Upload
dan-alexandrescu
View
271
Download
1
Embed Size (px)
Citation preview
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 1/101
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 2/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 2
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 3/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 3
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
placa din beton armat
= 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
⁄
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 4/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 4
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
⁄
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 5/101
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 6/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 6
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 7/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 7
= 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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 8/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 8
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 ·
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 9/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 9
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 ·
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 10/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 10
Fasia F6x
λ = =
.. → λ = 1
= 12.16 ·
= - 25.74 ·
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 11/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 11
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
·
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 12/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 12
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 ·
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 13/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 13
= 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 ·
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 14/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 14
Fasia F5y
λ = =
.. → λ = 1
= 0.0334 = 0.333
= · p · = 0.0334 · 14.26 · 5.7 → = 15.47 ·
= · · = . ·. · .
→ = 19.3 ·
= 11.2 ·
Fasia F6y
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 15/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 15
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 16/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 16
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 17/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 17
, = 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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 18/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 18
, = 0.0477 ·1000 · 122 · 16.66 → , = 11.82 ·
Pentru ≤ , → se armeaza cu , = 335
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 19/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 19
2.7 Armare placa etaj 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 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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 20/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 20
3. Calculul placii - terasa
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 21/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 21
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 22/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 22
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 23/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 23
, = 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 = 0.101
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 24/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 24
, = 0.0477 ·1000 · 122 · 16.66 → , = 11.82 ·
Pentru ≤ , → se armeaza cu , = 335
3.3 Armare placa terasa 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 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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 25/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 25
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 26/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 26
Dimensionarea cadrului
1. Evaluarea incarcarilor
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 27/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 27
1.1 Incarcari permanente, uniform distribuite
Nivel curent
Greutate permanenta grinda
= 0.6 · 0.3 · 25 → = 4.5 / Incarcari din planseu
placa din beton armat
= 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 ⁄
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 28/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 28
= 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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 29/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 29
Terasa
Greutate permanenta grinda
= 0.6 · 0.3 · 25 → = 4.5 / Incarcari din planseu
placa din beton armat
= 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 ⁄
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 30/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 30
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 ⁄
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 31/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 31
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 32/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 32
Utila 2_x
Utila 1_y
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 33/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 33
Utila 2_y
Utila
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 34/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 34
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
↓
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 35/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 35
=
= 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 ⁄
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 36/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 36
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
↓
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 37/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 37
=
= 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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 38/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 38
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 39/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 39
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 40/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 40
`
2. Proiectarea grinzilor cadrului
2.1 Solicitari
Directia X
Sir 1x
{ = 176.57 · = 93.17 · Sir 2x
{ = 223.51 · = 129.8 ·
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 41/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 41
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 ·
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 42/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 42
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 43/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 43
= 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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 44/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 44
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 45/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 45
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 46/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 46
- aria necesara
- aria efectiva
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 47/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 47
Dimensionarea armaturilor longitudinale de la nivelul 2
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 48/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 48
- aria necesara
- aria efectiva
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 49/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 49
2.3 Dimensionarea armaturilor longitudinale pentru grinzile sirului 5x
Definitivarea sectiunii
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 50/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 50
Dimensionarea armaturilor longitudinale de la nivelul 1
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 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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 51/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 51
- aria necesara
- aria efectiva
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 52/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 52
Dimensionarea armaturilor longitudinale de la nivelul 2
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 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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 53/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 53
- aria necesara
- aria efectiva
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 54/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 54
2.4 Dimensionarea armaturilor longitudinale pentru grinzile sirului 3y
Definitivarea sectiunii
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 55/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 55
Dimensionarea armaturilor longitudinale de la nivelul 1
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 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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 56/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 56
- aria necesara
- aria efectiva
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 57/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 57
Dimensionarea armaturilor longitudinale de la nivelul 2
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 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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 58/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 58
- aria necesara
- aria efectiva
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 59/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 59
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 60/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 60
2.7 Determinarea fortei taietoare de dimensionare pt. grinzile de pe directia X
d = 602.5 mm
= 47.5 mm
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 61/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 61
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
·
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 62/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 62
=
+
=
· ±
,+ ,
, = ·.
+. +.
. → , = 209.45
, = ·.
-. +.
. → , =38.04
Seism din dreapta
= g + ψ · q = 39.01 + 0.4 · 15 → = 45 ⁄
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 63/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 63
, = · ,
= 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 ·
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 64/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 64
= + = ·
±,+ ,
, = ·.
+. +.
. → , = 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 ⁄
, = · ,
= 1.0 ( pentru ductilitate M )
, = ,
, = · · ( d - ) = 762 · 345 · ( 602.5 – 47.5 )
, = 145.9 ·
, = 1.0 · 145.9 → , = 145.9 · , = · ,
, = , = 265.76 ·
, = 1.0 · 265.76 → , = 265.76 ·
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 65/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 65
= + = ·
±,+ ,
, =
·.
+. +.
