17,31,1,1in , =−== é #/or /

k"m M d 06,53min,1 =, 4 4r#4r4 ogi8i4 o 2i4r /6/r

0/r i#/0io44 / #oo / 04 r/0i08Bi4 48/4 o0

/09or:o0 #i#o0 44o0 r48/ 4 6/ri9i4:>o o

#o#/8o / $Q or/#!PILAR P'$

$3


82/102

I08r4:>o 3. - Po0i:>o o Pi4r P'$

NS Z .;,3 N

,V$3 Z $',.? N[#

,V$ Z $?,7' N[#

I08r4:>o 37 - S/:>o o Pi4r P'$

I08r4:>o 3? -Mo#/8o = /

/g4084#/8o P'$

- Mo#/8o #i#o / $Q or/#

( ) k"m M d 67,920,003,0015,034,460min,1 =×+=

- Rigi/ o 2i4r

3

3

in ,s, 10977,452900

12

200200

×=

×

== p p r r

Di08ribi:>o / #o#/8o o /i=o = - Rigi/ 4 6ig4 V$

3

3

10287,2495850

12

500140

×=

×

=vr

- Mo#/8o / /g4084#/8o

k"m M & eng 39,53

12

85,572,18 2

14, =×

=

- Mo#/8o 4 b40/ o 2i4r

( ) k"m M p 19,7

10287,249977,452

10977,4539,53

3

3

in , =×+×

××=


246i#/8o0

k"m M p 79,1019,75,1in , =×=

$


83/102

Co#o

k"m M M M 1#d !#d p 79,10,1,1in , =−== m

k"m M d 67,9min,1 =,

I08r4:>o 3 -Mo#/8o X /

/g4084#/8o P'$

Di08ribi:>o / #o#/8o o /i=o X

- Rigi/ 4 6ig4 V$3

3

3

10002,1224100

12

350140

×=

×

=vr

- Mo#/8o / /g4084#/8o

k"m M & eng 76,1712

1,468,12 2

, =×

=

- Mo#/8o 4 b40/ o 2i4r

( )

k"m M

M

p

p

82,3

10002,122977,452

10977,4576,17

in ,

3

3

in ,

=

×+×

××=

- Mo#/8o 4 b40/ o 2i4r o# i9Bi4

o0 o8ro0 246i#/8o0

k"m M p 73,582,35,1in , =×=

C

Aps 7° Semestre

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