Proiect Beton Armat

TEMA PROIECT

Se va realiza structura de rezistenta a unei cladiri din beton armat conform datelor si schitei anexe. Se va face calculul static al placilor si al cadrului din beton armat. Structura sa ve realiza cu regim de inaltime P+1.

Structura de rezistenta a cladirii este formata din: stalpi din beton armat grinzi din beton armat turnate monolit plansee din beton armat prefabricate

Se vor calcula:• plansee• stalpi

• grinziPiese desenate:

o plan partero plan general structura de rezistentao plan de armare pentru:

stalpi grinzi plansee

1). DATE INITIALE:

A. Evaluarea incarcarilor pentru planseul terasa Tabelul 1

Nr.Crt.

Denumirea incarcarii Incarcari normate

Coeficient de incarcare

Incarcare de calcul

1 Planseu beton armat0.13x2500

325.0 1.1 357.5

2 Sapa egalizatoare M1000.02x2100x1.0x1.0

42 1.3 54.6

3 Strat difuzie impaslitura de sticla 29 1.3 37.74 Bariera contra vaporilor; impaslitura fibra de

sticla biturnata23 1.3 29.9

5 Termoizolatie – cenusa termocentrala in vrac compactata (γ=850 daN/m3; d=16 cm) 0.16x850x1.0x1.0

136 1.2 163.2

6 Strat separator impaslitura fibra de sticla tip I A 900

21 1.3 27.3

7 Placi beton armat 7.5 cm (termoizolatie) 0.075x1.0x600

45 1.2 54

8 Sapa mortar M100 armata cu plasa Ф=3/15 cm 0.025x2100x1.0

52.5 1.3 68.3

9 Hidroizolatie p biturnata (panza)+LCB 17.5 1.3 22.810 Protectie hidroizolatie de 4 cm grosime Ф=3

0.004x1800x1.072 1.3 93.6

11 Incarcare din zapada zmac 120 1.4 168TOTAL INCARCARE 1076.9

B. Evaluarea incarcarilor pentru planseul intermediar Tabelul 2

Nr.crt.

Denumirea incarcarii Incarcari normate

Coeficient de incarcare

Incarcare de calcul

1 Planseu beton armat0.13x2500

325 1.1 357.5

2 Mozaic turnat de 1 cm grosime pe sapa mortar M200 de 2.5 cm0.025x2100

52.5 1.3 68.25

3 Incarcare utila 150 1.4 210Pereti despartitori 150 1.2 180

4 Pardoseala parchet 6 1.3 7.8TOTAL INCARCARE 824

I. CALCULUL CADRULUI PRIN PROCEDEUL CROSS

Schemele cadrelor sunt date in figura de mai jos.

Deoarece este structua simetrica figura se simplifica precum urmeaza.

Incarcarile pe cadru

a) Incarcarea data de terasa pe ml:

Nt 89,5050280,5

6,13107692

1

12 === xx

L

xQterasaxSN/ml

b) Incarcarea data de planseu pe ml:

Npl = 75,3864280,5

6,1382402

1

12 == xx

L

SxQplanseuxN/ml

c) Incarcarea data de peretii despartitori pe ml:

Np =1x0,2x2,73x1,3x25000=17745 N/ml

d) Incarcarea data de greutatea grinzii pe ml:

Ng = mlNxxx /33001,1250004,03,0 =

N1= Nt + Ng = 50502,89+3300=53802,89N/ml = 5380,289 daN/mlN2 = Npl + Ng + Np = 38642,75+3300+17745=59687,75 N/ml=5968,775 daN/ml

