Calculul stalpilor

Calculul stalpilor

1.Calculul la incovoiere (N^calcul, M^calcul)

a. N^calcul = N_g^ld N^seism

N^ld = N_ac^ld + N_pl^ld + N_gr^ld + N_pr^ld + N_st^ld

stalp central etaj :

N_gr^ld = b_gr^tr*(h_gr^tr - h_pl)*(L+l/2 - 0,4)*γ_b + b_gr^lg*(h_gr^lg - h_pl)*[(t₁ +t₂)/2 - 0,4]*γ_b

0,25*(0,5 - 0,14)*[(5.4+4.8)/2 - 0,4]*25 + 0,25*(0,50 - 0,14)*[(4,5 +4,2)/2 - 0,4]*25= 17,95 kN

A_af=(l₁+l₂)/2+(t₁+t₂)/2=(5,4+4,8)/2+(4,5+4,8)/2=22,18 m²

N_ac^ld = A_af*q_ac^ld = 22,18*7,58 = 168,12 kN

N_st^ld= b_st*h_st*(H-h_pl)* γ_b=0,4*0,4(3,1-0,14)*25=11,84 kN

N_sc^{ld E} = N_ac^ld + N_gr^ld + N_st^ld =17,95+168,12+11,84 = 178,23 kN

N^seism = V₁^as =[(M_cap^- + M_cap⁺)_gr/l₀]_AB- [(M_cap^- + M_cap⁺)_gr/l₀]_BC

N^seism =(78,71+47,44)/4,4 -(78,71+47,44)/5=3,44 kN

N₁^calcul = N^ld + N^seism = 178,23     + 3,44 = 201,35 kN

N₂^calcul = N^ld - N^seism = 178,23     - 3,44 = 194,47 kN

- stalp central parter

N_pl^ld = A_af*q_pl^ld = 22,18*6,64 = 147,27 kN

N_sm^ld = N_sc^{ld E} + N_pl^ld + N_gr^ld + N_st^ld = 197,91+147,27+17,97+11,84

= 374,99 kN

N^seism = V₁^as =[(M_cap^- + M_cap⁺)_gr/l₀]_AB- [(M_cap^- + M_cap⁺)_gr/l₀]_BC

N^seism =(55,83+99,16)/4,4 -(55,83+99,16)/5=4,22 kN

N₁^calcul = N^ld + N^seism = 374,99 + 3,44 + 4,22 = 382,65 kN

N₂^calcul = N^ld - N^seism = 374,99 - 3,44 - 4,22 = 367,323 kN

stalp marginal (2;A) etaj :

N_gr^ld = b_gr^tr*(h_gr^tr - h_pl)*(L/2 - 0,4)*γ_b + b_gr^lg*(h_gr^lg - h_pl)*[(t₁ +t₂)/2 - 0,4]*γ_b

0,25*(0,5 - 0,14)*(4.8/2 - 0,4)*25 + 0,25*(0,50 - 0,14)*[(4,5 +4,2)/2 - 0,4]*25= 12,64 kN

A_af=(l₁)/2+(t₁+t₂)/2=4,8/2+(4,5+4,8)/2=10,44 m²

N_ac^ld = A_af*q_ac^ld = 10,44*7,17 = 79,13 kN

N_st^ld= b_st*h_st*(H-h_pl)* γ_b=0,4*0,4(3,1-0,14)*25=11,84 kN

N_atic =l*h*b*γ_p=0,5*0,375*18,5*4,35=15,08 kN

N_sc^{ld E} = N_ac^ld + N_gr^ld + N_st^ld + N_atic =12,64+79,13+11,84+15,38 = 116,49 kN

N^seism = V₁^as =(M_cap^- + M_cap⁺)_gr/l₀

N^seism =(78,71+47,44)/4,1 =30,76 kN

N₁^calcul = N^ld - N^seism = 178,23     - 30,76 = 85,73 kN

N₂^calcul = N^ld + N^seism = 178,23     + 30,76 = 147,25 kN

- stalp marginal (2;A) parter

N_pl^ld = A_af*q_pl^ld = 10,44*5,24 = 54,7 kN

N_perete =l*h*b*γ_p=2,6*0,375*18,5*4,35= 78,67 kN

N_sm^ld = N_sc^{ld E} + N_pl^ld + N_gr^ld + N_st^ld + N_perete= 116,49+54,7+12,64+11,84+78,67

= 277,34 kN

N^seism = V₁^as =(M_cap^- + M_cap⁺)_gr/l₀

N^seism =(55,83+99,16)/4,1 =37,8 kN

N₁^calcul = N^ld - N^seism = 277,34 - 30,76 - 37,8 = 208,78 kN

N₂^calcul = N^ld + N^seism = 277,34 + 30,76 + 37,8 = 345,9 kN

stalp colt (1;C) etaj :

