Esercizio di esame Laboratorio di costruzioni in c.a.

ANALISI DEI CARICHI

γ_cls = 25 ^KN/_m³ γ_pon = 8 ^KN/_m³ γ_acc = 77 ^KN/_m³ γ_{in. acciaco} = 21 ^KN/_m³

G_K = γ h = b h_E γ = g_L [^KN/_m]

g₁ = 3,48 ^KN/_m² G_K = g₁ l_S = 3,48 ^KN/_m² 6 m = 20,88 ^KN/_m + 3,75 ^KN/_m G_K2 = 45,03 ^KN/_m

SLU: comb. sismica: F_d = G_K + H_K + E + Ψ₂Q_K = 53,83 ^KN/_m + 2^{00 KN} + 120 ^KN

1 capo → 3 gdl 5 gdl 2 v. spec.

ANALISI DEI CARICHI

s = S_j = G_k L

solaio

• soletta: 1 m · 0.05 m · 2⁴
• trave: 0.10 m, 0.20 m · 1 m)² = 1
• prororte: (0.90 m, 0.20 m - 0.10 m)/2 · ( 1 - 28 )
• mureto: 1 m, 0.08 m, 1 m 2⁴
• pror m 1 m:
• traceren
• inrer
• trave 0.30 m :
• taperte: 1 m, 2.5 m, 0.20,)
• Q_K = 4 m · 6 = 24

G_K = b h

g_i = 3.48

g_i = 2.55

G_R = g_i

l_s = 3.48

G_r = 2.55

5.5

G_K = 45.83

Q = 9

Strutt. Frame Isoterica

• E
• 1 corp
• 5 qdte#

Problema 0

X_A = -E = -120 kN

Y_A - M_K - q H = 0 → Y_A = 358,13 kN

M_A - E:3 - q11.5:5 = 0 → M_A = 2373,32 kNm

• TRAVE l N₀ T₀ M₀
• FD 6 0 -qx qx²/2
• DC 2 -9c 0 9q
• CB 5 0 -9c -qx²
• BA 3 -9c-91-11_K -E 9q9,5+Ex+q11₂

Problema 1

X_A = 0

Y_A = -1

M_A = -1.5

• TRAVE l N₁ T₁ M₁
• FD 6 0 0 0
• DC 2 0 0 0
• CB 5 0 1 -x
• BA 3 1 0 -5

Problema 2

X_A = 0

Y_A = -1

M_A = -1.1

• TRAVE l N₂ T₂ M₂
• FD 6 0 1 -x
• DC 2 0 0 -6
• CB 5 0 1 -6-x
• BA 3 1 0 -11

M₁₁ = ∫₀⁵ M₁ M₁ EI dx = ∫₀⁵ x² EI dx + ∫₀⁵ 23 EI dx = x³ 3 EI₅ + 25 x⁵₃ = 41,6 + 75 = 116,6 EI

M₁₀ = ∫₀⁵ M₁ M₀ EI dx = ∫₀⁵ (-x)(9 + 48q + 6x² + qx²) dx = ∫₀⁵ (-5q)(60,5 - E x) dx = ∫₀⁵ (-18q x - 6qx² - q x³ 2) dx =

+ ∫₀⁵ (-300q - 5Ex) dx = -18q x²₂⁵ - 6qx³₃⁵ - q x⁴₄² - 300q x³ - 5Ex⁵₃ =

= -225q - 250q - 78,125 q - 8100q - 225q = -86.475 q EI = -519025,25

M₁₂ = M₂₁ = ∫₀⁵ M₁ M₂ EI dx = ∫₀⁵ (-x)(-6 - x) dx + ∫₀⁵ (-5)(-x - 1) dx =

= ∫₀⁵ (-5 + 6x + 3x) dx + ∫₀⁵ 55 dx = 6 x² 2₅ + x³ 3₅ + 55 x⁵₃ =

= 75 + 41,6 + 165 = 281 EI

M₂₂ = ∫₀⁵ H2 M2 = EI dx = ∫₀⁶ x² dx + ∫₀^{5 36 dx + ∫₀5 (-6 - x)2 dx + ∫₀5 (-11)2 dx =}

= x³ 3₆ + 36x2₅ + ∫₀⁵ (36 + x² + 12x) dx + 121 x

= 72 + 72 + 36 x⁵ + x³ 3₅ + 12 x² 2₅ + 363 =

= 507 + 180 + 41,6 + 150 = 878,6 EI

M₂₀ = ∫₀⁶ H₁ M₀ EI dx = ∫₁⁶ (-x)(9x² 2) dx + ∫₂(-6) 9 x8 dx + ∫₅ (-6 - x)(18q + 6q + 9x² 2) dx =

+ ∫₃ (-1)(60,5q + E x) dx = -9 x³ 2 dx + ∫₅ -108q dx + ∫⁵ -108q - 36q² dx = 3q³ + ∫⁵ -665,5 q x³ - 11E x² =

= -81 + 507 + -108q x² 2₅ - x³ 3₅ - 180q x² 5₄ - 60q x³ 3₅ - x q⁴ 8₆ + -665,5 q + nEx =

= -162q - 216q - 90q - 450q - 135q - 225q - 250q - 78,125q - 198,5q - 495E =

= -4042,6q - 495 E = -241868 - 5340 = -247808

{x₁M₁₁ + x₂M₁₂ + M₁₀ + M_A = 0

x₁M₂₁ + x₂M₂₂ + M₂₀ + M_B = 0} ➔{ x₁ = - M₁₀ - M₁₂ x₂ ⁄ M₁₁

x₂ = M₂₀M₁₂ - M₁₀M₂₂ ⁄ M₂₂ - M₁₂ M₂₁ ⁄ M₁₁ }

x₂ = -519025,25 ⋅ 218 ⁄ 116,6 + 247,808 = -722582,26⁄ 878,6 - 281² ⁄ 116,6 = -3587,8 u 146,6 KN

x₁ = +519025,25 ⁄ 116,6 - 218 ⁄ 116,6 ⋅ (-3587,8)4451,3 + 6707,88 = 11159,2 = 370,6 KN

Y_A = Y^o_A + x₁Y^*_A + x₂Y^z_A = 358,13 + 370,6 ⋅ (-1)+ 146,6 ⋅ (-1) = 440,9 KH

M_A = M^o_A + x₁M^*_A + x₂M^z_A =3873,72 + 370,6 ⋅ (-5) + 146,6 ⋅ (-11) = 5146,12 KHcm 1853 162,6