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Calculul stalpilor

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Calculul stalpilor

1.Calculul la incovoiere (Ncalcul, Mcalcul)




a. Ncalcul = Ngld ± Nseism

Nld = Nacld + Nplld + Ngrld + Nprld + Nstld

stalp central etaj :

Ngrld = bgrtr*(hgrtr – hpl)*(L+l/2 – 0,4)*γb + bgrlg*(hgrlg – hpl)*[(t1 +t2)/2 – 0,4]*γb

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

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

Nacld = Aaf*qacld = 22,18*7,58 = 168,12 kN

Nstld= bst*hst*(H-hpl)* γb=0,4*0,4(3,1-0,14)*25=11,84 kN

Nscld E = Nacld + Ngrld + Nstld =17,95+168,12+11,84 = 178,23 kN

Nseism = V1as =[(Mcap- + Mcap+)gr/l0]AB- [(Mcap- + Mcap+)gr/l0]BC

Nseism =(78,71+47,44)/4,4 -(78,71+47,44)/5=3,44 kN

N1calcul = Nld + Nseism = 178,23     + 3,44 = 201,35 kN

N2calcul = Nld - Nseism = 178,23     - 3,44 = 194,47 kN

- stalp central parter

Nplld = Aaf*qplld = 22,18*6,64 = 147,27 kN

Nsmld = Nscld E + Nplld + Ngrld + Nstld = 197,91+147,27+17,97+11,84

= 374,99 kN

Nseism = V1as =[(Mcap- + Mcap+)gr/l0]AB- [(Mcap- + Mcap+)gr/l0]BC

Nseism =(55,83+99,16)/4,4 -(55,83+99,16)/5=4,22 kN

N1calcul = Nld + Nseism = 374,99 + 3,44 + 4,22 = 382,65 kN

N2calcul = Nld - Nseism = 374,99 - 3,44 – 4,22 = 367,323 kN

stalp marginal (2;A) etaj :

Ngrld = bgrtr*(hgrtr – hpl)*(L/2 – 0,4)*γb + bgrlg*(hgrlg – hpl)*[(t1 +t2)/2 – 0,4]*γb

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

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

Nacld = Aaf*qacld = 10,44*7,17 = 79,13 kN

Nstld= bst*hst*(H-hpl)* γb=0,4*0,4(3,1-0,14)*25=11,84 kN

Natic =l*h*b*γp=0,5*0,375*18,5*4,35=15,08 kN

Nscld E = Nacld + Ngrld + Nstld + Natic =12,64+79,13+11,84+15,38 = 116,49 kN

Nseism = V1as =(Mcap- + Mcap+)gr/l0

Nseism =(78,71+47,44)/4,1 =30,76 kN

N1calcul = Nld - Nseism = 178,23     - 30,76 = 85,73 kN

N2calcul = Nld + Nseism = 178,23     + 30,76 = 147,25 kN

- stalp marginal (2;A) parter

Nplld = Aaf*qplld = 10,44*5,24 = 54,7 kN

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

Nsmld = Nscld E + Nplld + Ngrld + Nstld + Nperete= 116,49+54,7+12,64+11,84+78,67

= 277,34 kN

Nseism = V1as =(Mcap- + Mcap+)gr/l0

Nseism =(55,83+99,16)/4,1 =37,8 kN

N1calcul = Nld - Nseism = 277,34 - 30,76 - 37,8 = 208,78 kN

N2calcul = Nld + Nseism = 277,34 + 30,76 + 37,8 = 345,9 kN

stalp colt (1;C) etaj :

Ngrld = bgrtr*(hgrtr – hpl)*(L/2 – 0,4)*γb + bgrlg*(hgrlg – hpl)*(t1 /2 – 0,4)*γb