N_gr^ld = b_gr^tr*(h_gr^tr - h_pl)*(L/2 - 0,4)*γ_b + b_gr^lg*(h_gr^lg - h_pl)*(t₁ /2 - 0,4)*γ_b

0,25*(0,5 - 0,14)*(4.8/2 - 0,4)*25 + 0,25*(0,50 - 0,14)*(4,5/2 - 0,4)*25

= 9,03 kN

A_af= l₁ /2+ t₁ /2=4,8/2+4,5/2=4,25 m²

N_ac^ld = A_af*q_ac^ld = 4,25*7,58 = 32,21 kN

N_st^ld= b_st*h_st*(H-h_pl)* γ_b=0,4*0,4(3,1-0,14)*25=11,84 kN

N_atic =l*h*b*γ_p=0,5*0,375*18,5*(2,2+2,05)=14,74 kN

N_sc^{ld E} = N_ac^ld + N_gr^ld + N_st^ld + N_atic =32,21+9,03+11,84+14,74 = 67,81 kN

N^seism = V₁^as =(M_cap^- + M_cap⁺)_gr/l₀

N^seism =(78,89+31,56)/4,1 =26,94 kN

N₁^calcul = N^ld - N^seism = 67,81 - 26,94 = 40,87 kN

N₂^calcul = N^ld + N^seism = 67,81     + 26,94 = 94,75 kN

- stalp colt (1;C) parter

N_pl^ld = A_af*q_pl^ld = 4,25* 4,25 = 22,27 kN

N_perete =l*h*b*γ_p=2,6*0,375*18,5*4,25= 76,66 kN

N_sm^ld = N_sc^{ld E} + N_pl^ld + N_gr^ld + N_st^ld + N_perete = 67,81+22,27+9,03+11,84

= 187,61 kN

N^seism = V₁^as =(M_cap^- + M_cap⁺)_gr/l₀

N^seism =(106,89+55,57)/4,1 =39,62 kN

N₁^calcul = N^ld - N^seism = 187,61 - 26,94 - 39,62 = 121,05 kN

N₂^calcul = N^ld + N^seism = 187,61 + 26,94 + 39,62 = 254,17 kN

b. M^calcul = k_m*ω*M_s

k_m = 1;1,4

= (Σ M_cap)_gr/(Σ M_ef)_gr > 1

stalp central cadru transversal-etaj

= (Σ M_cap)_gr/(Σ M_ef)_gr =(2*158,46+98,59+55,83)/(135,02+70,665+117,856+52,306)= 1,26 > 1

M^calcul = 1,4*1,26*29,73 = 52,44 kNm

stalp central cadru transversal-parter

= (Σ M_cap)_gr/(Σ M_ef)_gr =(2*158,46+98,59+55,83)/(135,02+70,665+117,856+52,306)= 1,26 > 1

M^calcul = 1*1,26*78,213 = 98,55 kNm

stalp marginal -etaj

- cadru transversal

= (Σ M_cap)_gr/(Σ M_ef)_gr =(2*158,46+98,59+55,83)/(135,02+70,665+117,856+52,306)= 1,26 > 1

M₁^calcul = 1,4*1,26*0,762 = 1,34 kNm

M₂^calcul = 1,4*1,26*70,351 = 124,09 kNm

- cadru longitudinal

= (Σ M_cap)_gr/(Σ M_ef)_gr =(3*106,2+3*55,57)/(54,19+32,924+40,031+104,61+92,21+96,53)= 1,15 > 1

M₁^calcul = 1,4*1,15*51,038 = 82,17 kNm

M₂^calcul = 1,4*1,15*39,622 = 63,79 kNm

stalp marginal -parter

- cadru transversal

= (Σ M_cap)_gr/(Σ M_ef)_gr =(2*158,46+98,59+55,83)/(135,02+70,665+117,856+52,306)= 1,26 > 1

M₁^calcul = 1*1,26*70,49 = 88,81 kNm

M₂^calcul = 1*1,26*99,727 = 125,65 kNm

- cadru longitudinal

= (Σ M_cap)_gr/(Σ M_ef)_gr =(3*106,2+3*55,57)/(54,19+32,924+40,031+104,61+92,21+96,53)= 1,15 > 1

M₁^calcul = 1*1,15*87,769 = 100,9 kNm

M₂^calcul = 1*1,15*83,36 = 95,86 kNm

stalp colt cadru longitudinal -etaj

= (Σ M_cap)_gr/(Σ M_ef)_gr =(3*106,2+3*55,57)/(54,19+32,924+40,031+104,61+92,21+96,53)= 1,15 > 1

