CALCULUL ARMATURII PLANSEULUI PESTE PARTER

CALCULUL ARMATURII PLANSEULUI PESTE PARTER

Evaluarea incarcarilor :

1. greutate proprie placa : l_b * h_p * n = 25 * 0.18 * 1.35 = 6.075 kN/m²
2. tencuiala  : l_t δ_t * n = 19 * 0.015 * 1.35 =0.3847 kN/m²
3. inc . utila  = 1.5 *n = 1.5 * 1.5 = 2.10 kN/m²

evaluarea incarcarilor la nivelul pardoseli:

o      pardoseala rece :

placi pardoseala ( gresie ceramica ) :

l * δ * n = 11 * 0.01 *1.35 = 0.148 kN/m²

mortar de ciment M 200 :

l * δ * n = 19 * 0.02 *1.35 = 0.513 kN/m²

strat de egalizare din mortar de ciment :

l * δ * n = 19 * 0.03 *1.35 = 0.769 kN/m²

g_pr = 1.43 kN/m²

o      pardoseala calda :

parchet laminat

l * δ * n = 4.8 * 0.01 *1.35 = 0.0648 kN/m²

strat de egalizare din mortar de ciment :

l * δ * n = 19 * 0.05 *1.35 = 1.282 kN/m²

g_pc = 1.347 kN/m²

4. pardoseala rece : g_pr = 1.43 kN/m²
5. pardoseala calda : g_pc = 1.347 kN/m²

Pardoseala calda :

Pardoseala rece :

Placa 1 : Zona WC 4.50 x 6.20

Pardoseala rece :

Momente maxime :

1 / 12 * ( g + p )* (3 * l_max - l_min ) * l²_min = 2 ( M₁ + M₂ ) + M₁^' + M₂^'

l

l

l=1.37 ......X

l

X = 0.23

=> M₁/M₂= 1.93 => M₁=1.93 M₂

l₂ / l'₂ = 6.20 / 3.30 = 1.87 => M₂/M₂^' = 0.8 => M₂^'= M₂/ 0.8

l₁ / l'₁ = 4.50 / 4.50 = 1.0 => M₁/M₁^'= 0.8 => M₁^'= M₁/ 0.5

1 / 12( 8.537+ 0 )(3*6.2 -4.50 ) 4.50² = 2( 1.93M₂+ M₂ ) + M₂/0.8+ M₂/0.8

203.127 = 8.36 * M₂

M₂=24.29 kNm

M'₂=24.29 / 0.8=30.37 kNm

M₁=24.29 * 1.93 = 46.87 kNm

M'₁=46.87 / 0.5 = 93.75 kNm

z₁ = 0.9 * h₀₁ = 0.9 * ( h -a - f₁ / 2 ) = 0.9 * ( 18.00 - 1.5 - 0.8 / 2 ) =

z₁ = 14.49 cm

z₂ = 0.9 * h₀₂ = 0.9 *( h -a - f₁ - f₁ / 2 ) = 0.9 *( 18.00 - 1.5 - 0.8 - 0.8 / 2 )

z₂ = 13.77 cm

CALCULUL ARMATURILOR :

A_a1 = = = 4.58 cm²

A_a1 = 4.58 / 3.90 = 1.17 cm²/m

A _a2 = = = 4.65 cm²

Aa₂ = 4.65 / 3.60 = 1.30 cm²/m

A'_a1 = = = 5.72 cm²

A'a₁ = 5.72 / 3.90 = 1.46 cm²/m

A'_a2 = = = 5.82 cm²

A'a₂ = 5.82 / 3.60 =1.61 cm²/m

Placa 2 : Living 4.80 x 3.90

Pardoseala calda :

Momente maxime :

