Esercizio di esame Laboratorio di costruzioni in c.a.

ANALISI DEI CARICHI

selciato g₁ = 1 m · 0,04 m · 1 m · 24 kN/m³ = 0,96 kN/m²soletta g₁ = (0,04 m - 0,16 m · 1 m) · 2 · 8 = 1,024promettte g₁ = (0,04 m · 0,16 m · 1 m · 2) · 25 = 0,8terovate g₁ = (0,3 m · 0,6) · 25 = 4,5 kN/mmonerte g₁ = 1 m · 0,08 m · 1 m · 24 = 1,92pori in arc g₂ = 1 m · 0,07 m · 1 m · 21 = 0,21intoneco g₂ = 1 m · 0,02 m · 1 m · 21 = 0,42

g^tot₁ = 2,88 kN/m² → G_R1 = g^tot₁ l_s = 13,82 kN/m + 4,5 kN/m = 18,42 kN/mg^tot₂ = 2,55G_R2 = g^tot₂ l_s = 12,75 kN/mQ_K = q_R l_s = 2 kN/m² · 5 m = 10 kN/m

zona rinforzo: SLU: comb. rinarm.: F_d = G_R1 + G_R2 + 2/3 Q_K = 34,17 kN/m

ANALISI DEI CARICHI

• soletta g₁ = 1m . 0,04m . 1m . 24 KN/m³ = 0,86 KN/m²

• solaio

  • progetto g₁ = (0,04m . 0,16m . 1m) 2 . 8 = 1,024
  • iprovetta g₁ = (0.04m . 0,16m . 1m) 2 . 25 = 0,8

• massetto g₂ = 1m . 0,08m . 1m . 24 = 1,92

• pav. in ac g₂ = 1m . 0,01m . 21 = 0,21

• intonaco g₂ = 1m . 0,02m . 21 = 0,42

Trave g_t = 0,3m . 0,6 . 25 = 4,5 KN/m

g₁^tot = 2,88 KN/m² → G_K1 = g₁^tot l_s = 13,82 KN/m + 4,5 KN/m = 18,42 KN/m

g₂^tot = 2,55 → G_K2 = g₂^tot l_s = 12,75 KN/m

Q_K = q_R l_s = 2 KN/m² . 5m = 10 KN/m

zona ricinato:

SLU: comb ricinato: F_d = G_k1 + G_k2 + (2/3) Q_k = 34,17 KN/m

Sforzi prime isostatica

100cp → sgd_v

sgd_m {2 vupest}

E₂ = 3

x → x = 3 ∙ 2 ∙ √2 / √2 = 3 √2

Problema 0

X_c = 0

Y_A = 8q = 273.36

ΣM^c = 0 : M_c + 4.5q - 8Y_A = 0 → M_c = 59.59 = 203.9.115

• TRAVE l N₀ T₀ M₀
• AB 3√2 193.3 -193.3 193.3x
• DB 3√2 9x√2/2 -9x -9x²
• CB 5 0 -9x qx²/2 = 2039.115

Problema 1

X_c = 1

Y_A = 0

ΣM^c = 0 M_c + 1.3 = 0 → M_c = -3

• TRAVE l N₁ T₁ M₁
• AB 3√2 0 0 0
• DB 3√2 -√2/2 -√2/2 -√2/2
• CB 5 -1 0 3

Problema 2

X_c = 0

Y_A = -1

ΣM^c = 0: M_c + 1.8 - Y_A 8 = 0

M_c = 8 - 8 = 0

• TRAVE l N₂ T₂ M₂
• AB 3√2 -√2/2 -√2/2
• DB 3√2 -√2/2 -√2/2
• CB 5 0 0 0

M_M = ∫₀⁵ M_m M_A ^. dx = ∫₂⁵ 2 ^. dx + ∫₅⁵ 2 dx = ∫₀⁵ (x³/6)₃³¹² + 45 = 57,72/EI

M_A0 = ∫₂⁵ M_A H_A ^. dx = ∫₂⁵ ( -¹²/21/92 _. )₃ 9x² dx = 6089,345 dx = ∫ (x⁵/4 + x⁴/3₁₂) ₄³¹² + (1/2) x⁵ 9 = -30846,725

= 1546,36 + 2433,625 - 30486,725 = -26 814,74/EI

M_A1 = M_A2 = ∫₀³¹² M_m H₂ ^. dx = ∫₀¹ x² dx ^{. 3/6 .} = 27,7 = ⁹/EI

M_A2 = ∫₃⁷ x² dx = 27/5 = ⁹/EI

M_A0 = ∫₂⁵ 133,3(x - ¹²/2 )₄² dx + ∫₃¹² (x²/5 - 1/92₅₂ )₄ x dx = - 136,7 3₃₁₂ = - 9√2₄ x⁴ =

= - 45,36 ^21,274 - ^9√2/16 . 81,4 = ^9457,8/EI

    3471,3      972,55

Χ₂ = - 26 814,74 + ∫₉ + ∫_4457,8

^57,72

18 - 81 / 57,72 = 276,97 / 16,53 = 16,67

Χ₁ = + 26 814,74 - ∫9/∫57,72 . 16,67 = 464,56 - 2,6 = 461,86

Υ_A = Υ^ο_A + 2Χ¹Υ²_A = 213,36 + ∅ - 16,67 = 256,69

Χ_C = Χ^ο_c + 2Χ^o_c + 2Χ^o_c = ∅ + 461,86 + ∅

Μ_c = Μ^ο_c + Χ^o_c + 2Χ^o_c + Χ^o_c ² = 2033,115 - 1385,88 + ∅ = 647,235

           256,69

                    9 - 34,14

         16,67        461,86

                                    461,86

                          647,235

TRAVE

• AB
• DB
• CB

ℓ

• 3\(\sqrt{2}\)
• 3\(\sqrt{2}\)
• 5

N

• 181,5
• -338,44 +9x
• -461,86

T

• -181,5
• +314,18 +9x
• -9x

M

• 181,5x
• -314,18x - 9\(\frac{x^{2}}{2}\)
• \(\frac{9x^{2}}{2}\) - 647,235

181,5

183,4

338,44

-461,86

181,5

314,18

453,18

470,85

1940,4

1640,46

333,7

647,235