Breviar de Calcul-MUZEU

8/18/2019 Breviar de Calcul-MUZEU

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Universitatea “POLITEHNICA “ din Timisoara

Facultatea de Constructii

Lucrare de Licenta Page 1

Breviar de calcul

Calculul functional al scarilor

1. Scari exterioare

n =

= = 6.66 → n = 7

H = 1 m

ℎ = max 15 cm

ℎ = → ℎ = → ℎ = 14.3 cm ≤ 15 cm

3 · ℎ + = 80 ÷ 85

3 · 14.3 + = 83 → = 40 cm

2. Scari interioare la parter

n =

=

. = 36.66 → n = 38

= 6.0 m

ℎ = max 16.5 cm

ℎ = =

→ ℎ = 15. 8 cm

2 · ℎ + = 62 ÷ 64

2 · 15.8 + = 62 → = 30.4 cm

3.

Scari interioare la subsol

n = =

. = 22.85 → n = 24

= 4.0 m

ℎ = max 17.5 cm

ℎ = =

→ ℎ = 16.7 cm

2 · ℎ + = 62

2 · 16.7 + = 62 → = 28.6 cm






4. Metoda grafica de balansare a treptelor scarii de la parter ( Metoda segmentelor egale )

Predimensionarea elementelor de rezistenta

1. Placa

=.. = 1.0 ≤ 2 → placa armata pe 2 directii

ℎ, =

=

→

ℎ, = 15 cm

2. Grinda de cadru

ℎ, =

· =

· 6000 → ℎ, = 600 mm

= 2 ↔

= 2 → = 300 mm

3. Stalp

Se aleg = ℎ = 500 mm






Calculul planseelor

1. Determinarea incarcarii placii planseului

1.1. Permanenta

Etaj curent

placa din beton armat

= ℎ · γ = 0.15 · 25 →

= 3.75 ⁄

tencuiala

=

ℎ · γ = 0.02 · 18 →

= 0.36

⁄

pardoseala : gresie ceramic + sapa 3 cm

= 0.9 ⁄

= 3.75 + 0.36 + 0.9 →

= 5.01 ⁄

Terasa necirculabila


= ℎ · γ = 0.15 · 25 →

= 3.75 ⁄

tencuiala

= ℎ · γ = 0.02 · 18 → = 0.36 ⁄

straturi terasa

strat de panta ( p = 3% )

ℎ · γ = 0.08 · 18 = 1.44 ⁄

sapa de egalizare

d · γ = 0.03 · 21 = 0.63

⁄

bariera de vapori

g = 0.06 ⁄

termoizolatie

g = 0.11 ⁄

folie impermeabila

suport hidroizolatie din sapa slab armata

d · γ = 0.04 · 22 = 0.88

⁄






strat de difuzie

g = 0.05 ⁄

hidroizolatie

g = 0.145 ⁄ = 1.44 + 0.63 +0.06 + 0.11 + 0.88 + 0.05 + 0.145

= 3.31 ⁄

= 3.75 + 0.36 + 3.31 → = 7.42 ⁄

1.2. Utila

Etaj curent

= 5.0 ⁄ ( C3 – muzeu )

Terasa

= 0.4 ⁄

1.3 Incarcare din zapada

= µ · · · ,

µ = 0.8

= 0.8 ( expunere totala ) = 1.0

, = 1.5 ⁄

= 0.8 · 0.8 · 1 · 1.5 → = 0.96 ⁄

1.4 Valorile de calcul ale actiunilor

Etaj curent

= 1.35 ·

= 1.35 · 5.01 → = 6.76 ⁄

= 1.5 ·

= 1.5 · 5 → = 7.5 ⁄

Terasa

= 1.35 · = 1.35 · 7.42 → = 10 ⁄

= 1.5 ·

= 1.5 · 0.96 →

= 1.44

⁄








2.1 Determinarea deschiderilor de calcul

= - = 6.0 - 0.3 → = 5.7 m

=

-

= 6.0 - 0.3 →

= 5.7 m

2.2 Determinarea incarcarilor conventionale de calcul

p = +

= 6.76 + 7.5 → p = 14.26 ⁄

′ = + 0.5 ·

= 6.76 + 0.5 · 7.5 → ′ = 10.51 ⁄

′′ = 0.5 · = 0.5 · 7.5 → ′′ = 3.75 ⁄

2.3 Schemele statice ale fasiilor si determinarea solicitarilor

Directia X

Fasia F1x

λ =

=

.

. → λ = 1






= 0.0269 ( placa tip 4 )

= 0.0226 ( placa tip 5 )

= 0.0365 ( placa tip 1 )

= 0.6667 ( placa tip 5 )

= ( · ′ + · ′′ ) ·

= ( 0.0269 · 10.51 + 0.0365 · 3.75 ) · 5.7 → = 13.63 · = ( · ′ + · ′′ ) ·

= ( 0.0226 · 10.51 + 0.0365 · 3.75 ) · 5.7 → = 12.16 · = · ·

= . ·. · . → = -30.88 ·

Fasia F2x

λ = =

.. → λ = 1

= 0.0334

= · p · = 0.0334 · 14.26 · 5.7 → = 15.47 ·

15.47






Fasia F3x

λ = =

.. → λ = 1

= 0.0226 ( placa tip 5 )

= 0.0179 ( placa tip 6 ) = 0.0365 ( placa tip 1 )

= 0.6667 ( placa tip 5 )

= 0.5 ( placa tip 6 )

= 12.16 ·

= ( · ′ + · ′′ ) ·

= ( 0.0179 · 10.51 + 0.0365 · 3.75 ) · 5.7 → = 10.55 ·

= · · = . ·. · . → = - 25.74 ·

= · · = . ·. · .

→ = - 19.3 ·

= · · = . ·. · .

→ = - 25.74 ·






Fasia F4x

λ = =

.. → λ = 1

= 13.63 ·

= 12.16 ·

= - 30.88 ·

= - 25.74 ·

Fasia F5x

λ = = .. → λ = 1

= 0.0267

= · p · = 0.0267 · 14.26 · 5.7 → = 12.37 ·






Fasia F6x

λ = =

.. → λ = 1

= 12.16 ·

= - 25.74 ·






Directia Y

Fasia F1y

λ = =

.. → λ = 1

= 0.0269 ( placa tip 4 )

= 0.0198 ( placa tip 5 )

= 0.0365 ( placa tip 1 )

= 0.5 ( placa tip 4 )

= ( · ′ + · ′′ ) ·

= ( 0.0269 · 10.51 + 0.0365 · 3.75 ) · 5.7 → = 12.16 ·

= ( · ′ + · ′′ ) ·

= ( 0.0198 · 10.51 + 0.0365 · 3.75 ) · 5.7 → = 11.2 ·

=

· ·

=

. ·. · .

→

= 23.16

·






Fasia F2y

λ = = .. → λ = 1

= 0.0179

= 0.0365

= 0.5

= ( · ′ + · ′′ ) ·

= ( 0.0179 · 10.51 + 0.0365 · 3.75 ) ·

5.7 →

= 10.55

·

= 11.2 ·

= · · = . ·. · .

→ = 23.16 ·

Fasia F3y

= 11.2 ·

= 10.55

·

= 12.16 ·






= 23.16 ·

Fasia F4y

λ = = .. → λ = 1

= 0.0179

= 0.333

= · p · = 0.0179 · 14.26 · 5.7 → = 8.29 ·

= · · = . ·. · .

→ = -15.44 ·

=

· ·

=

. ·. · .

→

= - 12.85

·

= 11.2 ·






Fasia F5y

λ = =

.. → λ = 1

= 0.0334 = 0.333

= · p · = 0.0334 · 14.26 · 5.7 → = 15.47 ·

= · · = . ·. · .

→ = 19.3 ·

= 11.2 ·

Fasia F6y






2.4 Definitivarea grosimii placii de la etaj

= 25

/ ( beton C25/30)

= =

. → = 16.66 /

=345 / ( PC52 )

= =

. → = 300 /

ℎ = + ,

= , · ·

, = 23.32 ·

% = 0.25 ÷ 0.5 % ( pentru placa armata pe 2 directii )

Aleg

% = 0.464 → µ = 0.08

= . · . · ·. → = 132.3 mm

, = +Ø

= + ∆

= max ( Ø12 ; 15 ; 10 ) → = 15 mm

∆ = 5 mm

= 15 + 5 →

= 20 mm

, = 20 + → , = 26 mm

ℎ = + , = 132.3 + 26 = 158.3 → ℎ = 160 mm






2.5 Reguli constructive

Directia X

, ≤ 0.04 · b ·

, = ω · b · ·

= ℎ - , = 160 – 26 → = 134 mm

ω = (1 – 1 2 · µ )

µ =, · · =

. · · ·. → µ = 0.078

ω = (1 √ 1 2 · 0 .0 7 8) → ω = 0.0813

, = 0.0813 · 1000 · 134 · . → , = 605

↕

Ø12/17 = 665

, = 665 ≤ 0.04 · 1000 · 160 ↔ 665 ≤ 6400

, ≥ 0.0013 · b ·

, = ω · b · ·

ω = (1 – 1 2 · µ )