PROCEDEUL CROSS

1. Se determina tipul de cadru. CNF sau CND .

NGLE=2n-(b+r)=2x5-(4+6)=0=>CNF

2. Constructia sistemului de baza prin blocarea rotirilor nodurilor rigide.

3. Calculul mo mentelor de incastrare perfecta

M14=12

2pl−=

12

)38,6(601,4563 2x−= -15474,82 daN/ml

M23=12

2pl−=

12

)38,6(241,3442 2x−= -11669,78 daN/ml

MOMENTE DE INCASTRARE PERFECTA

3

4

5

4. Calculul rigiditatilor barelor la rotire de noduri

K12= 2,8

Ex2I4=2,857EI

K15= 2,8

2IE4 x=2,857EI

K14= 6,38

2IE4 x=0,627EI

K23= 6,38

2IE4 x=0,627EI

∑ 1nodK =2,857+0,626+2,857=6,341EI

∑ 2nodK =2,857+0,626=3,484EI

5. Calculul factorilor de distributie

NOD 1

d12= ∑ 1

12

nodK

K=

EI

EI

34,6

857,2=0,451

d15= ∑ 1

15

nodK

K=

EI

EI

34,6

857,2=0,451

d14= ∑ 1

14

nodK

K=

EI

EI

34,6

627,0=0,099

Verificare:d12+d15+d14=0,451+0,451+0,099=1

NOD 2

d21= ∑ 2

21

nodK

K=

EI

EI

483,3

857,2=0,820

d23= ∑ 2

23

nodK

K=

EI

EI

483,3

627,0=0,180

Verificare:d21+d23=0,820+0,180=1

6. Calculul Momentelor maxime

( ) ( ) ⇔=⋅−+−⋅⇒=∑ 02

38,61073,4562058,16057343,1431038,60

2

144vM

342,1427938,6

205,91102092,92848715,174638,6 141414 =⇒=⇔=−+⋅⇔ vvv

( ) ( )0343,14310

2

38,61073,4562058,1605738,60

2

411=−++⋅−⇒=∑ vM

902,1482638,6

635,94595092,92848715,174638,6 144141 =⇒=⇔=++⋅−⇔ vvv

129,31073,4562

342,1427901073,4562342,142790 0000

=⇒=⇒=⋅−⇒= xxxTx

( )74,8036977,22332718,30369

2

129,31073,4562343,14310129,3342,14279

2

max =−=⋅−−⋅=M

( ) ( )

( ) ( )

18,1135638,6

434,7245269,70018744,243338,6

02

38,635,3440287,10047031,1248138,60

25,1059338,6

946,67584069,70018744,2433

02

38,635,3440031,12481287,1004738,60

323232

2

322

232323

2

233

=⇒=⇔+=⋅

⇔=⋅+−+⋅−⇒=

=⇒=⇒=−+⇔

⇔=⋅−+−⋅⇒=

∑

∑

vvv

vM

vvv

vM

079,335,3440

25,10593035,344025,105930 0000

=⇒=⇒=⋅−⇒= xxxTx

( )

65,6261

673,16307287,1004761,326162

079,335,3440287,10047079,325,10593

2

max

=

=−−=⋅−−⋅=M

II .CALCULUL PLACILOR

Se face conform STAS 10107/2 – 1992.

Placa tip 1

ly=5.8

lx=4.15

x

y

l

l=λ

A. Terasa

I. Momente in camp la centru

Mx = α1 x qterasa x lx2

My = α2 x qterasa x ly2

II. Momente negative maxime pe reazeme

M'x = -α3 x qterasa x lx2

M'y = -α4 x qterasa x ly2

III. Sageata la centru

w= α 0 x qterasa x lx4

E x h3

B. Planseu intermediar


Mx = α1 x qpl x lx2

My = α2 x qpl x ly2


M'x = -α3 x qpl x lx2

M'y = -α4 x qp lx ly2


w= α0 x qpl x lx4

E x h3

Placa tip 2

ly=5.8 λ= 5.8 = 1.39 4.15

lx=4.15

A. Terasa


Mx = α1 x qterasa x lx2

My = α2 x qterasa x ly2


M'x = -α3 x qterasa x lx2

M'y = -α4 x qterasa x ly2


w= α 0 x qterasa x lx4

E x h3

B. Planseu intermediar


Mx = α1 x qpl x lx2

My = α2 x qpl x ly2


M'x = -α3 x qpl x lx2

M'y = -α4 x qp lx ly2


w= α0 x qpl x lx4

E x h3

Valorile relatiilor de mai sus sunt centralizate in tabelul 3.