1 / 12 * ( g + p )* (3 * l_max - l_min ) * l²_min = 2 ( M₁ + M₂ ) + M₁^' + M₂^'

l = 4.80 / 3.90 = 1.23

l=1.2.....1.4

l=1.23 ......X

l=1.3......1.9

X = 0.15

=> M₁/M₂= 1.55 => M₁=1.55 M₂

l₂ / l'₂ = 4.80 / 3.60= 1.33 < 1.44=> M₂/M₂^'= 0.725 =>M₂^'= M₂ /0.725

l₁ / l'₁ = 3.90 / 2.10 = 1.85 > 1.17 => M₁/M₁^' = 0.8 => M₁^'= M₁/ 0.8

1 / 12( 685.33 + 0 )(3*4.80 -3.90 ) 3.90² = 2( 1.55M₂+ M₂ ) + 1.55 * M₂ /0.8

+ M₂/0.725

9121 = 8.42* M₂

M₂=1083.25 daNm

M₁=1083.25 * 1.55 = 1679.04 daNm

M'₂=1083.25 / 0.725 =1494.14 daNm

M'₁=1679.04 /0.8 = 2098.8 daNm

CALCULUL ARMATURILOR :

A_a1 = = = 8.01 cm²

A_a1 = 8.01 / 4.80 = 1.67 cm²/m

A _a2 = = = 5.56 cm²

Aa₂ = 5.56 / 3.90 = 1.43 cm²/m

A'_a1 = = = 10.00 cm²

A'a₁ = 10.00 / 4.80 = 2.08 cm²/m

A'_a2 = = = 7.68 cm²

A'a₂ = 7.68 / 3.90 =1.97 cm²/m

Placa 3 Dormitor mic 3.00 x 3.60

Pardoseala calda :

Momente maxime :

1 / 12 * ( g + p )* (3 * l_max - l_min ) * l²_min = 2 ( M₁ + M₂ ) + M₁^' + M₂^'

l = 3.60 / 3.00 = 1.20 => M₁/M₂= 1.40 => M₁=1.40 M₂

l₂ / l'₂ = 3.60 / 2.10 = 1. 71 > 1.08 => M₂/M₂^'= 0.8 => M₂^'= M₂ / 0.8

l₁ / l'₁ = 3.00 / 2.10 = 1.43 > 0.9 => M₁/M₁^'= 0.8 => M₁^'= M₁ / 0.8

1 / 12 ( 685.33 + 0 )(3 * 3.60 - 3.00 ) 3.00² = 2 ( 1.40 M₂+ M₂ ) +

1.40 M₂ / 0.8 + M₂ / 0.8

4009.2 = 7.80 * M₂

M₂=514 daNm

M'₂=514 / 0.8=642.5 daNm

M₁=514 * 1.40 = 719.60 daNm

M₁^'=642.5 * 2 = 1285 daNm

CALCULUL ARMATURILOR :

A_a1 = = = 3.43 cm²

A_a1 = 3.43/ 3.60 = 0.95 cm²/m

A _a2 = = = 2.64 cm²

Aa₂ = 2.64 / 3.00 = 0.88 cm²/m

A'_a1 = = = 6.13 cm²

Aa₁^' = 6.13 / 3.60 = 1.70 cm²/m

A' _a2 = = = 3.3 cm²

Aa₂^' = 3.3 / 3.00 =1.10 cm²/m

Placa 4 Baie 3.00 x 2.10

Pardoseala rece :

Momente maxime :

1/12 ( g + p ) ( 3 l_max-l_min) l²_min = 2 (M₁+M₂) + M₁^'+ M₂^'+ M₁^"