µ =, · · =

. · · ·. → µ = 0.0304

, = 9.10 ·

ω = (1 √ 12·0.0304) → ω = 0.0308

, = 0.0308 · 1000 · 134 ·. → , = 229.19

↕

Ø8/17 = 298

, = 298 ≥ 0.0013 · 1000 · 134 ↔ 298 ≥ 174.2

, = µ · b · ·

µ = – −

ω = · ·

=

· ·

. → ω = 0.04

µ = − −. → µ = 0.0392






, = 0.0392 ·1000 · 134 · 16.66 → , = 11.72 ·

Pentru ≤ , → se armeaza cu , = 298

Directia Y , ≤ 0.04 · b ·

, = ω · b · ·

= – Ø = 134 – 12 → = 122 mm

ω = (1 – 1 2 · µ )

µ =, · · =

. · · ·. → µ = 0.103

ω = (1 √ 1 2 · 0 .1 0 3) → ω = 0.109

, = 0.109 · 1000 · 122 ·. → , = 738.4

↕

Ø12/15 = 754

, = 754 ≤ 0.04 · 1000 · 160 ↔ 754 ≤ 6400

, ≥ 0.0013 · b ·

, = ω · b · ·

ω = (1 – 1 2 · µ )

µ =, · · =

. · · ·. → µ = 0.0237

ω = (1 √ 12·0.0237) → ω = 0.0239

, = 0.0239 · 1000 · 122 ·. → , = 162.51

↕

Ø8/15 = 335

, = 335 ≥ 0.0013 · 1000 · 122 ↔ 335 ≥ 158.6

, = µ · b · ·

µ = – −

ω =

·

·

=

· ·

. → ω = 0.049

µ = − −. → µ = 0.0477






, = 0.0477 ·1000 · 122 · 16.66 → , = 11.82 ·


2.6 Armare placa etaj pe directia X

Fasia Sectiune b d Fcd Fyd MEd As p% As,ef Armatura

[mm] [mm] [MP ] [MP] KN·m mm2 mm2

1 - c 15.41 0.05151 0.0529 393.75 0.29 462 Ø10/17

2 - r 23.02 0.07695 0.0802 596.55 0.45 665 Ø12/17

F1x 3 - c 12.49 0.04175 0.0427 317.47 0.24 462 Ø10/174 - r 23.32 0.07795 0.0813 604.67 0.45 665 Ø12/17

5 - c 15.89 0.05312 0.0546 406.37 0.3 462 Ø10/17

F2x 1 - c 17.44 0.0583 0.0601 447.27 0.33 462 Ø10/17

1 - c 10.39 0.03473 0.0354 263.11 0.2 298 Ø8/17

2 - r 17.75 0.05934 0.0612 455.48 0.34 462 Ø10/17

3 - c 9.98 0.03336 0.0339 252.54 0.19 298 Ø8/17

F3x 4 - r 16.54 0.05529 0.0569 423.49 0.32 462 Ø10/17

5 - c 9.1 0.03042 0.0309 229.92 0.17 298 Ø8/17

6 - r 18.72 0.06258 0.0647 481.23 0.36 665 Ø12/177 - c 1000 134 16.66 300 12.64 0.04225 0.0432 321.37 0.24 462 Ø10/17

8 - r 20.27 0.06776 0.0702 522.58 0.39 665 Ø12/17

9 - c 11.28 0.03771 0.0384 286.1 0.21 298 Ø8/17

1 - c 15.47 0.05171 0.0531 395.33 0.3 462 Ø10/17

2 - r 23.06 0.07709 0.0803 597.63 0.45 665 Ø12/17

3 - c 12.77 0.04269 0.0436 324.75 0.24 462 Ø10/17

F4x 4 - r 21.36 0.0714 0.0742 551.8 0.41 665 Ø12/17

5 - c 13.18 0.04406 0.0451 335.42 0.25 462 Ø10/17

6 - r 19.13 0.06395 0.0661 492.14 0.37 665 Ø12/17

7 - c 9.79 0.03273 0.0333 247.65 0.18 462 Ø10/17

F5x 1 - c 11.41 0.03814 0.0389 289.46 0.22 298 Ø8/17

1 - c 11.5 0.03844 0.0392 291.79 0.22 298 Ø8/17

F6x 2 - r 20.82 0.0696 0.0722 537.31 0.4 665 Ø12/17

3 - c 13.43 0.04489 0.046 341.94 0.26 462 Ø10/17

1 - c 2.43 0.00812 0.0082 60.695 0.05 298 Ø8/17

F7x 2 - r 4.18 0.01397 0.0141 104.72 0.08 298 Ø8/17

3 - c 2.03 0.00679 0.0068 50.67 0.04 298 Ø8/17






2.7 Armare placa etaj pe directia Y


[mm] [mm] [MP] [MP] KN·m mm2 mm2

1 - c 15.55 0.06271 0.0648 439.09 0.36 524 Ø10/15

2 - r 23.15 0.09336 0.0982 665.17 0.55 754 Ø12/15

F1y 3 - c 12.57 0.05069 0.052 352.62 0.29 524 Ø10/15

4 - r 23.18 0.09348 0.0983 666.08 0.55 754 Ø12/15

5 - c 15.83 0.06384 0.066 447.28 0.37 524 Ø10/15

1 - c 10.5 0.04234 0.0433 293.23 0.24 335 Ø8/15

2 - r 18.13 0.07311 0.076 514.92 0.42 524 Ø10/15F2y 3 - c 10 0.04033 0.0412 278.97 0.23 335 Ø8/15

4 - r 17.89 0.07215 0.075 507.83 0.42 524 Ø10/15

5 - c 10.32 0.04162 0.0425 288.09 0.24 335 Ø8/15

1 - c 11.62 0.04686 0.048 325.3 0.27 335 Ø8/15

2 - r 17.95 0.07239 0.0752 509.6 0.42 524 Ø10/15

F3y 3 - c 1000 122 16.66 300 9.37 0.03779 0.0385 261.04 0.21 335 Ø8/15

4 - r 20.94 0.08445 0.0883 598.57 0.49 524 Ø10/15

5 - c 14.9 0.06009 0.062 420.13 0.34 524 Ø10/15

1 - c 6.25 0.0252 0.0255 172.97 0.14 335 Ø8/15

2 - r 15.06 0.06073 0.0627 424.79 0.35 524 Ø10/153 - c 12.49 0.05037 0.0517 350.31 0.29 524 Ø10/15

F4y 4 - r 23.42 0.09445 0.0994 673.35 0.55 754 Ø12/15

5 - c 15.87 0.064 0.0662 448.45 0.37 524 Ø10/15

6 - r 23.31 0.094 0.0989 670.02 0.55 754 Ø12/15

7 - c 12.09 0.04876 0.05 338.8 0.28 524 Ø10/15

8 - r 20.07 0.08094 0.0845 572.55 0.47 754 Ø12/15

9 - c 12.22 0.04928 0.0506 342.54 0.28 524 Ø10/15

1 - c 11.71 0.04722 0.0484 327.88 0.27 335 Ø8/15

F5y 2 - r 25.59 0.1032 0.1092 739.54 0.61 754 Ø12/15

3 - c 19.9 0.08025 0.0838 567.48 0.47 754 Ø12/15

1 - c 5.89 0.02375 0.024 162.89 0.13 335 Ø8/15

F6y 14.44 0.05823 0.06 406.75 0.33 524 Ø10/15

11.97 0.04827 0.0495 335.35 0.27 335 Ø8/15






3. Calculul placii - terasa






3.1 Determinarea solicitarilor

Solicitarile s-au determinat cu programul AXIS VM/V9

3.2 Definitivarea grosimii placii - terasa

= 25 / ( beton C25/30)

= =

. → = 16.66 /

=345 / ( PC52 )

= =

. → = 300 /

ℎ = + ,

= , · ·

, = 25.33 ·

% = 0.25 ÷ 0.5 % ( pentru placa armata pe 2 directii )

Aleg % = 0.464 → µ = 0.08

= . · . · ·. → = 137 mm

, =

+

Ø

= + ∆

= max ( Ø12 ; 15 ; 10 ) → = 15 mm

∆ = 5 mm

= 15 + 5 → = 20 mm

, = 20 + → , = 26 mm

ℎ = + , = 137 + 26 = 163 → ℎ = 160 mm






3.2 Reguli constructive

Directia X

, ≤ 0.04 · b ·

, = ω · b · ·

= ℎ - , = 160 – 26 → = 134 mm

ω = (1 – 1 2 · µ )

µ =, · · =

. · · ·. → µ = 0.0846

ω = (1 √ 12·0.0846) → ω = 0.0885

, = 0.0885 · 1000 · 134 · . → , = 658.7

↕

Ø12/17 = 665

, = 665 ≤ 0.04 · 1000 · 160 ↔ 665 ≤ 6400

, ≥ 0.0013 · b ·

, = ω · b · ·

ω = (1 – 1 2 · µ )

µ =, · · =

. · · ·. → µ = 0.0265

, = 7.94 ·

ω = (1 √ 12·0.0265) → ω = 0.0268

, = 0.0268 · 1000 · 134 ·. → , = 199.8

↕

Ø8/17 = 298

, = 298 ≥ 0.0013 · 1000 · 134 ↔ 298 ≥ 174.2

, = µ · b · ·

µ = – −

ω = · ·

=

· ·

. → ω = 0.04

µ = − −. → µ = 0.0392






, = 0.0392 ·1000 · 134 · 16.66 → , = 11.72 ·


Directia Y , ≤ 0.04 · b ·

, = ω · b · ·

= – Ø = 134 – 12 → = 122 mm

ω = (1 – 1 2 · µ )