Tabel 3P

LAN

SE

U T

ER

AS

A PL

AC

A 1

ParametrulIn camp Pe reazeme

Directia x Directia y Directia y Directia x' Directia y'

α1 2 3 4 5 6

0.0263 0.0209 0.0221 0.0752 0.0657 0.0281l [m] 6.0800 6.3800 6.3800 6.0800 6.3800

q [N/m] 10769.0000 10769.0000 10769.0000 10769.0000 10769.0000 M [Nm] 10469.7976 9161.4248 9687.4396 29936.4554 28799.3114

Sageata [m] 0.0070

PL

AC

A 2


Directia x Directia y Directia x' Directia y'

α1 2 4 5 6

0.0217 0.0189 0.0649 0.0558 0.0236l [m] 6.0800 6.3800 6.0800 6.3800

q [N/m] 10769.0000 10769.0000 10769.0000 10769.0000 M [Nm] 8638.5782 8284.7334 25836.1164 24459.6891

Sageata [m] 0.0059

PLA

NS

EU

IN

TE

RM

ED

IAR

PL

AC

A 1


Directia x Directia y Directia y Directia x' Directia y'

α1 2 3 4 5 6

0.0263 0.0209 0.0221 0.0753 0.0657 0.0281l [m] 6.0800 6.3800 6.3800 6.0800 6.3800

q [N/m] 8509.0000 8509.0000 8509.0000 8509.0000 8509.0000 M [Nm] 8272.5887 7238.7932 7654.4176 23685.3964 22755.4407

Sageata [m] 0.0055

PL

AC

A 2


Directia x Directia y Directia x' Directia y'

α1 2 4 5 6

0.0217 0.0189 0.0649 0.0558 0.0236l [m] 6.0800 6.3800 6.0800 6.3800

q [N/m] 8509.0000 8509.0000 8509.0000 8509.0000 M [Nm] 6825.6720 6546.0857 20414.1066 19326.5387

Sageata [m] 0.0046

C ALCULUL ARIEI DE ARMARE PE PLACI SI AL NUMARULUI DE BARE

Parametrii geometrici ai placii sunt:

Grosime hp = 13 cmStrat de acoperire a = 1.5 cmLatimea fasiei de calcul b = 100 cm

h0 = hp - a = 11.5 cm Materiale folosite :

Beton BC 20 cu Rc = 115 daN/cm2

Otel PC52 cu Ra = 3000 daN/cm2

Ariile de armare pe cele doua directii se determina cu relatiile:

c20

x1 Rhb

Mm

⋅⋅=

11 m211 ⋅−−=ξ

100R

Rp

a

c11 ⋅⋅ξ=

0x

ax hb100

pA ⋅⋅=

Numarul de bare se calculeaza cu relatia:

2a

d25.0

An

⋅π⋅=

Rezultatele relatiilor de mai sus sunt centralizate in tabelele 4 si 5.

Tabelul 4P

LAN

SE

U T

ER

AS

A PL

AC

A 1


Directia x Directia y Directia y Directia x' Directia y'M [Nm] 10469.7976 9161.4248 9687.4396 29936.4554 28799.3114

m 0.0688 0.0602 0.0637 0.1968 0.1894ζ 0.0714 0.0622 0.0659 0.2213 0.2118

p [%] 0.2737 0.2383 0.2525 0.8484 0.8119Aa [mm2] 314.7056 274.0680 290.3576 975.6995 933.6278

PL

AC

A 2


Directia x Directia y Directia x' Directia y'M 8638.5782 8284.7334 25836.1164 24459.6891m 0.0568 0.0545 0.1699 0.1608ζ 0.0585 0.0560 0.1874 0.1764p 0.2243 0.2148 0.7185 0.6761Aa 257.9398 247.0603 826.3172 777.5492

PLA

NS

EU

IN

TE

RM

ED

IAR

PL

AC

A 1


Directia x Directia y Directia y Directia x' Directia y'M 8272.5887 7238.7932 7654.4176 23685.3964 22755.4407m 0.0544 0.0476 0.0503 0.1557 0.1496ζ 0.0560 0.0488 0.0517 0.1702 0.1629p 0.2145 0.1870 0.1980 0.6525 0.6244Aa 246.6874 215.0662 227.7504 750.4011 718.0592