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

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

Nacld = Aaf*qacld = 4,25*7,58 = 32,21 kN

Nstld= bst*hst*(H-hpl)* γb=0,4*0,4(3,1-0,14)*25=11,84 kN

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

Nscld E = Nacld + Ngrld + Nstld + Natic =32,21+9,03+11,84+14,74 = 67,81 kN

Nseism = V1as =(Mcap- + Mcap+)gr/l0

Nseism =(78,89+31,56)/4,1 =26,94 kN

N1calcul = Nld - Nseism = 67,81 - 26,94 = 40,87 kN

N2calcul = Nld + Nseism = 67,81     + 26,94 = 94,75 kN

- stalp colt (1;C) parter

Nplld = Aaf*qplld = 4,25* 4,25 = 22,27 kN

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

Nsmld = Nscld E + Nplld + Ngrld + Nstld + Nperete = 67,81+22,27+9,03+11,84

= 187,61 kN

Nseism = V1as =(Mcap- + Mcap+)gr/l0

Nseism =(106,89+55,57)/4,1 =39,62 kN

N1calcul = Nld - Nseism = 187,61 - 26,94 - 39,62 = 121,05 kN

N2calcul = Nld + Nseism = 187,61 + 26,94 + 39,62 = 254,17 kN

b. Mcalcul = km*ω*Ms

km = 1;1,4

= (Σ Mcap)gr/(Σ Mef)gr > 1

stalp central cadru transversal-etaj

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

Mcalcul = 1,4*1,26*29,73 = 52,44 kNm

stalp central cadru transversal-parter

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

Mcalcul = 1*1,26*78,213 = 98,55 kNm

stalp marginal –etaj

- cadru transversal

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

M1calcul = 1,4*1,26*0,762 = 1,34 kNm

M2calcul = 1,4*1,26*70,351 = 124,09 kNm

- cadru longitudinal

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

M1calcul = 1,4*1,15*51,038 = 82,17 kNm

M2calcul = 1,4*1,15*39,622 = 63,79 kNm

stalp marginal –parter

- cadru transversal

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

M1calcul = 1*1,26*70,49 = 88,81 kNm

M2calcul = 1*1,26*99,727 = 125,65 kNm

- cadru longitudinal

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

M1calcul = 1*1,15*87,769 = 100,9 kNm

M2calcul = 1*1,15*83,36 = 95,86 kNm

stalp colt cadru longitudinal –etaj



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

M1calcul = 1,4*1,15*65,933 = 75,82 kNm

M2calcul = 1,4*1,15*87,447 = 100,56 kNm

a. stalp central cadru transversal -etaj

2.Dimensionarea armaturii

Ncalcul = 201,35 kN

Mcalcul = 52,44 kNm

(1) Ncalcul = b*x*Rc’

(2) Mcalcul + Ncalcul*ha/2 = b*x* Rc’*(ha – x/2) + Aa*Ra*ha pentru x > 2*a’

(3) Mcalcul – Ncalcul*ha/2 = Aa*Ra*ha pentru x ≤ 2*a’

Rc’ = 0,85*Rc = 0,85*12,5 = 10,63 N/mm2

(1) => x = Ncalcul/( b*Rc’) = 52440/(400*10,63) = 47,35 mm

a’ = c + ф/2 = 25 + 16/2 = 33 mm

ha = h – 2*a’ = 400-66 = 334 mm

x =47,35 < 2*a’ = 66 mm

(3) => Aanec = (Mcalcul – Ncalcul*ha/2)/( Ra*ha) = (52,44*106 – 201,35*103*334/2)/(300*334)=187,76 mm2

aleg Aaef = 3 ф 12 = 339,29 mm2

pmin = 0,2 % (pentru o latura)

p = Aaef*100/(b*h0) = 339,29*100/(400*369) = 0,22 % < pmin = 0,2 %

pmintot = 0,8 %

ptot = Aatot*100/(b*h0) = 8*113,09*100/(400*369) = 0,61 < pmintot = 0,8 %

aleg Aaef = 4 ф 12 = 452,41 mm2

pmin = 0,2 % (pentru o latura)