µ =, · · =

. · · ·. → µ = 0.101

ω = (1 √ 1 2 · 0 .1 0 1) → ω = 0.1066

, = 0.1066 · 1000 · 122 ·. → , = 722.84

↕

Ø12/15 = 754

, = 754 ≤ 0.04 · 1000 · 160 ↔ 754 ≤ 6400

, ≥ 0.0013 · b ·

, = ω · b · ·

ω = (1 – 1 2 · µ )

µ =, · · =

. · · ·. → µ = 0.0225

ω = (1 √ 12·0.0225) → ω = 0.0227

, = 0.0227 · 1000 · 122 ·. → , = 153.79

↕

Ø8/15 = 335

, = 335 ≥ 0.0013 · 1000 · 122 ↔ 335 ≥ 158.6

, = µ · b · ·

µ = – −

ω =

·

·

=

· ·

. → ω = 0.049

µ = − −. → µ = 0.0477






, = 0.0477 ·1000 · 122 · 16.66 → , = 11.82 ·


3.3 Armare placa terasa pe directia X


[mm] [mm] [MP ] [MP] KN·m mm2 mm2

1 - c 12.82 0.04286 0.0438 326.05 0.24 462 Ø10/17

2 - r 25.28 0.08451 0.0884 657.94 0.49 665 Ø12/17

F1x 3 - c 10.8 0.0361 0.0368 273.69 0.2 298 Ø8/17

4 - r 23.39 0.07819 0.0815 606.56 0.45 665 Ø12/17

5 - c 10.91 0.03647 0.0372 276.53 0.21 298 Ø8/176 - r 23.52 0.07862 0.082 610.08 0.46 665 Ø12/17

7 - c 10.89 0.0364 0.0371 276.01 0.21 298 Ø8/17

8 - r 23.51 0.07859 0.0819 609.81 0.46 665 Ø12/17

9 - c 10.9 0.03644 0.0371 276.27 0.21 298 Ø8/17

1 - c 8.7 0.02908 0.0295 219.66 0.16 298 Ø8/17

2 - r 19.42 0.06492 0.0672 499.87 0.37 665 Ø12/17

3 - c 8.33 0.02785 0.0282 210.18 0.16 298 Ø8/17

4 - r 18.82 0.06291 0.065 483.89 0.36 665 Ø12/17

F2x 5 - c 8.21 0.02744 0.0278 207.11 0.15 298 Ø8/176 - r 1000 134 16.66 300 18.92 0.06325 0.0654 486.55 0.36 665 Ø12/17

7 - c 8.43 0.02818 0.0286 212.74 0.16 298 Ø8/17

8 - r 19 0.06351 0.0657 488.68 0.36 665 Ø12/17

9 - c 8.34 0.02788 0.0283 210.44 0.16 298 Ø8/17

1 - c 12.83 0.04289 0.0439 326.31 0.24 462 Ø10/17

2 - r 25.26 0.08444 0.0883 657.4 0.49 665 Ø12/17

3 - c 10.81 0.03614 0.0368 273.95 0.2 298 Ø8/17

4 - r 23.64 0.07902 0.0824 613.34 0.46 665 Ø12/17

F3x 5 - c 11.13 0.03721 0.0379 282.22 0.21 298 Ø8/176 - r 21.11 0.07057 0.0733 545.09 0.41 665 Ø12/17

7 - c 7.94 0.02654 0.0269 200.21 0.15 298 Ø8/17

8 - r 18.76 0.06271 0.0648 482.3 0.36 665 Ø12/17

9 - c 8.48 0.02835 0.0288 214.02 0.16 298 Ø8/17

1 - c 9.63 0.03219 0.0327 243.54 0.18 298 Ø8/17

F4x 2 - r 20.11 0.06722 0.0697 518.3 0.39 665 Ø12/17

3 - c 8.27 0.02765 0.028 208.65 0.16 298 Ø8/17

F5x 1 - c 10 0.03343 0.034 253.06 0.19 298 Ø8/17

2 - r 20.95 0.07003 0.0727 540.79 0.4 665 Ø12/173 - c 8.9 0.02975 0.0302 224.79 0.17 298 Ø8/17






3.4 Armare placa terasa pe directia Y

Fasia Sectiune b d Fcd Fyd MEd As p% As,ef Armatura[mm] [mm] [MP ] [MP] KN·m mm2 mm2

1 - c 13.04 0.05259 0.054 366.18 0.3 524 Ø10/15

2 - r 25.24 0.10179 0.1076 728.82 0.6 754 Ø12/15

F1y 3 - c 10.72 0.04323 0.0442 299.52 0.25 335 Ø8/15

4 - r 25.19 0.10159 0.1073 727.29 0.6 754 Ø12/15

5 - c 13.09 0.05279 0.0543 367.62 0.3 524 Ø10/15

1 - c 8.83 0.03561 0.0363 245.71 0.2 335 Ø8/15

2 - r 19.62 0.07912 0.0825 559.14 0.46 754 Ø12/15

F2y 3 - c 8.36 0.03371 0.0343 232.4 0.19 335 Ø8/154 - r 19.68 0.07937 0.0828 560.93 0.46 754 Ø12/15

5 - c 8.89 0.03585 0.0365 247.41 0.2 335 Ø8/15

1 - c 9.73 0.03924 0.04 271.28 0.22 335 Ø8/15

2 - r 20.23 0.08158 0.0852 577.33 0.47 754 Ø12/15

F3y 3 - c 8.39 0.03384 0.0344 233.25 0.19 335 Ø8/15

4 - r 19.89 0.08021 0.0837 567.18 0.46 754 Ø12/15

5 - c 9.14 0.03686 0.0376 254.51 0.21 335 Ø8/15

1 - c 5.58 0.0225 0.0228 154.21 0.13 335 Ø8/15

2 - r 17.72 0.07146 0.0742 502.81 0.41 524 Ø10/15

3 - c 11.21 0.04521 0.0463 313.54 0.26 335 Ø8/15

F4y 4 - r 1000 122 16.66 300 24.17 0.09747 0.1028 696.15 0.57 754 Ø12/15

5 - c 11.09 0.04472 0.0458 310.1 0.25 335 Ø8/15

6 - r 20.96 0.08453 0.0884 599.17 0.49 754 Ø12/15

7 - c 7.94 0.03202 0.0326 220.53 0.18 335 Ø8/15

8 - r 18.66 0.07525 0.0783 530.61 0.43 754 Ø12/15

9 - c 8.42 0.03396 0.0346 234.1 0.19 335 Ø8/15

10 - r 19.98 0.08058 0.0841 569.87 0.47 754 Ø12/15

11 - c 9.16 0.03694 0.0376 255.07 0.21 335 Ø8/15

1 - c 5.87 0.02367 0.024 162.33 0.13 335 Ø8/15F5y 2 - r 15.03 0.06061 0.0626 423.92 0.35 524 Ø10/15

3 - c 8.22 0.03315 0.0337 228.44 0.19 335 Ø8/15

4 - r 18.98 0.07654 0.0797 540.11 0.44 754 Ø12/15

5 - c 8.2 0.03307 0.0336 227.88 0.19 335 Ø8/15

6 - r 19.13 0.07715 0.0804 544.56 0.45 754 Ø12/15

7 - c 8.55 0.03448 0.0351 237.78 0.19 335 Ø8/15

8 - r 19.28 0.07775 0.081 549.02 0.45 754 Ø12/15

9 - c 8.41 0.03392 0.0345 233.82 0.19 335 Ø8/15

10 - r 19.92 0.08033 0.0838 568.08 0.47 754 Ø12/15

11 - c 9.12 0.03678 0.0375 253.94 0.21 335 Ø8/15






Dimensionarea cadrului

1. Evaluarea incarcarilor






1.1 Incarcari permanente, uniform distribuite

Nivel curent

Greutate permanenta grinda

= 0.6 · 0.3 · 25 → = 4.5 / Incarcari din planseu


= ℎ · γ = 0.16 · 25 →

= 4.0 ⁄

tencuiala

= ℎ · γ = 0.02 · 18 → = 0.36 ⁄

pardoseala : gresie ceramic + sapa 3 cm

= 0.9 ⁄

= 4.0 + 0.36 + 0.9 = 5.26 ⁄

o grinzi intermediare

= 5.26 ·

+ = 5.26 ·

+

= 15.78

o grinzi marginale

= 5.26 · = 5.26 ·

= 7.89

Incarcare din peretele de compartimentare

1 – tencuiala 1.5 cm ;

γ = 19

⁄

2 – Poroterm 250x380x238

g = 2.9 ⁄






= 2 · 19 · 0.015 + 2.9 → = 3.47 ⁄

= 3.47 · ( ℎ) = 3.47 · ( 6 – 0.6 ) → = 18.73

Grinzi intermediare

, = 4.5 + 15.78 + 18.73 → ,

= 39.01

Grinzi marginale

, = 4.5 + 7.89 + 18.73 → ,

= 31.12






Terasa

Greutate permanenta grinda

= 0.6 · 0.3 · 25 → = 4.5 / Incarcari din planseu


= ℎ · γ = 0.16 · 25 →

= 4.0 ⁄

tencuiala

= ℎ · γ = 0.02 · 18 → = 0.36 ⁄

straturi terasa

= 3.31 ⁄

= 4.0 + 0.36 + 3.31 = 7.67 ⁄

o grinzi intermediare

= 7.67 ·

+ = 7.67 ·

+

= 23.01

o grinzi marginale

= 7.67 ·

= 7.67 ·

= 11.5

Greutate atic

= · 1.0 → = 3.47

Grinzi intermediare

= 4.5 + 23.01 → = 27.51 ⁄

Grinzi marginale = 4.5 + 11.5 + 3.47 → = 19.47 ⁄






1.2 Incarcari permanente, concentrate

Nivel curent

Greutate stalp

= 0.5 · 0.5 · 25 → = 6.25 ⁄

= 6.25 · 6 → = 37.5

1.3 Incarcare din zapada

= µ · · · ,

µ = 0.8

= 0.8 ( expunere totala )