. →
, = 198.59
, = ·.
-. +.
. → , =48.9
Seism din dreapta
= g + ψ · q = 39.01 + 0.4 · 15 → = 45 ⁄
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 66/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 66
, = · ,
, = , = 291.04 ·
, = 1.0 · 291.04 → , = 291.04 ·
, = · , , = , = 145.9 ·
, = 1.0 · 145.9 → , = 145.9 ·
= + = ·
±
,+ ,
, = ·. + .+.. → , = 203.19
, = ·.
-.+.
. → , =44.3
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 67/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 67
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 68/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 68
Deschiderea lc4 = lc5
Seism stanga
, = 198.59 , = 48.9
Seism dreapta
, = 198.59
, = 48.9
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 69/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 69
Diagrama de forte maxime infasuratoare
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 70/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 70
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 71/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 71
Se impune Ø10 = 0.785
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
↕
=
·
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 72/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 72
=. · . · = 1.08 mm
Se impune Ø10 = 0.785
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
Se impune Ø10 = 0.785
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 73/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 73
2.9 Determinarea fortei taietoare de dimensionare pt. grinzile de pe directia Y
d = 602.5 mm
= 47.5 mm
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 74/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 74
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 → = 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 ·
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 75/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 75
= + = ·
±,+ ,
, = ·. + . +.. → , = 204.86
, = ·.
-. +.
. → , = 42.63
Seism din dreapta
= g + ψ · q = 39.01 + 0.4 · 15 → = 45 ⁄
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 76/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 76
, = · ,
= 1.0 ( clasa de ductilitate M )
, = ,
, = 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 ·
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 77/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 77
= + = ·
±,+ ,
, = ·.
+. +.
. → , = 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 ⁄
, = · ,
= 1.0 ( pentru ductilitate M )
, = ,
, = · · ( d - ) = 762 · 345 · ( 602.5 – 47.5 )
, = 145.9 ·
, = 1.0 · 145.9 → , = 145.9 · , = · ,
, = , = 265.76 ·
, = 1.0 · 265.76 → , = 265.76 ·
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 78/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 78
= + = ·
±,+ ,
, =
·.
+. +.
. →
, = 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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 79/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 79
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 80/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 80
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
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 < 169.86 KN
↕
=
·
=. · . · = 0.9 mm
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 81/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 81
Se impune Ø10 = 0.785
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
↕
=
·
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 82/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 82
=. · . · = 1.06 mm
Se impune Ø10 = 0.785
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 83/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 83
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
Stalpi dreptunghiulari
= 1354.18
Directia 5x
Stalpi circulari
= 1595.73
Directia 6x
Stalpi circulari
= 1596.81
Directia 7x
Stalpi dreptunghiulari
= 1115.13
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 84/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 84
Stalpi nivel 1
Directia 1x
Stalpi circulari
= 578.4 Directia 2x
Stalpi circulari
= 858.81
Stalpi dreptunghiulari
= 594.76
Directia 3x
Stalpi circulari = 896.3
Stalpi dreptunghiulari
= 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
Stalpi dreptunghiulari
= 671.57
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 85/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 85
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
↓
, =∗ − . · −. ·
. · − ∗ = · , ·
∑ ∑ ,
= 1.2 ( clasa de ductilitate M )
, = 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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 86/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 86
= · . ·
→ = 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 · ∑ ∑ ,
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 87/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 87
∑ = 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 ·
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 88/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 88
∑ = 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 ·
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 89/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 89
=. =
. → = 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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 90/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 90
Verificarea armaturilor cu AxisVM vs 9.0
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 91/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 91
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 92/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 92
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
↓
, =∗ − ∗ . · −. ·
. · −
∗ = · , ·∑ ∑ ,
= 1.2 ( clasa de ductilitate M )
, = η · ·
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 93/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 93
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 )
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 94/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 94
Verificarea armaturilor cu AxisVM vs 9.0
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 95/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 95
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 96/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 96
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
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 97/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 97
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 98/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 98
1.5. Calculul ariilor de armatura
Ariile de armatura s-au determinat cu AxisVM vs 9.0
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 99/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 99
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
Directia longitudinala
o Pe toata lungimea
, = 7.02 → Ø12/15 = 7.54
Directia transversala
o Reazem partea inferioara l = 70 cm
, = 17.74
↓
Ø16/11 = 18,28
o Pe restul de lungime
, = 8.49 → Ø12/13 → 8.7
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 100/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii
Lucrare de Licenta Page 100
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 )
Directia transversala
, = 2.17 → Ø8/20 = 2.51
Directia longitudinala
, = 4.88 → Ø12/20 = 5.65
Grinda de vang
= 3.59 → 4Ø12 = 4.52
8/18/2019 Breviar de Calcul-MUZEU
http://slidepdf.com/reader/full/breviar-de-calcul-muzeu 101/101
Universitatea “POLITEHNICA “ din Timisoara
Facultatea de Constructii