p = Aaef*100/(b*h0) = 452,41*100/(400*369) = 0,30 % > pmin = 0,2 %

pmintot = 0,8 %

ptot = Aatot*100/(b*h0) = 1357,08*100/(400*369) = 0,91 > pmintot = 0,8 %

3. Verificare a stalp central-etaj

x = 47,35 mm

a’ = c + ф/2 = 25 + 12/2 = 31 mm

ha = h – 2*a’ = 338 mm

(3) Mcap = Ncalcul*ha/2 + Aaef*Ra*ha = 201,35*103*338/2 + 452,41*300*338

Mcap =79,32 kNm

Mcap = 79,32 kNm > Mcalcul = 52,44 kNm

4.Calculul la forta taietoare si armarea la forta taietoare

a.       Calculul la forta taietoare

Tcalcul = kT*ω*Ts

kT = 1,2

Ts = (Mi + Ms)/H = (29,733+52,282)/3,1 = 26,45 kN

Tsccalcul = 1,2*1,26*26,45 = 40 kN

b. Dimensionarea armaturii

Tcalcul = Tcalcul/(b*h0*Rt’)

Rt’ = 0,85* Rt' = 0,85*0,95 = 0,81 N/mm2

Tsmcalcul = 40*103/(400*367*0,81) = 0,33 <Tmin = 0,5=> armare constructiva

-Zona disipativa

aed = 100 mm

-Zona disipativa

aed = 200 mm

- stabilirea zonelor disipative

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

b. stalp central cadru transversal -parter

2.Dimensionarea armaturii

Ncalcul = 382,65 kN

Mcalcul = 98,55 kNm

(1) Ncalcul = b*x*Rc’

(2) Mcalcul + Ncalcul*ha/2 = b*x* Rc’*(ha – x/2) + Aa*Ra*ha pentru x > 2*a’

(3) Mcalcul – Ncalcul*ha/2 = Aa*Ra*ha pentru x ≤ 2*a’

Rc’ = 0,85*Rc = 0,85*12,5 = 10,63 N/mm2

(1) => x = Ncalcul/( b*Rc’) = 382650/(400*10,63) = 89,99 mm

a’ = c + ф/2 = 25 + 16/2 = 33 mm

ha = h – 2*a’ = 400-66 = 334 mm

x =89,99 > 2*a’ = 66 mm

(2) => Aanec = (Mcalcul + Ncalcul*ha/2 - b*x* Rc’*(ha – x/2))/( Ra*ha) =

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

aleg Aaef = 4 ф 14 = 615,75 mm2

pmin = 0,2 % (pentru o latura)

p = Aaef*100/(b*h0) = 615,75*100/(400*367) = 0,41 % > pmin = 0,2 %

pmintot = 0,8 %

ptot = Aatot*100/(b*h0) = 12*153,93*100/(400*367) = 0.98 > pmintot = 0,8 %

3. Verificare a stalp central-parter

x = 89,99 mm

a’ = c + ф/2 = 25 + 14/2 = 33 mm

ha = h – 2*a’ = 334 mm

(2) Mcap = b*x* Rc’*(ha – x/2) + Aa*Ra*ha - Ncalcul*ha/2 = 400*10,63*89,99(344-89,99/2)-382,65*103*334/2 + 615,75*300*338

Mcap =108,37 kNm

Mcap = 108,37 kNm > Mcalcul = 98,55 kNm

4.Calculul la forta taietoare si armarea la forta taietoare

a.Calculul la forta taietoare

Tcalcul = kT*ω*Ts

kT = 1,2

Ts = (Mi + Ms)/H = (78,213+51,62)/3,1 = 41,88 kN

Ms= (Mcap inf/ Mef inf )* Mcap sup =(108,37/98,55)*44,569=51,62

Tsccalcul = 1,2*1,26*41,88 = 63,32 kN

b. Dimensionarea armaturii

Tcalcul = Tcalcul/(b*h0*Rt’)

Rt’ = 0,85* Rt' = 0,85*0,95 = 0,81 N/mm2

Tsmcalcul = 63,32*103/(400*367*0,81) = 0,52 >Tmin = 0,5=> armare din calcul

qenec,sm=T2/(4*b*h02*mt* Rt’*p1/2)= 63,322*106/(4*400*3362*1,11*0,81*0,67)