= 1.0

, = 1.5 ⁄

= 0.8 · 0.8 · 1.0 · 1.5 → = 0.96 ⁄






Grinzi intermediare

= 0.96 ·+

= 0.96 ·+

→ = 2.88 ⁄

Grinzi marginale

= 0.96 · = 0.96 · → = 1.44 ⁄

1.4 Utila

Nivel curent

= 5.0 ⁄ ( Categoria C3 – muzeu )

Grinzi intermediare

= 5.0 ·+

= 5.0 ·

+

→

= 15

⁄

Grinzi marginale

= 5.0 ·

= 5.0 · →

= 7.5 ⁄

Terasa

= 0.4 ⁄ ( terasa necirculabila )

Grinzi intermediare

= 0.4 ·

+

= 0.4 ·

+

→

= 1.2

⁄

Grinzi marginale

= 0.4 · = 0.4 ·

→ = 0.6 ⁄

Utila 1_x






Utila 2_x

Utila 1_y






Utila 2_y

Utila






1.5 Incarcari din vant

= · ·

= 0.4 ⁄ ( Timisoara ) = 12 . } → = 1.68

. ↔ zone urbane cu densitate redusa de constructii

= ?

Vant pe directie transversala

Plan

h = 12 m

e = min ( b; 2h ) = min ( 33 ; 24 ) → e = 24 m

Pentru d = 54 m ˃ e = 24 m

↓






=

= 4.5 ˃ 4

↓

Zona , = · · [ ⁄ ]

A -1.0 0.4 · 1.68 · ( - 1) = - 0.67

B -0.8 0.4 · 1.68 · ( - 0.8) = - 0.54

C -0.5 0.4 · 1.68 · ( - 0.5) = - 0.33

D 0.6 0.4 · 1.68 · 0.6 = 0.4

E -0.3 0.4 · 1.68 · ( - 0.3) = - 0.2

Plan

Zona D

cadru marginal

0.4 · 3 = 1.2 ⁄

cadru intermediar

0.4 · 6 = 2.4

⁄

Zona E

cadru marginal

0.2 · 3 = 0.6 ⁄

cadru intermediar

0.2 · 6 = 1.2 ⁄

Zona A

cadru marginal

0.67 · 3 = 2.01 ⁄






Zona B

cadru intermediar

0.54 · 6 = 3.24 ⁄

Zona C cadru marginal

0.33 · 3 = 0.99 ⁄

cadru intermediar

0.33 · 6 = 1.98 ⁄

Zona B-C

0.54 · 3 + 0.33 · 3 = 2.61 ⁄

Vant pe directia longitudinal

Plan

h = 12 m

e = min ( b ; 2h ) = min ( 54 ; 24 ) → e = 24 m

Pentru d = 33 m ˃ e = 24 m

↓






=

= 2.75 ↔ 1 < 2.75 < 4

↕ Zona , = · · [ ⁄ ]

A -1.0 0.4 · 1.68 · ( - 1) = - 0.67

B -0.8 0.4 · 1.68 · ( - 0.8) = - 0.54

C -0.5 0.4 · 1.68 · ( - 0.5) = - 0.33

D 0.68 0.4 · 1.68 · 0.68 = 0.45

E -0.3 0.4 · 1.68 · ( - 0.3) = - 0.2

Plan






Zona D

cadru marginal

0.45 · 3 = 1.35 ⁄

cadru intermediar0.45 · 6 = 2.7 ⁄

Zona E

cadru marginal

0.2 · 3 = 0.6 ⁄

cadru intermediar

0.2 · 6 = 1.2 ⁄

Zona A cadru marginal

0.67 · 3 = 2.01 ⁄

cadru intermediar

0.67 · 6 = 4.02 ⁄

1.6 Actiunea seismica

= 0.16 g ( Timisoara )

· g = 1.6

= 0.7 s ( TM )

= 0.07 s

= 3 s

= 0.16 g ≤ 0.16 g

↕

Clasa de ductilitate M

q = 3.5 ( pt cadru )

= 1.35 ( cadre cu mai multe niveluri si deschideri )

q = 3.5 · 1.35 → q = 4.72

γ = 1.2 ( coefficient de importanta al cladirii )

β = 3.0






1.6 Combinatii de incarcari

Nume Tip Perm Utila1_x Utila2_x Utila1_y Utila2_y Zapada Vant_long Vant_transv Utila SM + SM -

1 Ci 1 SLU 1.35 0 0 0 0 0 0 0 1.50 0 0

2 Ci 2 SLU 1.35 1.50 0 0 0 0 0 0 0 0 0

3 Ci 3 SLU 1.35 0 1.50 0 0 0 0 0 0 0 0

4 Ci 4 SLU 1.35 0 0 1.50 0 0 0 0 0 0 0

5 Ci 5 SLU 1.35 0 0 0 1.50 0 0 0 0 0 0

6 Ci 6 SLU 1.35 0 0 0 0 1.50 0 0 0 0 0

7 Ci 7 SLU 1.35 0 0 0 0 0 1.50 0 0 0 0

8 Ci 8 SLU 1.35 0 0 0 0 0 0 1.50 0 0 0

9 Ci 9 SLU 1.35 0 0 0 0 1.05 0 0 1.50 0 0

10 Ci 10 SLU 1.35 1.50 0 0 0 1.05 0 0 0 0 0

11 Ci 11 SLU 1.35 0 1.50 0 0 1.05 0 0 0 0 0

12 Ci 12 SLU 1.35 0 0 1.50 0 1.05 0 0 0 0 0

13 Ci 13 SLU 1.35 0 0 0 1.50 1.05 0 0 0 0 0

14 Ci 14 SLU 1.35 0 0 0 0 1.50 0 0 1.05 0 0

15 Ci 15 SLU 1.35 1.05 0 0 0 1.50 0 0 0 0 0

16 Ci 16 SLU 1.35 0 1.05 0 0 1.50 0 0 0 0 0

17 Ci 17 SLU 1.35 0 0 1.05 0 1.50 0 0 0 0 0

18 Ci 18 SLU 1.35 0 0 0 1.05 1.50 0 0 0 0 0

19 Ci 19 SLU 1.35 0 0 0 0 0 1.50 0 1.05 0 0

20 Ci 20 SLU 1.35 1.05 0 0 0 0 1.50 0 0 0 0

21 Ci 21 SLU 1.35 0 1.05 0 0 0 1.50 0 0 0 0

22 Ci 22 SLU 1.35 0 0 1.05 0 0 1.50 0 0 0 0

23 Ci 23 SLU 1.35 0 0 0 1.05 0 1.50 0 0 0 0

24 Ci 24 SLU 1.35 0 0 0 0 0 0 1.50 1.05 0 0

25 Ci 25 SLU 1.35 1.05 0 0 0 0 0 1.50 0 0 0

26 Ci 26 SLU 1.35 0 1.05 0 0 0 0 1.50 0 0 0

27 Ci 27 SLU 1.35 0 0 1.05 0 0 0 1.50 0 0 0

28 Ci 28

SLU

1.35

0

0

0

1.05

0

0

1.50

0

0

0

29 Ci 29 SLU 1.00 0 0 0 0 0.40 0 0 0.40 0 0

30 Ci 30 SLU 1.00 0 0 0 0 0.40 0 0 0.40 1.20 0

31 Ci 31 SLU 1.00 0 0 0 0 0.40 0 0 0.40 0 1.20






`

2. Proiectarea grinzilor cadrului

2.1 Solicitari

Directia X

Sir 1x

{ = 176.57 · = 93.17 · Sir 2x

{ = 223.51 · = 129.8 ·






Sir 3x

{ = 274.8 ·

= 144.8 · Sir 4x

{ = 323.4 · = 154 · Sir 5x

{ = 331.92 · = 164.8 · Sir 6x

{ = 319.2 · = 155.2 · Sir 7x

{ = 262.8 · = 120.6 · Directia Y

Sir 1y

{ = 265.49 · = 127.7 · Sir 2y

{ = 331.60 · = 153.8 · Sir 3y

{ = 340.63 · = 160.3 · Sir 4y

{ = 320.64 · = 240.4 · Sir 5y

{ = 334.44 · = 236.1 ·






2.2 Dimensionarea armaturilor longitudinale pentru grinzile sirului 3x

Definitivarea sectiunii

d =

· ·

5220/25 = 1 % µ = 0.2

= =

. → = 16.66 ⁄

= 274.8 ·

d = . · . · · . → d = 524 mm

h = d + 50 mm = 524 + 50 = 574 → h = 600 mm b = 300 mm

=

= 2 < 3

Dimensionarea armaturilor longitudinale de la nivelul 1

Camp 1

=,−

= =

. → = 345 ⁄ ( combinatie cu seism )

= +Ø

= + ∆

∆ = 10 mm






= max ( Ø ; , ; 10 )