PL

AC

A 2


Directia x Directia y Directia x' Directia y'M 6825.6720 6546.0857 20414.1066 19326.5387m 0.0449 0.0430 0.1342 0.1271ζ 0.0459 0.0440 0.1447 0.1364p 0.1761 0.1687 0.5547 0.5228Aa 202.4964 194.0108 637.8606 601.1824

Tabelul 5P

LAN

SE

U T

ER

AS

A

PLA

CA

1Parametrul

In camp Pe reazemeDirectia x Directia y Directia y Directia x' Directia y'

Momente [Nm] 10469.7976 9161.4248 9687.4396 29936.4554 28799.3114Aria armaturii [mm2] 314.7056 274.0680 290.3576 975.6995 933.6278Nr. bare calculat [bare/m] 6.2640 5.4552 5.7794 19.4208 18.5834

Ø8 / Ø10 4.0090 3.4913 3.6988 12.4293 11.8933Nr. bare adoptat Ø10 [bare/m] 4 3 4 13 12

PLA

CA

2


Directia x Directia y Directia x' Directia y'Momente [Nm] 8638.5782 8284.7334 29936.4554 24459.6891Aria armaturii [mm2] 257.9398 247.0603 975.6995 777.5492Nr. bare calculat [bare/m] 5.1342 4.9176 19.4208 15.4767

Ø8 / Ø10 3.2859 3.1473 12.4293 9.9051Nr. bare adoptat Ø10 [bare/m] 4 4 13 10

PLA

NS

EU

IN

TE

RM

ED

IAR

PLA

CA

1


Directia x Directia y Directia y Directia x' Directia y'Momente [Nm] 8272.5887 7238.7932 7654.4176 23685.3964 22755.4407Aria armaturii [mm2] 246.6874 215.0662 227.7504 750.4011 718.0592Nr. bare calculat [bare/m] 4.9102 4.2808 4.5332 14.9363 14.2926

Ø8 / Ø10 3.1425 2.7397 2.9013 9.5592 9.1473Nr. bare adoptat Ø10 [bare/m] 4 3 3 10 10

PLA

CA

2


Directia x Directia y Directia x' Directia y'Momente [Nm] 6825.6720 6546.0857 23685.3964 19326.5387Aria armaturii [mm2] 202.4964 194.0108 750.4011 601.1824Nr. bare calculat [bare/m] 4.0306 3.8617 14.9363 11.9662

Ø8 / Ø10 2.5796 2.4715 9.5592 7.6584Nr. bare adoptat Ø10 [bare/m] 3 3 10 8

III. CALCULUL INCARCARILOR PE GRINZI

ssssssssssssssssssssPPbLLPPPPP

Structura este alcatuita numai din grinzi principale.

c20

x1 Rhb

Mm

⋅⋅=

11 m211 ⋅−−=ξ

100R

Rp

a

c11 ⋅⋅ξ=

0x

ax hb100

pA ⋅⋅=

Numarul de bare se calculeaza cu relatia:

2a

d25.0

An

⋅π⋅=

GRINZI ETAJ

Greutatea proprie a grinzii pe ml este: 3301,125004,03,0 =⋅⋅⋅=gG daN/mlS1 = 13,6 m2

S2 = 7,2 m2

Incarcarile pe grinzi se calculeaza dupa cum urmeaza:

G Longitudinala1

346,180833015,4

9,10768,621 =+⋅=+⋅= g

terasaGP G

L

qSq

daN/ml

Aria de armare =4.8136 echivalent cu 4 bare Φ 14

G Longitudinala 2

69,328633015,4

9,10768,622 22 =+⋅⋅=+⋅= g

terasaGP G

LqS

q daN/ml


G Transversala 3

91,19613308,5

9,10768,613 =+⋅=+⋅= g

terasaGP G

L

qSq

daN/ml


G Transversala 4

82,35933308,5

9,10768,622 24 =+⋅⋅=+⋅= g

terasaGP G

LqS

q daN/ml


Proiect Beton Armat

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