M₁^calcul = 1,4*1,15*65,933 = 75,82 kNm

M₂^calcul = 1,4*1,15*87,447 = 100,56 kNm

a. stalp central cadru transversal -etaj

2.Dimensionarea armaturii

N^calcul = 201,35 kN

M^calcul = 52,44 kNm

(1) N^calcul = b*x*R_c'

(2) M^calcul + N^calcul*h_a/2 = b*x* R_c'*(h_a - x/2) + Aa*R_a*h_a pentru x > 2*a'

(3) M^calcul - N^calcul*h_a/2 = Aa*R_a*h_a pentru x ≤ 2*a'

R_c' = 0,85*R_c = 0,85*12,5 = 10,63 N/mm²

(1) => x = N^calcul/( b*R_c') = 52440/(400*10,63) = 47,35 mm

a' = c + ф/2 = 25 + 16/2 = 33 mm

h_a = h - 2*a' = 400-66 = 334 mm

x =47,35 < 2*a' = 66 mm

(3) => Aa^nec = (M^calcul - N^calcul*h_a/2)/( R_a*h_a) = (52,44*10⁶ - 201,35*10³*334/2)/(300*334)=187,76 mm²

aleg Aa^ef = 3 ф 12 = 339,29 mm²

p_min = 0,2 % (pentru o latura)

p = Aa^ef*100/(b*h₀) = 339,29*100/(400*369) = 0,22 % < p_min = 0,2 %

p_min^tot = 0,8 %

p^tot = Aa^tot*100/(b*h₀) = 8*113,09*100/(400*369) = 0,61 < p_min^tot = 0,8 %

aleg Aa^ef = 4 ф 12 = 452,41 mm²

p_min = 0,2 % (pentru o latura)

p = Aa^ef*100/(b*h₀) = 452,41*100/(400*369) = 0,30 % > p_min = 0,2 %

p_min^tot = 0,8 %

p^tot = Aa^tot*100/(b*h₀) = 1357,08*100/(400*369) = 0,91 > p_min^tot = 0,8 %

3. Verificare a stalp central-etaj

x = 47,35 mm

a' = c + ф/2 = 25 + 12/2 = 31 mm

h_a = h - 2*a' = 338 mm

(3) M_cap = N^calcul*h_a/2 + Aa^ef*R_a*h_a = 201,35*10³*338/2 + 452,41*300*338

M_cap =79,32 kNm

M_cap = 79,32 kNm > M^calcul = 52,44 kNm

4.Calculul la forta taietoare si armarea la forta taietoare

a.       Calculul la forta taietoare

T^calcul = k_T*ω*T_s

k_T = 1,2

T_s = (M_i + M_s)/H = (29,733+52,282)/3,1 = 26,45 kN

T_sc^calcul = 1,2*1,26*26,45 = 40 kN

b. Dimensionarea armaturii

T^calcul = T^calcul/(b*h₀*R_t')

R_t' = 0,85* R_t' = 0,85*0,95 = 0,81 N/mm²

T_sm^calcul = 40*10³/(400*367*0,81) = 0,33 <T_min = 0,5=> armare constructiva

-Zona disipativa

a_e^d = 100 mm

-Zona disipativa

a_e^d = 200 mm

- stabilirea zonelor disipative

l_p = max(600 mm; H/6 = 516,6 mm; b = 400 mm) = 600 mm

b. stalp central cadru transversal -parter

2.Dimensionarea armaturii

N^calcul = 382,65 kN

M^calcul = 98,55 kNm

(1) N^calcul = b*x*R_c'

(2) M^calcul + N^calcul*h_a/2 = b*x* R_c'*(h_a - x/2) + Aa*R_a*h_a pentru x > 2*a'

(3) M^calcul - N^calcul*h_a/2 = Aa*R_a*h_a pentru x ≤ 2*a'

R_c' = 0,85*R_c = 0,85*12,5 = 10,63 N/mm²

(1) => x = N^calcul/( b*R_c') = 382650/(400*10,63) = 89,99 mm

a' = c + ф/2 = 25 + 16/2 = 33 mm

h_a = h - 2*a' = 400-66 = 334 mm

x =89,99 > 2*a' = 66 mm

(2) => Aa^nec = (M^calcul + N^calcul*h_a/2 - b*x* R_c'*(h_a - x/2))/( R_a*h_a) =

(98,55*10⁶ + 382,65*10³*334/2 - 400*10,63*89,99(344-89,99/2)/(300*334)=517,93 mm²

aleg Aa^ef = 4 ф 14 = 615,75 mm²

p_min = 0,2 % (pentru o latura)

p = Aa^ef*100/(b*h₀) = 615,75*100/(400*367) = 0,41 % > p_min = 0,2 %

p_min^tot = 0,8 %

p^tot = Aa^tot*100/(b*h₀) = 12*153,93*100/(400*367) = 0.98 > p_min^tot = 0,8 %

3. Verificare a stalp central-parter

x = 89,99 mm

a' = c + ф/2 = 25 + 14/2 = 33 mm

h_a = h - 2*a' = 334 mm

(2) M_cap = b*x* R_c'*(h_a - x/2) + Aa*R_a*h_a - N^calcul*h_a/2 = 400*10,63*89,99(344-89,99/2)-382,65*10³*334/2 + 615,75*300*338