= ( 25 ; 15 ; 10 ) → = 25 mm

= 25 + 10 → = 35 mm

= = 35 + → = = 47.5 mm

d = h - = 600 – 47.5 → d = 552.5 mm

, = 137.41 ·

=. ·

.−. → = 7.88 ≥ ,

↕

4Ø16 = 8.08

, = 0.5 ·

· b · d

= 0.3 · / = 0.3 · 20/ = 2.21 ⁄

, = 0.5 ·. · 300 · 552.5 → , = 5.3

= 7.88 ˃ , = 5.3

p = · · 100 =

·. · 100 → p = 0.47 %

Camp 2

= ,− , = 126.62 ·

=. ·

.−. → = 7.26 ≥ ,

↕

4Ø16 = 8.08

= 7.26 ˃ , = 5.3

p = · · 100 = ·. · 100 → p = 0.47 %

Camp 3

= = 7.88

↕

4Ø16 = 8.08






Reazem A

µ =,− · ·

· ·

ℎ = h -

-

= 600 – 47.5 – 47.5 →

ℎ = 505 mm

, = 233.51 ·

= 788

µ =. · – · ·

· . ·. → µ = 0.06

µ = 0.06 ˃ 0

↕

ζ = 1.25 · (1 – 1 2 µ ) = 1.25 · (1 √ 1 2 · 0 . 0 6) = 0.077

ζ = 0.077 < 0.25 ↕

= ζ · d = 0.077 · 552.5 → = 42.54

= · = 1.88 · 47.5 → = 89.3

= 42.54 < = 89.3

↕

=, · =

. · · → = 13.4

↕

2Ø20 + 2Ø22 = 13.88

, = 0.5 · · b · d

= 0.3 · / = 0.3 · 20/ = 2.21 ⁄

, = 0.5 ·. · 300 · 552.5 → , = 5.3

= 13.4

˃

, = 5.3

Reazem B

µ =,− · ·

· ·

, = 223.24 ·

= 726

µ =. · − · ·

· . ·. → µ = 0.0634






µ = 0.0634 ˃ 0

↕

ζ = 1.25 · (1 – 1 2 µ ) = 1.25 · (1 √ 1 2 · 0 . 0 6 3) = 0.081

ζ = 0.081 < 0.25 ↕

= ζ · d = 0.081 · 552.5 → = 44.75

= · = 1.88 · 47.5 → = 89.3

= 44.75 < = 89.3

↕

=, · =

. · · → = 12.81

↕

4Ø20 = 12.56

= 12.81 ˃ , = 5.3

Reazem C

= = 12.81

↕

4Ø20 = 12.56

Reazem D

= = 13.4

↕

2Ø20 + 2Ø22 = 13.88






- aria necesara

- aria efectiva







Nivelul Sectiune b dss = dsi d hs f cd f yd MEd µ ζ Xu Xmin As As,min p% As,ef Armatura

[mm] [mm] [mm] [mm] [MP] [MP] KN · m mm2 mm2 mm2

1 - r 232.89 0.0577 0.0744 41.09 89.3 1336.72 530 0.8065 1388 2Ø22+2Ø20

2 - c 144.81 - - - - 831.167 530 0.5015 1016 4Ø18

3 - r 194.43 0.0726 0.0943 52.11 89.3 1115.97 530 0.6733 1256 4Ø20

2 4 - c 300 47.5 552.5 505 16.66 345 83.66 - - - - 480.184 530 0.2897 616 4Ø14

5 - r 194.43 0.0726 0.0943 52.11 89.3 1115.97 530 0.6733 1256 4Ø20

6 - c 144.81 - - - - 831.167 530 0.5015 1016 4Ø18

7 - r 232.89 0.0577 0.0744 41.09 89.3 1336.72 530 0.8065 1388 2Ø22+2Ø20






- aria necesara

- aria efectiva






2.3 Dimensionarea armaturilor longitudinale pentru grinzile sirului 5x


d = · ·

5220/25 = 1 % µ = 0.2

= =

. → = 16.66 ⁄

= 331.92 ·

d = . · . · · . → d = 576 mm

h = d + 50 mm = 576 + 50 = 626 → h = 650 mm

b = 300 mm

=

= 2.16 < 3

d = h - = 650 – 47.5 → d = 602.5 mm

ℎ = h -

-

= 650 – 47.5 – 47.5 →

ℎ = 555 mm









1 - r 270.57 0.0583 0.0751 45.26 89.3 1413.08 5.78 0.7818 1388 2Ø22+2Ø20

2 - c 164.82 - - - - 860.791 5.78 0.4762 942 3Ø20

3 - r 282.42 0.0861 0.1127 67.9 89.3 1474.97 5.78 0.816 1520 4Ø22

1 4 - c 126.22 - - - - 659.198 5.78 0.3647 762 3Ø18

5 - r 256.32 0.0717 0.0931 56.09 89.3 1338.66 5.78 0.7406 1388 2Ø22+2Ø20

6 - c 300 47.5 602.5 555 16.66 345 128.92 - - - - 673.299 5.78 0.3725 762 3Ø18

7 - r 256.22 0.0707 0.0918 55.31 89.3 1338.14 5.78 0.7403 1388 2Ø22+2Ø20

8 - c 127.86 - - - - 667.763 5.78 0.3694 762 3Ø18

9 - r 257.19 0.0713 0.0925 55.75 89.3 1343.2 5.78 0.7431 1388 2Ø22+2Ø20

10 - c 129.4 - - - - 675.806 5.78 0.3739 762 3Ø18






- aria necesara

- aria efectiva









1 - r 246.81 0.0534 0.0687 41.39 89.3 1288.99 5.78 0.7131 1388 2Ø22+2Ø20

2 - c 149.85 - - - - 782.609 5.78 0.433 762 3Ø18

3 - r 252.68 0.0677 0.0877 52.87 89.3 1319.65 5.78 0.7301 1388 2Ø22+2Ø20

2 4 - c 129.79 - - - - 677.843 5.78 0.375 762 3Ø18

5 - r 234.47 0.0577 0.0743 44.78 89.3 1224.55 5.78 0.6775 1256 4Ø20

6 - c 300 47.5 602.5 555 16.66 345 130 - - - - 678.94 5.78 0.3756 762 3Ø18

7 - r 236.77 0.0588 0.0759 45.71 89.3 1236.56 5.78 0.6841 1256 4Ø20

8 - c 135.13 - - - - 705.732 5.78 0.3904 762 3Ø18

9 - r 224.84 0.0776 0.101 60.88 89.3 1174.25 5.78 0.6497 1256 4Ø20

10 - c 84.1 - - - - 439.222 5.78 0.243 762 3Ø18






- aria necesara

- aria efectiva






2.4 Dimensionarea armaturilor longitudinale pentru grinzile sirului 3y


d = · ·

5220/25 = 1 % µ = 0.2

= =

. → = 16.66 ⁄

= 340.63 ·

d =

. ·

. · · . → d = 583.7 mm

h = d + 50 mm = 583.7 + 50 = 633.7mm → h = 650 mm

b = 300 mm

=

= 2.16 < 3

d = h - = 650 – 47.5 → d = 602.5 mm

ℎ = h - - = 650 – 47.5 – 47.5 → ℎ = 555 mm









1 - r 294.41 0.075 0.0975 58.75 89.3 1537.59 5.78 0.8506 1520 4Ø22

2 - c 158.39 - - - - 827.21 5.78 0.4576 942 3Ø20

3 - r 265.95 0.0772 0.1006 60.59 89.3 1388.95 5.78 0.7684 1388 2Ø22+2Ø20

1 4 - c 300 47.5 602.5 555 16.66 345 125.86 - - - - 657.318 5.78 0.3636 762 3Ø18

5 - r 267.26 0.0779 0.1015 61.18 89.3 1395.8 5.78 0.7222 1388 2Ø22+2Ø20

6 - c 160.36 - - - - 837.498 5.78 0.4633 942 3Ø20

7 - r 293.14 0.0732 0.0951 57.3 89.3 1530.96 5.78 0.847 1520 4Ø22






- aria necesara

- aria efectiva









1 - r 282.52 0.0768 0.1 60.26 89.3 1475.49 5.78 0.8163 1520 4Ø22

2 - c 143.16 - - - - 747.669 5.78 0.4136 762 3Ø18

3 - r 241.83 0.0609 0.0786 47.33 89.3 1262.98 5.78 0.6987 1256 4Ø20

2 4 - c 300 47.5 602.5 555 16.66 345 131.39 - - - - 686.199 5.78 0.3796 762 3Ø18

5 - r 243.21 0.0616 0.0796 47.94 89.3 1270.19 5.78 0.7027 1256 4Ø20

6 - c 144.4 - - - - 754.145 5.78 0.4172 762 3 Ø18

7 - r 281.59 0.0756 0.0984 59.28 89.3 1470.64 5.78 0.8136 1520 4Ø22






- aria necesara

- aria efectiva






2.5 Lungimea de ancoraj

= max {

= · · · · · , ˃ ,

; ; = 1.0

= 0.7

, = · Ø

pentru barele de la prtea superioara a reazemului

, = 44 · 22 = 968 mm ( cond slabe de aderenta in comb cu seismul )

pentru barele de la partea inferioara a reazemului

, = 31 · 20 = 620 mm ( cond. bune de aderenta in comb cu seismul )

, = max ( 0.3 · , ; 10 Ø ; 100 mm )

, = max ( 0.3 · 968 ; 10 · 22 ; 100 mm ) → , = 290 mm

= 1 · 0.7 · 968 → = 678 mm ˃ , = 290 mm

= ℎ = 650 mm ( clasa de ductilitate M )

= 0.5 · z · ctg θ = 0.5 · 0.9 · d

= 0.5 · 0.9 · 602.5 →

= 271.12 mm

= 678 271.12 = 949 650 271.12 = 921 → = 949 mm

2.6 Lungimea de suprapunere

= 200 mm






2.7 Determinarea fortei taietoare de dimensionare pt. grinzile de pe directia X

d = 602.5 mm

= 47.5 mm






Deschiderea lc1

= 6.0 – 0.25 – 0.25 → = 5.5 m

Seism din stanga

= g + ψ · q = 39.01 + 0.4 · 15 → = 45 ⁄

, = · ,

= 1.0 ( pentru ductilitate M )

, =

,

, = · · ( d - ) = 942 · 345 · ( 602.5 – 47.5 )

, = 180.36 ·

, = 1.0 · 180.36 → , = 180.36 ·

, = · ,

, = ,

, = f ( )

= − . · · · = −. · ·. · 345 → = 49.87

= · = 1.88 · 47.5 → = 89.3

= 49.87 < = 89.3

↓

, = · · ( d - ) = 1520 · 345 · ( 602.5 – 47.5 )

, = 291.04 ·

, = 1.0 · 291.04 →

, = 291.04

·






=

+

=

· ±

,+ ,

, = ·.