l = 3.00 / 2.10 = 1.43

l=1.4.....2.3

l=1.43 ......X

l=1.5......3.1

X = 0.24

=> M₁/M₂= 2.54 => M₂ = M₁/ 2.54

M₁ = M₂* 2.54

l₂ / l'₂ = 3.00 / 2.10 = 1.43 > 0.9 => M₂/M₂^'= 0.8 => M₂^'= M₂ / 0.8

l₁ / l'₁ = 3.80 / 2.10 = 1.81 > 1.14 => M₁/M₁^'= 0.8 => M₁^'= M₁/ 0.8

= 3.60 / 2.10 = 1.71 > 1.08 => M₁/M₁^''= 0.8 => M₁^''= M₁/ 0.8

1 / 12 ( 715.45 + 0 )(3 * 3.00 - 2.10 ) 2.10² = 2 ( M₁+ M₁/2.54 ) +

M₁/ 0.8 + 0.8* M₁/2.54 + M₁/0.8

1814.2 = 4.4 * M₁

M₁ = 412.3 daNm

M₂ = 412.3 / 2.54 = 162.33 daNm

M'₂ = 162.33 /0.8 = 202.3 daNm

M ₁^' = 412.3 / 0.8 = 515.38 daNm

M₁^'' = 412.3 / 0.8 = 515.38 daNm

CALCULUL ARMATURILOR :

A_a1 = = = 1.97 cm²

A_a1 = 1.97/ 3.00 = 0.65 cm²/m

A _a2 = = = 0.83 cm²

Aa₂ = 0.83 / 2.10 = 0.40 cm²/m

A'_a1 = = = 2.46 cm²

Aa₁^' = 1.77 / 3.00 = 0.82 cm²/m

A' _a2 = = = 1.10 cm²

Aa₂^' = 1.10 / 2.10 =0.53 cm²/m

A'' _a1 = = = 2.46 cm²

Aa₁^''= 2.46 / 3.00 =0.82 cm²/m

Placa 5 Dormitor 3.80 x 3.00

Pardoseala calda :

Momente maxime :

1/12(g+p)(3l_max-l_min)l²_min=2(M₁+M₂)+M₁^'+M₂^'+M₂^"

l = 3.80 / 3.00 = 1.27

l=1.2.....1.4

l=1.27 ......X

l=1.3......1.9

X = 0.35

=> M₁/M₂= 1.75 => M₁ = 1.75 * M₂

l₂ / l'₂ = 3.80 / 2.10 = 1.81 > 1.14 => M₁/M₁^'= 0.8 => M₁^'= M₁/ 0.8

= 3.80 / 1.60 = 2.4 > 1.14 => M₂/M₂^''= 0.8 => M₂^''= M₂/ 0.8

l₁ / l'₁ = 3.00 / 2.10 = 1.43 > 0.9 => M₂/M₂^'= 0.8 => M₂^'= M₂ / 0.8

1 / 12 (685.33+ 0 )(3 * 3.80 - 3.00 ) 3.00² = 2 ( 1.75*M₂+ M₂) +

1.75* M₂ /0.8+ M₂ / 0.8 + M₂ / 0.8

4317.58= 10.2 * M₂

M₂ = 423.29 daNm

M₁ = 1.75* 423.29 = 740.9daNm

M'₂ = 423.29/ 0.8 = 529.11daNm

M ₁^' = 740.9/ 0.8 = 926.13daNm

M₂^'' = 423.29/ 0.8 = 529.11daNm

CALCULUL ARMATURILOR :

A_a1 = = = 3.53 cm²

A_a1 = 3.53/ 3.80 = 0.93 cm²/m

A _a2 = = = 2.17 cm²

Aa₂ = 2.17 / 3.00 = 0.72 cm²/m

A'_a1 = = = 4.41 cm²

Aa₁^' = 4.41 / 3.80 = 1.16 cm²/m

A' _a2 = = = 2.72 cm²

Aa₂^' = 2.72 / 3.00 =0.91 cm²/m

A'' _a2 = = = 2.71 cm²

Aa₂^''= 2.71 / 3.00 =0.91 cm²/m

Placa 6 : Debara 3.00 x 1.60

Pardoseala calda :

p = 1850 * 2.8 * 0.125 * 1.35 = 874.13 daN =>

p = 245 daN/m²

Momente maxime :