M_cap =108,37 kNm

M_cap = 108,37 kNm > M^calcul = 98,55 kNm

4.Calculul la forta taietoare si armarea la forta taietoare

a.Calculul la forta taietoare

T^calcul = k_T*ω*T_s

k_T = 1,2

T_s = (M_i + M_s)/H = (78,213+51,62)/3,1 = 41,88 kN

M_s= (M_{cap inf}/ M_{ef inf} )* M_{cap sup} =(108,37/98,55)*44,569=51,62

T_sc^calcul = 1,2*1,26*41,88 = 63,32 kN

b. Dimensionarea armaturii

T^calcul = T^calcul/(b*h₀*R_t')

R_t' = 0,85* R_t' = 0,85*0,95 = 0,81 N/mm²

T_sm^calcul = 63,32*10³/(400*367*0,81) = 0,52 >T_min = 0,5=> armare din calcul

q_e^nec,sm=T²/(4*b*h₀²*m_t* R_t'*p^1/2)= 63,32²*10⁶/(4*400*336²*1,11*0,81*0,67)

= 36,84 N/mm

m_t = 1 + 0,5*n = 1 + 0,5*0,22=1.11

n = N^calcul/(b*h₀* R_t') = 374/(400*338*10,63) = 0.22

Aa_e^ef = Aa_e^min = 8f =50,26 mm²

a_e^nec = n_r*Aa_e*R_ae/q_e^nec,sc = 4*50,26*(0,8*210)/36,84 = 900mm

-Zona disipativa

a_c= -<8f =96 mm

->100

-<h/5=80

=> din conditii constructive a_e^d = 100 mm in zona disipativa

p_etr = n_r*Aa_e/(b*a_e) = 4*50,26*100/(400*100) = 0,50 %

p_etr^min = 10*R_c'*(0,4 + n)/R_a = 10*10,36*(0,4+0,22)/210 = 0,22 %

=> p_etr = 0,50 % > p_etr^min = 0.22%

-Zona nedisipativa

a_c= -< 200 mm

-<15f =5*14=210 mm

=> din conditii constructive a_e^d = 200 mm in zona disipativa

p_etr = n_r*Aa_e/(b*a_e) = 4*50,26*100/(400*200) = 0,25 %

=> p_etr = 0,25 % > p_etr^min = 0,15%

- stabilirea zonelor disipative

l_p = max(600 mm; H/6 = 516,6 mm; b = 400 mm) = 600 mm

c. stalp marginal -etaj

2.Dimensionarea armaturii

- directie transversala

-varianta 1:

N^calcul = 85,73 kN

M^calcul = 1,34 kNm è armare minima

-varianta 2:

N^calcul = 147,25 kN

M^calcul = 124,09 kNm

(1) N^calcul = b*x*R_c'

(2) M^calcul + N^calcul*h_a/2 = b*x* R_c'*(h_a - x/2) + Aa*R_a*h_a pentru x > 2*a'

(3) M^calcul - N^calcul*h_a/2 = Aa*R_a*h_a pentru x ≤ 2*a'

R_c' = 0,85*R_c = 0,85*12,5 = 10,63 N/mm²

(1) => x = N^calcul/( b*R_c') = 147250/(400*10,63) = 34,63 mm

a' = c + ф/2 = 25 + 16/2 = 33 mm

h_a = h - 2*a' = 400-66 = 334 mm

x =34,63 < 2*a' = 66 mm

(3) => Aa^nec = (M^calcul - N^calcul*h_a/2)/( R_a*h_a) = (124,09*10⁶ - 147,25*10³*334/2)/(300*334)=933 mm²

aleg Aa^ef = 4 ф 18 = 1017,87 mm²

p_min = 0,2 % (pentru o latura)

p = Aa^ef*100/(b*h₀) = 1017,87*100/(400*366) = 0,69 % > p_min = 0,2 %

- directie longitudinala

-varianta 1:

N^calcul = 118,91 kN

M^calcul = 82,17 kNm

(1) N^calcul = b*x*R_c'

(2) M^calcul + N^calcul*h_a/2 = b*x* R_c'*(h_a - x/2) + Aa*R_a*h_a pentru x > 2*a'