= 36,84 N/mm

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

n = Ncalcul/(b*h0* Rt’) = 374/(400*338*10,63) = 0.22

Aaeef = Aaemin = 8f =50,26 mm2

aenec = nr*Aae*Rae/qenec,sc = 4*50,26*(0,8*210)/36,84 = 900mm

-Zona disipativa

ac= -<8f =96 mm

->100

-<h/5=80

=> din conditii constructive aed = 100 mm in zona disipativa

petr = nr*Aae/(b*ae) = 4*50,26*100/(400*100) = 0,50 %

petrmin = 10*Rc’*(0,4 + n)/Ra = 10*10,36*(0,4+0,22)/210 = 0,22 %

=> petr = 0,50 % > petrmin = 0.22%

-Zona nedisipativa

ac= -< 200 mm

-<15f =5*14=210 mm

=> din conditii constructive aed = 200 mm in zona disipativa

petr = nr*Aae/(b*ae) = 4*50,26*100/(400*200) = 0,25 %

=> petr = 0,25 % > petrmin = 0,15%

- stabilirea zonelor disipative

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

c. stalp marginal -etaj

2.Dimensionarea armaturii

- directie transversala

-varianta 1:

Ncalcul = 85,73 kN

Mcalcul = 1,34 kNm è armare minima

-varianta 2:

Ncalcul = 147,25 kN

Mcalcul = 124,09 kNm

(1) Ncalcul = b*x*Rc’

(2) Mcalcul + Ncalcul*ha/2 = b*x* Rc’*(ha – x/2) + Aa*Ra*ha pentru x > 2*a’

(3) Mcalcul – Ncalcul*ha/2 = Aa*Ra*ha pentru x ≤ 2*a’

Rc’ = 0,85*Rc = 0,85*12,5 = 10,63 N/mm2

(1) => x = Ncalcul/( b*Rc’) = 147250/(400*10,63) = 34,63 mm

a’ = c + ф/2 = 25 + 16/2 = 33 mm

ha = h – 2*a’ = 400-66 = 334 mm

x =34,63 < 2*a’ = 66 mm

(3) => Aanec = (Mcalcul – Ncalcul*ha/2)/( Ra*ha) = (124,09*106 – 147,25*103*334/2)/(300*334)=933 mm2

aleg Aaef = 4 ф 18 = 1017,87 mm2

pmin = 0,2 % (pentru o latura)

p = Aaef*100/(b*h0) = 1017,87*100/(400*366) = 0,69 % > pmin = 0,2 %

- directie longitudinala

-varianta 1:

Ncalcul = 118,91 kN

Mcalcul = 82,17 kNm

(1) Ncalcul = b*x*Rc’

(2) Mcalcul + Ncalcul*ha/2 = b*x* Rc’*(ha – x/2) + Aa*Ra*ha pentru x > 2*a’



(3) Mcalcul – Ncalcul*ha/2 = Aa*Ra*ha pentru x ≤ 2*a’

Rc’ = 0,85*Rc = 0,85*12,5 = 10,63 N/mm2

(1) => x = Ncalcul/( b*Rc’) = 118910/(400*10,63) = 27,96 mm

a’ = c + ф/2 = 25 + 16/2 = 33 mm

ha = h – 2*a’ = 400-66 = 334 mm

x =27,96 < 2*a’ = 66 mm

(3) => Aanec = (Mcalcul – Ncalcul*ha/2)/( Ra*ha) = (81,17*106 – 118,91*103*334/2)/(300*334)=611,89 mm2

-varianta 2:

Ncalcul = 114,07 kN

Mcalcul = 63,79 kNm

(1) => x = Ncalcul/( b*Rc’) = 114070/(400*10,63) = 26,82 mm

a’ = c + ф/2 = 25 + 16/2 = 33 mm

ha = h – 2*a’ = 400-66 = 334 mm

x =26,82 < 2*a’ = 66 mm

(3) => Aanec = (Mcalcul – Ncalcul*ha/2)/( Ra*ha) = (63,79*106 – 114,07*103*334/2)/(300*334)=446,51 mm2