+. +.

. → , = 209.45

, = ·.

-. +.

. → , =38.04

Seism din dreapta

= g + ψ · q = 39.01 + 0.4 · 15 → = 45 ⁄






, = · ,

= 1.0 ( clasa de ductilitate M )

, = ,

, = f ( ) = − . · · · =

−. · ·. · 345 → = 38.48

= · = 1.88 · 47.5 → = 89.3

= 38.48 < = 89.3

↓

, = · · ( d - ) = 1388 · 345 · ( 602.5 – 47.5 )

, = 265.72

·

, = 1.0 · 265.76 → , = 265.76 ·

, = · ,

, = , = 180.36 ·

, = 1.0 · 180.36 → , = 180.36 ·






= + = ·

±,+ ,

, = ·.

+. +.

. → , = 204.86

, =

·.

-. +.

. →

, =42.63

Deschiderea lc2

= 6.0 – 0.25 – 0.25 → = 5.5 m

Seism din stanga

= g + ψ · q = 39.01 + 0.4 · 15 → = 45 ⁄

, = · ,


, = ,

, = · · ( d - ) = 762 · 345 · ( 602.5 – 47.5 )

, = 145.9 ·

, = 1.0 · 145.9 → , = 145.9 · , = · ,

, = , = 265.76 ·

, = 1.0 · 265.76 → , = 265.76 ·






= + = ·

±,+ ,

, =

·.

+. +.

. →

, = 198.59

, = ·.

-. +.

. → , =48.9

Seism din dreapta

= g + ψ · q = 39.01 + 0.4 · 15 → = 45 ⁄






, = · ,

, = , = 291.04 ·

, = 1.0 · 291.04 → , = 291.04 ·

, = · , , = , = 145.9 ·

, = 1.0 · 145.9 → , = 145.9 ·

= + = ·

±

,+ ,

, = ·. + .+.. → , = 203.19

, = ·.

-.+.

. → , =44.3






Deschiderea lc3

= 6.0 – 0.25 – 0.25 →

= 5.5 m

Seism din stanga

, = · ,

, = , = 145.9 ·

, = 1.0 · 145.9 → , = 145.9 ·

, = · ,

, = , = 265.76 ·

, = 1.0 · 265.76 →

, = 265.76

·

= + = · ± ,+ ,

, = ·.

+. +.

. → , = 198.59

, = ·.

-. +.

. → , =48.9

Seism din dreapta

, =

·

,

, = , = 265.76 ·

, = 1.0 · 265.76 → , = 265.76 ·

, = · ,

, = , = 145.9 ·

, = 1.0 · 145.9 → , = 145.9 ·

= + = ·

±

,+ ,

, = ·. + . +.. → , =198.59

, = ·.

-. +.

. → , = 48.9






Deschiderea lc4 = lc5

Seism stanga

, = 198.59 , = 48.9

Seism dreapta

, = 198.59

, = 48.9






Diagrama de forte maxime infasuratoare






2.8 Dimensionarea armaturilor transversale pentru grinzile de pe directia X

Camp 1, = ϑ · b · d

ϑ = , · k · 100 · · /

, =.

=.. → , = 0.12

k = 1 + = 1 +

. → k = 1.576 ≤ 2.0

=

· =

·. = 0.0052 ≤ 0.02

ϑ = 0.12 · 1.576 · 100 ·0.0052 ·20/ → ϑ = 0.41 ⁄

, = 0.41 · 300 · 602.5 → , = 74.1

Zona 1

, < ↔ 74.1 < 209.45 KN

↕

=

·

z = 0.9 · d = 0.9 · 602.5 → z = 542.2

=. · . · = 1.12 mm

Se impune Ø10 = 0.785

Ø = → = n · Ø = 2 · 0.785 → = 1.57

= 1.12 → s =. =

. = 140.17 mm → s = 14 cm

↕

Ø10/14

Zona 2

, < ↔ 74.1 < 144.93 KN

↕

=

·

=. · . · = 0.77 mm







Ø = → = n · Ø = 2 · 0.785 → = 1.57

= 0.77 → s =

. =

. = 203 mm → s = 20 cm

↕

Ø10/20

Verificari

Zona 1

= ·

· ≥ , =. ·

= · · = 0.0074

, =. ·√

= 0.00104

= 0.0074 ≥ 0.00104 ( verifica )

Zona 2

= ·

· = 0.0052 ≥ , = 0.00104

Camp 2

, = ϑ · b · d

ϑ = , · k · 100 · · /

, =.

=.. → , = 0.12

k = 1 + = 1 +

. → k = 1.576 ≤ 2.0

=

· =

·.

= 0.0042 ≤ 0.02

ϑ = 0.12 · 1.576 · 100 ·0.0042·20/ → ϑ = 0.384 ⁄

, = 0.384 · 300 · 602.5 → , = 69.4

Zona critica

, < ↔ 69.4 < 203.19 KN

↕

=

·






=. · . · = 1.08 mm


Ø =

→

= n ·

Ø = 2 · 0.785 →

= 1.57

= 1.08 → s = . = . = 145 mm → s = 14 cm

↕

Ø10/14

Verificari

= ·

· = ·

· = 0.0074 ≥ , = 0.00104

Camp 3

, = 69.4

Zona critica

, < ↔ 69.4 < 198.59 KN

↕

=

·

= . · . · = 1.06 mm


Ø = → = n · Ø = 2 · 0.785 → = 1.57

= 1.06 → s =. =

. = 148 mm → s = 14 cm

↕

Ø10/14

Camp4 = Camp 5 = Camp 3

Zona critica

↕

Ø10/14






2.9 Determinarea fortei taietoare de dimensionare pt. grinzile de pe directia Y

d = 602.5 mm

= 47.5 mm






Deschiderea lc1

= 6.0 – 0.25 – 0.25 → = 5.5 m

Seism din stanga

= g + ψ · q = 39.01 + 0.4 · 15 → = 45 ⁄

, = · ,


, = ,

, = · · ( d - ) = 942 · 345 · ( 602.5 – 47.5 )

, = 180.36 · , = 1.0 · 180.36 → , = 180.36 ·

, = · ,

, = ,

, = f ( )

= − . · · · =

−. · ·. · 345 → = 38.48

=

·

= 1.88 · 47.5 →

= 89.3

= 38.48 < = 89.3

↓

, = · · ( d - ) = 1388 · 345 · ( 602.5 – 47.5 )

, = 265.76 ·

, = 1.0 · 265.76 → , = 265.76 ·






= + = ·

±,+ ,

, = ·. + . +.. → , = 204.86

, = ·.

-. +.

. → , = 42.63

Seism din dreapta

= g + ψ · q = 39.01 + 0.4 · 15 → = 45 ⁄






, = · ,


, = ,

, = f ( ) = − . · · · =

− . · ·. · 345 → = 49.87

= · = 1.88 · 47.5 → = 89.3

= 49.87 < = 89.3

↓

, = · · ( d - ) = 1520 · 345 · ( 602.5 – 47.5 )

, = 291.04

·

, = 1.0 · 291.04 → , = 291.04 ·

, = · ,

, = , = 180.36 ·

, = 1.0 · 180.36 → , = 180.36 ·






= + = ·

±,+ ,

, = ·.

+. +.

. → , = 209.45

, =

·.

-. +.

. →

, = 38.04

Deschiderea lc2

= 6.0 – 0.25 – 0.25 → = 5.5 m

Seism din stanga

= g + ψ · q = 39.01 + 0.4 · 15 → = 45 ⁄

, = · ,


, = ,

, = · · ( d - ) = 762 · 345 · ( 602.5 – 47.5 )

, = 145.9 ·

, = 1.0 · 145.9 → , = 145.9 · , = · ,

, = , = 265.76 ·

, = 1.0 · 265.76 → , = 265.76 ·






= + = ·

±,+ ,

, =

·.

+. +.

. →

, = 198.59

, = ·.

-. +.

. → , = 48.9

Seism din dreapta

, = 198.59

, = 48.9

Deschiderea lc3

Seism din stanga

, = 209.45

, = 38.04

Seism din dreapta

, = 204.86

, = 42.63











2.10 Dimensionarea armaturilor transversale pentru grinzile de pe directia Y

Camp 1

, = ϑ · b · d

ϑ = , · k · 100 · · /

, =.