(3) M^calcul - N^calcul*h_a/2 = Aa*R_a*h_a pentru x ≤ 2*a'

R_c' = 0,85*R_c = 0,85*12,5 = 10,63 N/mm²

(1) => x = N^calcul/( b*R_c') = 118910/(400*10,63) = 27,96 mm

a' = c + ф/2 = 25 + 16/2 = 33 mm

h_a = h - 2*a' = 400-66 = 334 mm

x =27,96 < 2*a' = 66 mm

(3) => Aa^nec = (M^calcul - N^calcul*h_a/2)/( R_a*h_a) = (81,17*10⁶ - 118,91*10³*334/2)/(300*334)=611,89 mm²

-varianta 2:

N^calcul = 114,07 kN

M^calcul = 63,79 kNm

(1) => x = N^calcul/( b*R_c') = 114070/(400*10,63) = 26,82 mm

a' = c + ф/2 = 25 + 16/2 = 33 mm

h_a = h - 2*a' = 400-66 = 334 mm

x =26,82 < 2*a' = 66 mm

(3) => Aa^nec = (M^calcul - N^calcul*h_a/2)/( R_a*h_a) = (63,79*10⁶ - 114,07*10³*334/2)/(300*334)=446,51 mm²

è varianta 1 Aa^nec = 611,89 mm²

aleg Aa^ef = 2 ф 12 +2 ф 18 = 226,19+ 508,93 = 735,12 mm²

p_min = 0,2 % (pentru o latura)

p = Aa^ef*100/(b*h₀) = 735,12*100/(400*366) = 0,50 % > p_min = 0,2 %

p_min^tot = 0,8 %

p^tot = Aa^tot*100/(b*h₀) =(4 ф 12 +8 ф 18 ) *100/(400*366) = 1,69 > p_min^tot = 0,8 %

3. Verificare a stalp marginal-etaj

- directie transversala

x = 34,63 mm

a' = c + ф/2 = 25 + 18/2 = 34 mm

h_a = h - 2*a' = 332 mm

(3) M_cap = N^calcul*h_a/2 + Aa^ef*R_a*h_a = 1147250*332/2 + 1017,87*300*332

= 126,20 kNm

M_cap = 126,20 kNm > M^calcul = 124,09 kNm

- directie transversala

x = 27,96 mm

a' = c + ф/2 = 25 + 18/2 = 34 mm

h_a = h - 2*a' = 332 mm

(3) M_cap = N^calcul*h_a/2 + Aa^ef*R_a*h_a = 114070*332/2 + 735,12*300*332

= 92,43 kNm

M_cap = 92,43 kNm > M^calcul = 82,17 kNm

4.Calculul la forta taietoare si armarea la forta taietoare

a.       Calculul la forta taietoare

T^calcul = k_T*ω*T_s

k_T = 1,2

T_s = (M_i + M_s)/H = (87,447+45,616)/3,1 = 42,92 kN

T_sc^calcul = 1,2*1,15*42,92 = 59,22 kN

b. Dimensionarea armaturii

T^calcul = T^calcul/(b*h₀*R_t')

R_t' = 0,85* R_t' = 0,85*0,95 = 0,81 N/mm²

T_sm^calcul = 59,22*10³/(400*367*0,81) = 0,498 >T_min = 0,5=> armare constructiva

-Zona disipativa

a_e^d = 100 mm

-Zona disipativa

a_e^d = 200 mm

- stabilirea zonelor disipative

l_p = max(600 mm; H/6 = 516,6 mm; b = 400 mm) = 600 mm

d. stalp marginal -parter

2.Dimensionarea armaturii

- directie transversala

-varianta 1:

N^calcul = 208,78 kN

M^calcul = 88,81 kNm

(1) N^calcul = b*x*R_c'

(2) M^calcul + N^calcul*h_a/2 = b*x* R_c'*(h_a - x/2) + Aa*R_a*h_a pentru x > 2*a'

(3) M^calcul - N^calcul*h_a/2 = Aa*R_a*h_a pentru x ≤ 2*a'

R_c' = 0,85*R_c = 0,85*12,5 = 10,63 N/mm²

(1) => x = N^calcul/( b*R_c') = 208780/(400*10,63) = 49,10 mm

a' = c + ф/2 = 25 + 16/2 = 33 mm

h_a = h - 2*a' = 400-66 = 334 mm

x =49,10 < 2*a' = 66 mm

(3) => Aa^nec = (M^calcul - N^calcul*h_a/2)/( R_a*h_a) = (88,81*10⁶ - 1208,78*10³*334/2)/(300*334)=468,5 mm²

-varianta 2:

N^calcul = 282,87 kN

M^calcul = 100,9 kNm

(1) => x = N^calcul/( b*R_c') = 345900/(400*10,63) = 81,34 mm

a' = c + ф/2 = 25 + 16/2 = 33 mm

h_a = h - 2*a' = 400-66 = 334 mm

x =81,34 < 2*a' = 66 mm

(2) => Aa^nec = (M^calcul + N^calcul*h_a/2 - b*x* R_c'*(h_a - x/2))/( R_a*h_a) =

(125,65*10⁶ + 282,87*10³*334/2 - 400*10,63*81,34(344-81,34/2)/(300*334)=818,01 mm²

aleg Aa^ef = 4 ф 18 = 1017,87 mm²

p_min = 0,2 % (pentru o latura)

p = Aa^ef*100/(b*h₀) = 1017,87*100/(400*366) = 0,69 % > p_min = 0,2 %

- directie longitudinala

-varianta 1:

N^calcul = 282,87 kN

M^calcul = 100,9 kNm

(1) N^calcul = b*x*R_c'

(2) M^calcul + N^calcul*h_a/2 = b*x* R_c'*(h_a - x/2) + Aa*R_a*h_a pentru x > 2*a'

(3) M^calcul - N^calcul*h_a/2 = Aa*R_a*h_a pentru x ≤ 2*a'

R_c' = 0,85*R_c = 0,85*12,5 = 10,63 N/mm²

(1) => x = N^calcul/( b*R_c') = 282870/(400*10,63) = 66,5 mm

a' = c + ф/2 = 25 + 16/2 = 33 mm

h_a = h - 2*a' = 400-66 = 334 mm

x =66,5 > 2*a' = 66 mm

(2) => Aa^nec = (M^calcul + N^calcul*h_a/2 - b*x* R_c'*(h_a - x/2))/( R_a*h_a) =

=629,73 mm²

-varianta 2:

N^calcul = 271,81 kN

M^calcul = 95,86 kNm

(1) => x = N^calcul/( b*R_c') = 271,81/(400*10,63) = 63 mm

a' = c + ф/2 = 25 + 16/2 = 33 mm

h_a = h - 2*a' = 400-66 = 334 mm

x =63 < 2*a' = 66 mm

(3) => Aa^nec = (M^calcul - N^calcul*h_a/2)/( R_a*h_a) = (95,86*10⁶ - 271,81*10³*334/2)/(300*334)=503,66 mm²

è varianta 1 Aa^nec = 611,89 mm²

aleg Aa^ef = 2 ф 12 +2 ф 18 = 226,19+ 508,93 = 735,12 mm²

p_min = 0,2 % (pentru o latura)

p = Aa^ef*100/(b*h₀) = 735,12*100/(400*366) = 0,50 % > p_min = 0,2 %

p_min^tot = 0,8 %

p^tot = Aa^tot*100/(b*h₀) =(4 ф 12 +8 ф 18 ) *100/(400*366) = 1,69 > p_min^tot = 0,8 %

3. Verificare a stalp marginal-parter

- directie transversala

x = 81,34 mm

a' = c + ф/2 = 25 + 18/2 = 34 mm

h_a = h - 2*a' = 332 mm

(2) M_cap = b*x* R_c'*(h_a - x/2) + Aa*R_a*h_a - N^calcul*h_a/2 = 400*10,63*81,34(344-81,34/2)-345,9*10³*334/2 + 1017,87*300*338

M_cap = 144,71 kNm > M^calcul = 124,09 kNm

- directie transversala

x = 66,5 mm

a' = c + ф/2 = 25 + 18/2 = 34 mm

h_a = h - 2*a' = 332 mm

(3) M_cap = N^calcul*h_a/2 + Aa^ef*R_a*h_a = 282870*332/2 + 735,12*300*332

= 120,53 kNm

M_cap = 120,53 kNm > M^calcul = 95,96 kNm

4.Calculul la forta taietoare si armarea la forta taietoare

b.      Calculul la forta taietoare

T^calcul = k_T*ω*T_s

k_T = 1,2

T_s = (M_i + M_s)/H = (99,727+101,92)/3,1 = 65,04 kN

M_s= (M_{cap inf}/ M_{ef inf} )* M_{cap sup} =(144,71/125,65)*44,569=101,92

T_sc^calcul = 1,2*1,26*65,04 = 98,35 kN

b. Dimensionarea armaturii

T^calcul = T^calcul/(b*h₀*R_t')

R_t' = 0,85* R_t' = 0,85*0,95 = 0,81 N/mm²

T_sm^calcul = 98,35*10³/(400*367*0,81) = 0,82 >T_min = 0,5=> armare din calcul

q_e^nec,sm=T²/(4*b*h₀²*m_t* R_t'*p^1/2)= 98,35²*10⁶/(4*400*336²*1,11*0,81*0,67)