è varianta 1 Aanec = 611,89 mm2

aleg Aaef = 2 ф 12 +2 ф 18 = 226,19+ 508,93 = 735,12 mm2

pmin = 0,2 % (pentru o latura)

p = Aaef*100/(b*h0) = 735,12*100/(400*366) = 0,50 % > pmin = 0,2 %

pmintot = 0,8 %

ptot = Aatot*100/(b*h0) =(4 ф 12 +8 ф 18 ) *100/(400*366) = 1,69 > pmintot = 0,8 %

3. Verificare a stalp marginal-etaj

- directie transversala

x = 34,63 mm

a’ = c + ф/2 = 25 + 18/2 = 34 mm

ha = h – 2*a’ = 332 mm

(3) Mcap = Ncalcul*ha/2 + Aaef*Ra*ha = 1147250*332/2 + 1017,87*300*332

= 126,20 kNm

Mcap = 126,20 kNm > Mcalcul = 124,09 kNm

- directie transversala

x = 27,96 mm

a’ = c + ф/2 = 25 + 18/2 = 34 mm

ha = h – 2*a’ = 332 mm

(3) Mcap = Ncalcul*ha/2 + Aaef*Ra*ha = 114070*332/2 + 735,12*300*332

= 92,43 kNm

Mcap = 92,43 kNm > Mcalcul = 82,17 kNm

4.Calculul la forta taietoare si armarea la forta taietoare

a.       Calculul la forta taietoare

Tcalcul = kT*ω*Ts

kT = 1,2

Ts = (Mi + Ms)/H = (87,447+45,616)/3,1 = 42,92 kN

Tsccalcul = 1,2*1,15*42,92 = 59,22 kN

b. Dimensionarea armaturii

Tcalcul = Tcalcul/(b*h0*Rt’)

Rt’ = 0,85* Rt' = 0,85*0,95 = 0,81 N/mm2

Tsmcalcul = 59,22*103/(400*367*0,81) = 0,498 >Tmin = 0,5=> armare constructiva

-Zona disipativa

aed = 100 mm

-Zona disipativa

aed = 200 mm

- stabilirea zonelor disipative

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

d. stalp marginal -parter

2.Dimensionarea armaturii

- directie transversala

-varianta 1:

Ncalcul = 208,78 kN

Mcalcul = 88,81 kNm

(1) Ncalcul = b*x*Rc’

(2) Mcalcul + Ncalcul*ha/2 = b*x* Rc’*(ha – x/2) + Aa*Ra*ha pentru x > 2*a’

(3) Mcalcul – Ncalcul*ha/2 = Aa*Ra*ha pentru x ≤ 2*a’

Rc’ = 0,85*Rc = 0,85*12,5 = 10,63 N/mm2

(1) => x = Ncalcul/( b*Rc’) = 208780/(400*10,63) = 49,10 mm

a’ = c + ф/2 = 25 + 16/2 = 33 mm

ha = h – 2*a’ = 400-66 = 334 mm

x =49,10 < 2*a’ = 66 mm

(3) => Aanec = (Mcalcul – Ncalcul*ha/2)/( Ra*ha) = (88,81*106 – 1208,78*103*334/2)/(300*334)=468,5 mm2

-varianta 2:

Ncalcul = 282,87 kN

Mcalcul = 100,9 kNm

(1) => x = Ncalcul/( b*Rc’) = 345900/(400*10,63) = 81,34 mm

a’ = c + ф/2 = 25 + 16/2 = 33 mm

ha = h – 2*a’ = 400-66 = 334 mm

x =81,34 < 2*a’ = 66 mm

(2) => Aanec = (Mcalcul + Ncalcul*ha/2 - b*x* Rc’*(ha – x/2))/( Ra*ha) =

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

aleg Aaef = 4 ф 18 = 1017,87 mm2

pmin = 0,2 % (pentru o latura)

p = Aaef*100/(b*h0) = 1017,87*100/(400*366) = 0,69 % > pmin = 0,2 %

- directie longitudinala

-varianta 1:

Ncalcul = 282,87 kN

Mcalcul = 100,9 kNm

(1) Ncalcul = b*x*Rc’

(2) Mcalcul + Ncalcul*ha/2 = b*x* Rc’*(ha – x/2) + Aa*Ra*ha pentru x > 2*a’