=.. → , = 0.12

k = 1 + = 1 +

. → k = 1.576 ≤ 2.0

= · =

·. = 0.0052 ≤ 0.02

ϑ = 0.12 · 1.576 · 100 ·0.0052 ·20/ → ϑ = 0.41 ⁄

, = 0.41 · 300 · 602.5 → , = 74.1

Zona 1

, < ↔ 74.1 < 209.45 KN

↕

=

·

z = 0.9 · d = 0.9 · 602.5 → z = 542.2 =. · . · = 1.12 mm


Ø = → = n · Ø = 2 · 0.785 → = 1.57

= 1.12 → s =. =

. = 140.17 mm → s = 14 cm

↕

Ø10/14 Zona 2

, < ↔ 74.1 < 169.86 KN

↕

=

·

=. · . · = 0.9 mm







Ø = → = n · Ø = 2 · 0.785 → = 1.57

= 0.9 → s =

. =

. = 174 mm → s = 17 cm

↕

Ø10/17

Verificari

Zona 1

= ·

· ≥ , =. ·

= · · = 0.0074

, =. ·√

= 0.00104

= 0.0074 ≥ 0.00104 ( verifica )

Zona 2

= ·

· = 0.0061 ≥ , = 0.00104

Camp 2

, = ϑ · b · d

ϑ = , · k · 100 · · /

, =.

=.. → , = 0.12

k = 1 + = 1 +

. → k = 1.576 ≤ 2.0

=

· =

·.

= 0.0042 ≤ 0.02

ϑ = 0.12 · 1.576 · 100 ·0.0042·20/ → ϑ = 0.384 ⁄

, = 0.384 · 300 · 602.5 → , = 69.4

Zona critica

, < ↔ 69.4 < 198.59 KN

↕

=

·






=. · . · = 1.06 mm


Ø =

→

= n ·

Ø = 2 · 0.785 →

= 1.57

= 1.06 → s = . = . = 148 mm → s = 14 cm

↕

Ø10/14

Verificari

= ·

· = ·

· = 0.0074 ≥ , = 0.00104

Camp 3

Zona 1

Ø10/14

Zona 1

Ø10/17






3. Proiectarea stalpilor

3.1 Solicitari

Stalpi nivel 1

Directia 1x

Stalpi circulari

= 1003.85

Directia 2x

Stalpi circulari

= 1457.11

Stalpi dreptunghiulari = 1027.04

Directia 3x

Stalpi circulari

= 1502.66

Stalpi dreptunghiulari

= 1075.38

Directia 4x

Stalpi circulari

= 1366.34


= 1354.18

Directia 5x

Stalpi circulari

= 1595.73

Directia 6x

Stalpi circulari

= 1596.81

Directia 7x


= 1115.13






Stalpi nivel 1

Directia 1x

Stalpi circulari

= 578.4 Directia 2x

Stalpi circulari

= 858.81


= 594.76

Directia 3x

Stalpi circulari = 896.3


= 650.75

Directia 4x

Stalpi circulari

= 775.92

Stalpi dreptunghiulari = 831.77

Directia 5x

Stalpi circulari

= 977.78

Directia 6x

Stalpi circulari

= 978.31

Directia 7x


= 671.57






3.2 Dimensionarea armaturilor longitudinale pentru stalpii nivelului 1

Sectiune dreptunghiulara ( 500 x 500 )

= - 1354.18

( din combinatia cu seismul )

, = 214.3 ·

= 227.56 ·

= · ≤ 0.55 ( clasa de ductilitate M )

= =

. → = 16.66 ⁄

=. ·

· ·. = 0.33 ≤ 0.55 ( verifica )

∗ = f ( ) → ∗ = 1314.15

x =∗. · · =

. · . · ·. → x = 197.2 mm

= ·

= +Ø = 35 +

→ = 47.5 mm

= 1.88 · 47.5 → = 89.3 mm

x = 197.2 mm ˃ = 89.3 mm

↓

, =∗ − . · −. ·

. · − ∗ = · , ·

∑ ∑ ,


, = η · ·

η = −

= · ·

E = 30000 ⁄ ( C20/25 )

I = ·

= ·

→ I = 5.2 · 10

· = 0.3 · · = 0.3 · 30000 · 5.2 · 10

↓

· = 4.68 · 10

= 1.0 · L = 1.0 · 4000 → = 4000 mm






= · . ·

→ = 28868.5

η =

−.

→

η = 1.06

,, = η · (, · )

,, = 1.06 · 214.3·10 20 · 1314150 → ,, = 255.01

,, = η · (, · )

,, = 1.06 · 227.5·10 20 · 1314150 → ,, = 269.07

,∗ = 1.2 · 255.01 · ∑ ∑ ,

,∗ = 1.2 · 269.07 · ∑ ∑ ,






∑ = 180.35 · 2 + 191.04 · 2 + 145.9 · 7 + 265.76 · 7 → ∑ = 3624.4 ·

(∑ , )= ( 142.73 + 260.62 ) + ( 77.29 + 239.44 ) + ( 83.22 + 247.96 ) + ( 49.34 +235.79 ) + ( 8.58 +211.74 ) + ( 17.18 +248.33 ) +

+ ( 85.51 + 244.73 ) + ( 81.4 +239.2 ) + ( 91.46 + 260.6 ) → (∑ , ) = 2825.12 ·

∑ ∑ , =.

. = 1.282

,∗ = 1.2 · 255.01 · 1.282 → ,∗ = 392.3 ·






∑ = 180.36 · 2 + 145.9 · 4 + 265.76 · 5 + 291.04 → ∑ = 2564.16 ·

(∑ , )= ( 205.36 + 242.34 ) + ( 81.85 + 243.08 ) + ( 86.59 + 252.44 ) + ( 50.93 +235.59 ) + ( 13.11 + 220.55 ) + ( 40.39 + 275.89 )

↓

(∑ , )= 1948.12 ·

∑ ∑ , = .. = 1.316

,∗ = 1.2 · 269.07 · 1.316 → ,∗ = 424.91 ·






=. =

. → = 345 ⁄

, =,∗ − · . · − . ·

· . · − =. · − . · · . · −. ·.

· . · −.

, = 2396

=, · =

· = 0.0095

0.008 < = 0.0095 < 0.04 ( Verifica )

, =,∗ − · . · − . ·

· . · − =. · − . · · . · −. ·.

· . · −.

, = 2863

=, · =

· = 0.011

0.008 < = 0.011 < 0.04 ( Verifica )

, = , + , = 2396 + 2863 → , = 5259

↓

8Ø25 + 4Ø22 = 5448






Verificarea armaturilor cu AxisVM vs 9.0






Flambajparametrii

Nx[kN]

My i [kNm]

Mzi [kNm]

Mys [kNm]

Mzs [kNm]

e0by [mm]

e0bz [mm]

e0ty [mm]

e0tz [mm]

eay [mm]

eaz [mm]

Corespunzator

ηyy = 1.06 daηzz = 1.06

L = 4.000 m

18 -1354.186 -130.704 -111.134 -204.134 -227.566 -82.1 96.5 -168.0 150.7 20.0 20.0 da

-1354.186 -130.704 -111.134 -204.134 208.454 -82.1 96.5 153.9 150.7 20.0 20.0 da

-1354.186 -130.704 142.759 -204.134 -227.566 105.4 96.5 -168.0 150.7 20.0 20.0 da

-1354.186 -130.704 142.759 -204.134 208.454 105.4 96.5 153.9 150.7 20.0 20.0 da

-1354.186 -130.704 -111.134 214.305 -227.566 -82.1 96.5 -168.0 -158.3 20.0 20.0 da

-1354.186 -130.704 -111.134 214.305 208.454 -82.1 96.5 153.9 -158.3 20.0 20.0 da

-1354.186 -130.704 142.759 214.305 -227.566 105.4 96.5 -168.0 -158.3 20.0 20.0 da

-1354.186 -130.704 142.759 214.305 208.454 105.4 96.5 153.9 -158.3 20.0 20.0 da

-1354.186 110.225 -111.134 -204.134 -227.566 -82.1 -81.4 -168.0 150.7 20.0 20.0 da

-1354.186 110.225 -111.134 -204.134 208.454 -82.1 -81.4 153.9 150.7 20.0 20.0 da

-1354.186 110.225 142.759 -204.134 -227.566 105.4 -81.4 -168.0 150.7 20.0 20.0 da

-1354.186 110.225 142.759 -204.134 208.454 105.4 -81.4 153.9 150.7 20.0 20.0 da

-1354.186 110.225 -111.134 214.305 -227.566 -82.1 -81.4 -168.0 -158.3 20.0 20.0 da

-1354.186 110.225 -111.134 214.305 208.454 -82.1 -81.4 153.9 -158.3 20.0 20.0 da

-1354.186 110.225 142.759 214.305 -227.566 105.4 -81.4 -168.0 -158.3 20.0 20.0 da

-1354.186 110.225 142.759 214.305 208.454 105.4 -81.4 153.9 -158.3 20.0 20.0 da

-1314.150 -130.704 -111.134 -204.134 -227.566 -84.6 99.5 -173.2 155.3 20.0 20.0 da

-1314.150 -130.704 -111.134 -204.134 208.454 -84.6 99.5 158.6 155.3 20.0 20.0 da

-1314.150 -130.704 142.759 -204.134 -227.566 108.6 99.5 -173.2 155.3 20.0 20.0 da

-1314.150 -130.704 142.759 -204.134 208.454 108.6 99.5 158.6 155.3 20.0 20.0 da

-1314.150 -130.704 -111.134 214.305 -227.566 -84.6 99.5 -173.2 -163.1 20.0 20.0 da