= 70,11 N/mm

m_t = 1 + 0,5*n = 1 + 0,5*0,22=1.11

n = N^calcul/(b*h₀* R_t') = 345,9/(400*366*10,63) = 0.22

Aa_e^ef = Aa_e^min = 8f =50,26 mm²

a_e^nec = n_r*Aa_e*R_ae/q_e^nec,sc = 4*50,26*(0,8*210)/70,11 = 475mm

-Zona disipativa

a_c= -<8f =96 mm

->100

-<h/5=80

=> din conditii constructive a_e^d = 100 mm in zona disipativa

p_etr = n_r*Aa_e/(b*a_e) = 4*50,26*100/(400*100) = 0,50 %

p_etr^min = 10*R_c'*(0,4 + n)/R_a = 10*10,36*(0,4+0,22)/210 = 0,22 %

=> p_etr = 0,50 % > p_etr^min = 0.22%

-Zona nedisipativa

a_c= -< 200 mm

-<15f =5*14=210 mm

=> din conditii constructive a_e^d = 200 mm in zona disipativa

p_etr = n_r*Aa_e/(b*a_e) = 4*50,26*100/(400*200) = 0,25 %

=> p_etr = 0,25 % > p_etr^min = 0,15%

- stabilirea zonelor disipative

l_p = max(600 mm; H/6 = 516,6 mm; b = 400 mm) = 600 mm

e. stalp colt directie longitudinala -etaj

2.Dimensionarea armaturii

-varianta 1:

N^calcul = 40,87 kN

M^calcul = 8,52 kNm è armare minima

-varianta 2:

N^calcul = 94,57 kN

M^calcul = 73,44 kNm

(1) N^calcul = b*x*R_c'

(2) M^calcul + N^calcul*h_a/2 = b*x* R_c'*(h_a - x/2) + Aa*R_a*h_a pentru x > 2*a'

(3) M^calcul - N^calcul*h_a/2 = Aa*R_a*h_a pentru x ≤ 2*a'

R_c' = 0,85*R_c = 0,85*12,5 = 10,63 N/mm²

(1) => x = N^calcul/( b*R_c') = 94750/(400*10,63) = 22,28 mm

a' = c + ф/2 = 25 + 16/2 = 33 mm

h_a = h - 2*a' = 400-66 = 334 mm

x =22,28 < 2*a' = 66 mm

(3) => Aa^nec = (M^calcul - N^calcul*h_a/2)/( R_a*h_a) = (73,44*10⁶ - 94,75*10³*334/2)/(300*334)= 575,01 mm²

aleg Aa^ef = 4 ф 14 = 615,75 mm²

p_min = 0,2 % (pentru o latura)

p = Aa^ef*100/(b*h₀) = 615,75*100/(400*367) = 0,41 % > p_min = 0,2 %

p_min^tot = 0,8 %

p^tot = Aa^tot*100/(b*h₀) =(12 ф 14 ) *100/(400*367) = 1,25 > p_min^tot = 0,8 %

3. Verificare a stalp colt-etaj

- directie transversala

x = 22,28 mm

a' = c + ф/2 = 25 + 18/2 = 34 mm

h_a = h - 2*a' = 332 mm

(3) M_cap = N^calcul*h_a/2 + Aa^ef*R_a*h_a = 94750*332/2 + 615,75*300*332

= 77,75 kNm

M_cap = 77,75 kNm > M^calcul = 73,44 kNm

4.Calculul la forta taietoare si armarea la forta taietoare

a.       Calculul la forta taietoare

T^calcul = k_T*ω*T_s

k_T = 1,2

T_s = (M_i + M_s)/H = (53,616+45,616)/3,1 = 32,01 kN

T_sc^calcul = 1,2*1,15*32,01 = 44,17 kN

b. Dimensionarea armaturii

T^calcul = T^calcul/(b*h₀*R_t')

R_t' = 0,85* R_t' = 0,85*0,95 = 0,81 N/mm²

T_sm^calcul = 44,17*10³/(400*367*0,81) = 0,37 <T_min = 0,5=> armare constructiva

-Zona disipativa

a_e^d = 100 mm

-Zona disipativa

a_e^d = 200 mm

- stabilirea zonelor disipative

l_p = max(600 mm; H/6 = 516,6 mm; b = 400 mm) = 600 mm

e. stalp colt directie longitudinala -parter

2.Dimensionarea armaturii

-varianta 1:

N^calcul = 121,05 kN

M^calcul = 75,82 kNm

-varianta 2:

N^calcul = 254,17 kN

M^calcul = 100,56 kNm

(1) N^calcul = b*x*R_c'

(2) M^calcul + N^calcul*h_a/2 = b*x* R_c'*(h_a - x/2) + Aa*R_a*h_a pentru x > 2*a'