(3) Mcalcul – Ncalcul*ha/2 = Aa*Ra*ha pentru x ≤ 2*a’

Rc’ = 0,85*Rc = 0,85*12,5 = 10,63 N/mm2

(1) => x = Ncalcul/( b*Rc’) = 282870/(400*10,63) = 66,5 mm

a’ = c + ф/2 = 25 + 16/2 = 33 mm

ha = h – 2*a’ = 400-66 = 334 mm

x =66,5 > 2*a’ = 66 mm

(2) => Aanec = (Mcalcul + Ncalcul*ha/2 - b*x* Rc’*(ha – x/2))/( Ra*ha) =

=629,73 mm2

-varianta 2:

Ncalcul = 271,81 kN

Mcalcul = 95,86 kNm

(1) => x = Ncalcul/( b*Rc’) = 271,81/(400*10,63) = 63 mm

a’ = c + ф/2 = 25 + 16/2 = 33 mm

ha = h – 2*a’ = 400-66 = 334 mm

x =63 < 2*a’ = 66 mm

(3) => Aanec = (Mcalcul – Ncalcul*ha/2)/( Ra*ha) = (95,86*106 – 271,81*103*334/2)/(300*334)=503,66 mm2

è varianta 1 Aanec = 611,89 mm2

aleg Aaef = 2 ф 12 +2 ф 18 = 226,19+ 508,93 = 735,12 mm2

pmin = 0,2 % (pentru o latura)

p = Aaef*100/(b*h0) = 735,12*100/(400*366) = 0,50 % > pmin = 0,2 %

pmintot = 0,8 %

ptot = Aatot*100/(b*h0) =(4 ф 12 +8 ф 18 ) *100/(400*366) = 1,69 > pmintot = 0,8 %

3. Verificare a stalp marginal-parter

- directie transversala

x = 81,34 mm

a’ = c + ф/2 = 25 + 18/2 = 34 mm

ha = h – 2*a’ = 332 mm

(2) Mcap = b*x* Rc’*(ha – x/2) + Aa*Ra*ha - Ncalcul*ha/2 = 400*10,63*81,34(344-81,34/2)-345,9*103*334/2 + 1017,87*300*338

Mcap = 144,71 kNm > Mcalcul = 124,09 kNm

- directie transversala

x = 66,5 mm

a’ = c + ф/2 = 25 + 18/2 = 34 mm

ha = h – 2*a’ = 332 mm

(3) Mcap = Ncalcul*ha/2 + Aaef*Ra*ha = 282870*332/2 + 735,12*300*332

= 120,53 kNm

Mcap = 120,53 kNm > Mcalcul = 95,96 kNm

4.Calculul la forta taietoare si armarea la forta taietoare

b.      Calculul la forta taietoare

Tcalcul = kT*ω*Ts

kT = 1,2

Ts = (Mi + Ms)/H = (99,727+101,92)/3,1 = 65,04 kN

Ms= (Mcap inf/ Mef inf )* Mcap sup =(144,71/125,65)*44,569=101,92

Tsccalcul = 1,2*1,26*65,04 = 98,35 kN

b. Dimensionarea armaturii

Tcalcul = Tcalcul/(b*h0*Rt’)

Rt’ = 0,85* Rt' = 0,85*0,95 = 0,81 N/mm2

Tsmcalcul = 98,35*103/(400*367*0,81) = 0,82 >Tmin = 0,5=> armare din calcul

qenec,sm=T2/(4*b*h02*mt* Rt’*p1/2)= 98,352*106/(4*400*3362*1,11*0,81*0,67)