-1314.150 -130.704 -111.134 214.305 208.454 -84.6 99.5 158.6 -163.1 20.0 20.0 da

-1314.150 -130.704 142.759 214.305 -227.566 108.6 99.5 -173.2 -163.1 20.0 20.0 da

-1314.150 -130.704 142.759 214.305 208.454 108.6 99.5 158.6 -163.1 20.0 20.0 da

-1314.150 110.225 -111.134 -204.134 -227.566 -84.6 -83.9 -173.2 155.3 20.0 20.0 da

-1314.150 110.225 -111.134 -204.134 208.454 -84.6 -83.9 158.6 155.3 20.0 20.0 da

-1314.150 110.225 142.759 -204.134 -227.566 108.6 -83.9 -173.2 155.3 20.0 20.0 da

-1314.150 110.225 142.759 -204.134 208.454 108.6 -83.9 158.6 155.3 20.0 20.0 da

-1314.150 110.225 -111.134 214.305 -227.566 -84.6 -83.9 -173.2 -163.1 20.0 20.0 da

-1314.150 110.225 -111.134 214.305 208.454 -84.6 -83.9 158.6 -163.1 20.0 20.0 da

-1314.150 110.225 142.759 214.305 -227.566 108.6 -83.9 -173.2 -163.1 20.0 20.0 da

-1314.150 110.225 142.759 214.305 208.454 108.6 -83.9 158.6 -163.1 20.0 20.0 da






Sectiune circulara ( O 500 )

= 1596.81

, = 171.02 ·

, = 153.03 ·

=

√ 171.02

153.03 →

= 229.49

= · ≤ 0.55 ( clasa de ductilitate M )

= ·

= ·

→ = 196349.5

=. ·

. ·. = 0.48 < 0.55 ( verifica )

∗ = f ( ) → ∗ = 1477.02

x =∗. · · =

. · . · ·. → x = 221.64 mm

= 89.3 mm

x = 221.64 ˃ = 89.3 mm

↓

, =∗ − ∗ . · −. ·

. · −

∗ = · , ·∑ ∑ ,


, = η · ·






η = −

= · ·

E = 30000 ⁄ ( C20/25 )

I = ·

= ·

→ I = 3.06 · 10

· = 0.3 · · = 0.3 · 30000 · 3.06 · 10

· = 2.75 · 10

= 1.0 · L = 1.0 · 4000 → = 4000 mm

= · . ·

→ = 16963.38

η = − .. → η = 1.1

, = η · ·

, = 1.1 · 229.49·10 20 · 1477020 → , = 284.93

∑ ∑ , = 1.316

∗ = 1.2 · 284.93 · 1.316 → ∗ = 449.9 ·

, =∗ − · . · − . ·

· . · −

, = . · − . · · . · −. · . · . · −.

↓ , = 5840

↓

12Ø25 = 5892

ρ =, =

. → ρ = 0.03

0.008 <

ρ =0.03 < 0.04 ( verifica )






Verificarea armaturilor cu AxisVM vs 9.0






Flambajparametrii

Nx[kN]

My i [kNm]

Mzi [kNm]

Mys [kNm]

Mzs [kNm]

e0by [mm]

e0bz [mm]

e0ty [mm]

e0tz [mm]

eay [mm]

eaz [mm]

Corespunzator

ηyy = 1.1 daηzz = 1.1

L = 4.000 m

33 -1596.812 -132.690 -117.206 -166.881 -155.088 -73.4 83.1 -97.1 104.5 20.0 20.0 da

-1596.812 -132.690 -117.206 -166.881 153.034 -73.4 83.1 95.8 104.5 20.0 20.0 da

-1596.812 -132.690 120.782 -166.881 -155.088 75.6 83.1 -97.1 104.5 20.0 20.0 da

-1596.812-132.690 120.782 -166.881 153.034 75.6 83.1 95.8 104.5 20.0 20.0 da

-1596.812 -132.690 -117.206 171.026 -155.088 -73.4 83.1 -97.1 -107.1 20.0 20.0 da

-1596.812 -132.690 -117.206 171.026 153.034 -73.4 83.1 95.8 -107.1 20.0 20.0 da

-1596.812 -132.690 120.782 171.026 -155.088 75.6 83.1 -97.1 -107.1 20.0 20.0 da

-1596.812 -132.690 120.782 171.026 153.034 75.6 83.1 95.8 -107.1 20.0 20.0 da

-1596.812 124.651 -117.206 -166.881 -155.088 -73.4 -78.1 -97.1 104.5 20.0 20.0 da

-1596.812 124.651 -117.206 -166.881 153.034 -73.4 -78.1 95.8 104.5 20.0 20.0 da

-1596.812 124.651 120.782 -166.881 -155.088 75.6 -78.1 -97.1 104.5 20.0 20.0 da

-1596.812 124.651 120.782 -166.881 153.034 75.6 -78.1 95.8 104.5 20.0 20.0 da

-1596.812 124.651 -117.206 171.026 -155.088 -73.4 -78.1 -97.1 -107.1 20.0 20.0 da

-1596.812 124.651 -117.206 171.026 153.034 -73.4 -78.1 95.8 -107.1 20.0 20.0 da

-1596.812 124.651 120.782 171.026 -155.088 75.6 -78.1 -97.1 -107.1 20.0 20.0 da

-1596.812 124.651 120.782 171.026 153.034 75.6 -78.1 95.8 -107.1 20.0 20.0 da

-1477.020 -132.690 -117.206 -166.881 -155.088 -79.4 89.8 -105.0 113.0 20.0 20.0 da

-1477.020 -132.690 -117.206 -166.881 153.034 -79.4 89.8 103.6 113.0 20.0 20.0 da

-1477.020 -132.690 120.782 -166.881 -155.088 81.8 89.8 -105.0 113.0 20.0 20.0 da

-1477.020 -132.690 120.782 -166.881 153.034 81.8 89.8 103.6 113.0 20.0 20.0 da

-1477.020 -132.690 -117.206 171.026 -155.088 -79.4 89.8 -105.0 -115.8 20.0 20.0 da

-1477.020 -132.690 -117.206 171.026 153.034 -79.4 89.8 103.6 -115.8 20.0 20.0 da

-1477.020 -132.690 120.782 171.026 -155.088 81.8 89.8 -105.0 -115.8 20.0 20.0 da

-1477.020 -132.690 120.782 171.026 153.034 81.8 89.8 103.6 -115.8 20.0 20.0 da

-1477.020 124.651 -117.206 -166.881 -155.088 -79.4 -84.4 -105.0 113.0 20.0 20.0 da

-1477.020 124.651 -117.206 -166.881 153.034 -79.4 -84.4 103.6 113.0 20.0 20.0 da

-1477.020 124.651 120.782 -166.881 -155.088 81.8 -84.4 -105.0 113.0 20.0 20.0 da

-1477.020 124.651 120.782 -166.881 153.034 81.8 -84.4 103.6 113.0 20.0 20.0 da

-1477.020 124.651 -117.206 171.026 -155.088 -79.4 -84.4 -105.0 -115.8 20.0 20.0 da

-1477.020 124.651 -117.206 171.026 153.034 -79.4 -84.4 103.6 -115.8 20.0 20.0 da

-1477.020 124.651 120.782 171.026 -155.088 81.8 -84.4 -105.0 -115.8 20.0 20.0 da

-1477.020 124.651 120.782 171.026 153.034 81.8 -84.4 103.6 -115.8 20.0 20.0 da






Calculul scării

1. Scara de la parter

1.1. Predimensionare

ℎ = 16 cm

ℎ = 15.8 cm

= 30.4 cm

1.2. Evaluarea incarcarilor

Incarcari permanente

rampa

= ℎ · = 0.16 · 25 → = 4 ⁄

trepte

= · =

. → = 1.98 ⁄

finisaje

= 1.0 ⁄

Incarcari pe rampa

= 4.0 + 1.98 + 1.0 → = 6.98 ⁄

Incarcari pe podest

= 4.0 + 1.0 → = 5.0 ⁄

Incarcarea utila

= 5.0 ⁄

1.3. Combinatii

1.35 · g + 1.5 · q

1.4. Calculul static

Calculul static s-a realizat cu programul AxisVM vs 9.0 iar modelul

de calcul este unul spatial . Pe baza solicitarilor rezultate din programul de

calcul s-a realizat armarea rampelor, a grinzilor de vang si grinzilor de podest.

S-au anexat figure cu modelarea scarii si cu solicitarile rezultate











1.5. Calculul ariilor de armatura

Ariile de armatura s-au determinat cu AxisVM vs 9.0






Rampa balansata

Aria de armatura de la partea inferioara

Directia longitudinala

, = 3.0 → Ø8/15 = 3.35

Directia transversala

, = 6.98 → Ø12/15 = 7.54

Aria de armatura de la partea superioara


o Pe toata lungimea

, = 7.02 → Ø12/15 = 7.54


o Reazem partea inferioara l = 70 cm

, = 17.74

↓

Ø16/11 = 18,28

o Pe restul de lungime

, = 8.49 → Ø12/13 → 8.7






Rampa dreapta

Aria de armatura din camp

, = 3.54 → Ø8/12 = 4.19

Aria din reazemul superior , = 9.31 → Ø12/12 = 9.42

Podest intermediar ( placa armata pe 2 directii )


, = 2.17 → Ø8/20 = 2.51


, = 4.88 → Ø12/20 = 5.65

Grinda de vang

= 3.59 → 4Ø12 = 4.52





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