(3) M^calcul - N^calcul*h_a/2 = Aa*R_a*h_a pentru x ≤ 2*a'

R_c' = 0,85*R_c = 0,85*12,5 = 10,63 N/mm²

(1) => x = N^calcul/( b*R_c') = 121050/(400*10,63) = 28,46 mm

a' = c + ф/2 = 25 + 16/2 = 33 mm

h_a = h - 2*a' = 400-66 = 334 mm

x =28,46 < 2*a' = 66 mm

(3) => Aa^nec = (M^calcul - N^calcul*h_a/2)/( R_a*h_a) = (75,82*10⁶ - 121,05*10³*334/2)/(300*334)= 554,93 mm²

-varianta 2:

N^calcul = 254,17 kN

M^calcul = 100,56 kNm

(1) N^calcul = b*x*R_c'

(2) M^calcul + N^calcul*h_a/2 = b*x* R_c'*(h_a - x/2) + Aa*R_a*h_a pentru x > 2*a'

(3) M^calcul - N^calcul*h_a/2 = Aa*R_a*h_a pentru x ≤ 2*a'

R_c' = 0,85*R_c = 0,85*12,5 = 10,63 N/mm²

(1) => x = N^calcul/( b*R_c') = 254,17/(400*10,63) = 59,8 mm

a' = c + ф/2 = 25 + 16/2 = 33 mm

h_a = h - 2*a' = 400-66 = 334 mm

x =59,8 < 2*a' = 66 mm

(3) => Aa^nec = (M^calcul - N^calcul*h_a/2)/( R_a*h_a) = (100,56*10⁶ - 254,17*10³*334/2)/(300*334)= 579,97 mm²

aleg Aa^ef = 4 ф 14 = 615,75 mm²

p_min = 0,2 % (pentru o latura)

p = Aa^ef*100/(b*h₀) = 615,75*100/(400*367) = 0,41 % > p_min = 0,2 %

p_min^tot = 0,8 %

p^tot = Aa^tot*100/(b*h₀) =(12 ф 14 ) *100/(400*367) = 1,25 > p_min^tot = 0,8 %

3. Verificare a stalp colt-etaj

- directie transversala

x = 59,8 mm

a' = c + ф/2 = 25 + 14/2 = 33 mm

h_a = h - 2*a' = 336 mm

(3) M_cap = N^calcul*h_a/2 + Aa^ef*R_a*h_a = 254170*336/2 + 615,75*300*336

= 104,76 kNm

M_cap = 104,76 kNm > M^calcul = 100,56 kNm

4.Calculul la forta taietoare si armarea la forta taietoare

b.      Calculul la forta taietoare

T^calcul = k_T*ω*T_s

k_T = 1,2

T_s = (M_i + M_s)/H = (87,447+70,8)/3,1 = 51,04 kN

T_sc^calcul = 1,2*1,15*51,04 = 70,44 kN

b. Dimensionarea armaturii

T^calcul = T^calcul/(b*h₀*R_t')

R_t' = 0,85* R_t' = 0,85*0,95 = 0,81 N/mm²

T_sm^calcul = 70,44*10³/(400*367*0,81) = 0,62 >T_min = 0,5=> armare din calcul

q_e^nec,sm=T²/(4*b*h₀²*m_t* R_t'*p^1/2)= 70,44²*10⁶/(4*400*336²*1,08*0,81*0,67)

= 47,34 N/mm

m_t = 1 + 0,5*n = 1 + 0,5*0,16=1.08

n = N^calcul/(b*h₀* R_t') = 254,18/(400*366*10,63) = 0.16

Aa_e^ef = Aa_e^min = 8f =50,26 mm²

a_e^nec = n_r*Aa_e*R_ae/q_e^nec,sc = 4*50,26*(0,8*210)/47,34 = 700mm

-Zona disipativa

a_c= -<8f =96 mm

->100

-<h/5=80

=> din conditii constructive a_e^d = 100 mm in zona disipativa

p_etr = n_r*Aa_e/(b*a_e) = 4*50,26*100/(400*100) = 0,50 %

p_etr^min = 10*R_c'*(0,4 + n)/R_a = 10*10,36*(0,4+0,16)/210 = 0,09 %

=> p_etr = 0,50 % > p_etr^min = 0.09%

-Zona nedisipativa

a_c= -< 200 mm

-<15f =5*14=210 mm

=> din conditii constructive a_e^d = 200 mm in zona disipativa

p_etr = n_r*Aa_e/(b*a_e) = 4*50,26*100/(400*200) = 0,25 %

=> p_etr = 0,25 % > p_etr^min = 0,15%

- stabilirea zonelor disipative

l_p = max(600 mm; H/6 = 516,6 mm; b = 400 mm) = 600 mm