= 70,11 N/mm

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

n = Ncalcul/(b*h0* Rt’) = 345,9/(400*366*10,63) = 0.22

Aaeef = Aaemin = 8f =50,26 mm2

aenec = nr*Aae*Rae/qenec,sc = 4*50,26*(0,8*210)/70,11 = 475mm

-Zona disipativa

ac= -<8f =96 mm

->100

-<h/5=80



=> din conditii constructive aed = 100 mm in zona disipativa

petr = nr*Aae/(b*ae) = 4*50,26*100/(400*100) = 0,50 %

petrmin = 10*Rc’*(0,4 + n)/Ra = 10*10,36*(0,4+0,22)/210 = 0,22 %

=> petr = 0,50 % > petrmin = 0.22%

-Zona nedisipativa

ac= -< 200 mm

-<15f =5*14=210 mm

=> din conditii constructive aed = 200 mm in zona disipativa

petr = nr*Aae/(b*ae) = 4*50,26*100/(400*200) = 0,25 %

=> petr = 0,25 % > petrmin = 0,15%

- stabilirea zonelor disipative

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

e. stalp colt directie longitudinala -etaj

2.Dimensionarea armaturii

-varianta 1:

Ncalcul = 40,87 kN

Mcalcul = 8,52 kNm è armare minima

-varianta 2:

Ncalcul = 94,57 kN

Mcalcul = 73,44 kNm

(1) Ncalcul = b*x*Rc’

(2) Mcalcul + Ncalcul*ha/2 = b*x* Rc’*(ha – x/2) + Aa*Ra*ha pentru x > 2*a’

(3) Mcalcul – Ncalcul*ha/2 = Aa*Ra*ha pentru x ≤ 2*a’

Rc’ = 0,85*Rc = 0,85*12,5 = 10,63 N/mm2

(1) => x = Ncalcul/( b*Rc’) = 94750/(400*10,63) = 22,28 mm

a’ = c + ф/2 = 25 + 16/2 = 33 mm

ha = h – 2*a’ = 400-66 = 334 mm

x =22,28 < 2*a’ = 66 mm

(3) => Aanec = (Mcalcul – Ncalcul*ha/2)/( Ra*ha) = (73,44*106 – 94,75*103*334/2)/(300*334)= 575,01 mm2

aleg Aaef = 4 ф 14 = 615,75 mm2

pmin = 0,2 % (pentru o latura)

p = Aaef*100/(b*h0) = 615,75*100/(400*367) = 0,41 % > pmin = 0,2 %

pmintot = 0,8 %

ptot = Aatot*100/(b*h0) =(12 ф 14 ) *100/(400*367) = 1,25 > pmintot = 0,8 %

3. Verificare a stalp colt-etaj

- directie transversala

x = 22,28 mm

a’ = c + ф/2 = 25 + 18/2 = 34 mm

ha = h – 2*a’ = 332 mm

(3) Mcap = Ncalcul*ha/2 + Aaef*Ra*ha = 94750*332/2 + 615,75*300*332

= 77,75 kNm

Mcap = 77,75 kNm > Mcalcul = 73,44 kNm

4.Calculul la forta taietoare si armarea la forta taietoare

a.       Calculul la forta taietoare

Tcalcul = kT*ω*Ts

kT = 1,2

Ts = (Mi + Ms)/H = (53,616+45,616)/3,1 = 32,01 kN

Tsccalcul = 1,2*1,15*32,01 = 44,17 kN

b. Dimensionarea armaturii

Tcalcul = Tcalcul/(b*h0*Rt’)

Rt’ = 0,85* Rt' = 0,85*0,95 = 0,81 N/mm2

Tsmcalcul = 44,17*103/(400*367*0,81) = 0,37 <Tmin = 0,5=> armare constructiva

-Zona disipativa

aed = 100 mm

-Zona disipativa

aed = 200 mm

- stabilirea zonelor disipative

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

e. stalp colt directie longitudinala -parter

2.Dimensionarea armaturii

-varianta 1:

Ncalcul = 121,05 kN

Mcalcul = 75,82 kNm

-varianta 2:

Ncalcul = 254,17 kN

Mcalcul = 100,56 kNm

(1) Ncalcul = b*x*Rc’

(2) Mcalcul + Ncalcul*ha/2 = b*x* Rc’*(ha – x/2) + Aa*Ra*ha pentru x > 2*a’

(3) Mcalcul – Ncalcul*ha/2 = Aa*Ra*ha pentru x ≤ 2*a’