1 / 12 * ( g + p )* (3 * l_max - l_min ) * l²_min = 2 ( M₁ + M₂ ) + M₁^' + M₂^'

l = 3.00 / 1.60 = 1.88

l=1.8.....4.9

l=1.88 ......X

l=1.9......5.5

X = 0.48

=> M₁/M₂= 5.38 => M₁=5.38 M₂

l₂ / l'₂ = 3.00 / 3.00= 1=> M₂/M₂^'= 0.5 => M₂^'=2* M₂

l₁ / l'₁ = 3.80 / 1.60=2.37 > 1.33 => M₁/M₁^'= 0.8 => M₁^'= M₁ / 0.8

1 / 12( 685.33 + 245 )(3*3.00 -1.60 ) 1.60² = 2( 5.38M₂+ M₂ ) + 5.38 M₂/0.8

+ 2 * M₂

1491.1 = 21.48* M₂

M₂=965.19 daNm

M₁=965.19 * 1.55 = 1496.04 daNm

M'₂=965.19 /0.8 =1206.49 daNm

M'₁=1496.04 * 2 = 2992.1 daNm

CALCULUL ARMATURILOR :

A_a1 = = = 7.13 cm²

A_a1 = 7.13 / 4.80 = 1.49 cm²/m

A _a2 = = = 4.96 cm²

Aa₂ = 3.95 / 3.90 = 1.01 cm²/m

A'_a1 = = = 14.26 cm²

A'a₁ = 4.85 / 4.80 = 1.01 cm²/m

A'_a2 = = = 6.20 cm²

A'a₂ = 7.90 / 3.90 =2.03 cm²/m

Placa 7: Hol 2.10 x 11.10

Pardoseala calda :

l_max/l_min = 11.10 / 2.10 = 5.29 => armare pe o singura directie

Schema de calcul :

M₁ = = = 947.6 daNm

M_B = = = 744.56 daNm

M_C = = = 560.72 daNm

M₂ = - =

= - = 469.71 daNm

z₁ = 0.9 * h₀₁ = 0.9 * ( h -a - f₁ / 2 ) = 0.9 * ( 13.00 - 1.5 - 0.8 / 2 ) =

z₁ = 9.99 cm

z₂ = 0.9 * h₀₁ = 0.9 *( h -a - f₁ - f₁ / 2 ) = 0.9 *( 13.00 - 1.5 - 0.8 - 0.8 / 2 )

z₂ = 9.27 cm

CALCULUL ARMATURILOR :

Aa₁ = = = 2.37 cm²

Aa₁ = 2.37 / 2.10 = 1.13 cm²/m

A'a₁ = = = 3.82 cm²

A'a₁ = 3.82 / 2.10 = 1.82 cm²/m

Placa 8 Balcon 3.00 x 2.10

Pardoseala rece :

Momente maxime :

1/12 ( g + p ) ( 3 l_max-l_min) l²_min = 2 (M₁+M₂) + M₁^'

l = 3.00 / 2.10 = 1.43

l=1.4.....2.3

l=1.43 ......X

l=1.5......3.1

X = 0.24

=> M₁/M₂= 2.54 => M₂ = M₁/ 2.54

M₁ = M₂* 2.54

l₂ / l'₂ = 3.00 / 2.10 = 1.43 > 0.9 => M₂/M₂^'= 0.8 => M₂^'= M₂ / 0.8

l₁ / l'₁ = 3.80 / 2.10 = 1.81 > 1.14 => M₁/M₁^'= 0.8 => M₁^'= M₁/ 0.8

1 / 12 (925.45+ 0 )(3 * 3.00 - 2.10 ) 2.10² = 2 ( M₁+ M₁/2.54 ) + M₁/ 0.8

2346.70 = 2.04* M₁

M₁ = 1150.35 daNm

M₂ = 1150.35 / 2.54 = 469.53 daNm

M ₁^' = 1150.35 / 0.8 = 1438.94 daNm

CALCULUL ARMATURILOR :

A_a1 = = = 5.48 cm²

A_a1 = 5.48/ 3.00 = 1.83 cm²/m

A _a2 = = = 2.41 cm²

Aa₂ = 2.41 / 2.10 = 1.41 cm²/m

A'_a1 = = = 6.85 cm²

Aa₁^' = 6.85 / 3.00 = 2.28cm²/m

Extras de armatura pentru placa peste subsol :