Rc’ = 0,85*Rc = 0,85*12,5 = 10,63 N/mm2

(1) => x = Ncalcul/( b*Rc’) = 121050/(400*10,63) = 28,46 mm

a’ = c + ф/2 = 25 + 16/2 = 33 mm

ha = h – 2*a’ = 400-66 = 334 mm

x =28,46 < 2*a’ = 66 mm

(3) => Aanec = (Mcalcul – Ncalcul*ha/2)/( Ra*ha) = (75,82*106 – 121,05*103*334/2)/(300*334)= 554,93 mm2

-varianta 2:

Ncalcul = 254,17 kN

Mcalcul = 100,56 kNm

(1) Ncalcul = b*x*Rc’

(2) Mcalcul + Ncalcul*ha/2 = b*x* Rc’*(ha – x/2) + Aa*Ra*ha pentru x > 2*a’

(3) Mcalcul – Ncalcul*ha/2 = Aa*Ra*ha pentru x ≤ 2*a’

Rc’ = 0,85*Rc = 0,85*12,5 = 10,63 N/mm2

(1) => x = Ncalcul/( b*Rc’) = 254,17/(400*10,63) = 59,8 mm

a’ = c + ф/2 = 25 + 16/2 = 33 mm

ha = h – 2*a’ = 400-66 = 334 mm

x =59,8 < 2*a’ = 66 mm

(3) => Aanec = (Mcalcul – Ncalcul*ha/2)/( Ra*ha) = (100,56*106 – 254,17*103*334/2)/(300*334)= 579,97 mm2

aleg Aaef = 4 ф 14 = 615,75 mm2

pmin = 0,2 % (pentru o latura)

p = Aaef*100/(b*h0) = 615,75*100/(400*367) = 0,41 % > pmin = 0,2 %

pmintot = 0,8 %

ptot = Aatot*100/(b*h0) =(12 ф 14 ) *100/(400*367) = 1,25 > pmintot = 0,8 %

3. Verificare a stalp colt-etaj

- directie transversala

x = 59,8 mm

a’ = c + ф/2 = 25 + 14/2 = 33 mm

ha = h – 2*a’ = 336 mm

(3) Mcap = Ncalcul*ha/2 + Aaef*Ra*ha = 254170*336/2 + 615,75*300*336

= 104,76 kNm

Mcap = 104,76 kNm > Mcalcul = 100,56 kNm

4.Calculul la forta taietoare si armarea la forta taietoare

b.      Calculul la forta taietoare

Tcalcul = kT*ω*Ts

kT = 1,2

Ts = (Mi + Ms)/H = (87,447+70,8)/3,1 = 51,04 kN

Tsccalcul = 1,2*1,15*51,04 = 70,44 kN

b. Dimensionarea armaturii

Tcalcul = Tcalcul/(b*h0*Rt’)

Rt’ = 0,85* Rt' = 0,85*0,95 = 0,81 N/mm2

Tsmcalcul = 70,44*103/(400*367*0,81) = 0,62 >Tmin = 0,5=> armare din calcul

qenec,sm=T2/(4*b*h02*mt* Rt’*p1/2)= 70,442*106/(4*400*3362*1,08*0,81*0,67)

= 47,34 N/mm

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

n = Ncalcul/(b*h0* Rt’) = 254,18/(400*366*10,63) = 0.16

Aaeef = Aaemin = 8f =50,26 mm2

aenec = nr*Aae*Rae/qenec,sc = 4*50,26*(0,8*210)/47,34 = 700mm

-Zona disipativa

ac= -<8f =96 mm

->100

-<h/5=80

=> din conditii constructive aed = 100 mm in zona disipativa

petr = nr*Aae/(b*ae) = 4*50,26*100/(400*100) = 0,50 %

petrmin = 10*Rc’*(0,4 + n)/Ra = 10*10,36*(0,4+0,16)/210 = 0,09 %

=> petr = 0,50 % > petrmin = 0.09%

-Zona nedisipativa

ac= -< 200 mm

-<15f =5*14=210 mm

=> din conditii constructive aed = 200 mm in zona disipativa

petr = nr*Aae/(b*ae) = 4*50,26*100/(400*200) = 0,25 %

=> petr = 0,25 % > petrmin = 0,15%

- stabilirea zonelor disipative

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



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