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UNIVERSIDAD CENTRAL DEL ECUADOR
FACULTAD DE INGENIERIA, CIENCIAS FISICAS Y MATEMÁTICA
ESCUELA DE INGENIERIA CIVIL
HORMIGON ARMADO III
DEBER Nº2
TEMA: CÁLCULO DEL LOS PUNTOS NOTABLES DEL DIAGRAMA DE ITERACCION
NOMBRE: Orozco Ronquillo Franklin Danilo.
SEMESTRE: Séptimo PARALELO: Primero.
Fecha: 16/11/09

Ast=12ϕ20mm
f'c=280kg/cm2
fy=4200kg/cm2
θ=360ºN.VARILLAθ=36012=30º
r=h2-6.25 r=40-6.25 r=33.75cm
s3=rcos2θ=33.75*cos60º s3=17cm=s4
(s2+s3)=rcosθ=33.75*cos30º (s2+s3)=29.228cm
s2=29.228-16.875 s2=12.445cm=s5
s1+s2+s3=r
s1=r-s2+s3=33.75-29.228
s1=4.55cm=s6

1.- CÁLCULO DE Po
Po=0.85*f'c*Ag+Ast*fyPo=0.85*280*46.188+92.3762*80*2+37.70*4200-π*20²4
Po=2796284.4 kg

2.- PARA C = 240 cm

x1=0
x2=s1=4.522cm
x3=s1+s2=16.875cm
x4=s1+s2+s3=33.750cm
x5=s1+s2+s3+s4=50.625cm
x6=s1+s2+s3+s4+s5=62.978cm
x7=s1+s2+s3+s4+s5+s6=67.500cm

εsi=cte*yi
εsi=cte*xi ; cte=εcuc=0.00373.75

εs1=cte*x1=cte*0=0
εs2=cte*x2=cte*4.522=0.00018mmmm
εs3=cte*x3=cte*16.875=0.00069mmmm
εs4=cte*x4=cte*33.750=0.00137mmmmεs5=cte*x5=cte*50.625=0.00206mmmm
εs6=cte*x6=cte*62.978=0.00256mmmm
εs7=cte*x7=cte*67.50=0.00275mmmm

CALCULO DE ESFUERZOS:

Refuerzos:
εy=fyES=42002.1x106

εy=0.002mmmm
εsi Vs εyi
εs1<εyZ.Efs1=Es*εs1=2.1x106*0fs1=0kgcm2
εs2<εyZ.Efs2=Es*εs2=2.1x106*0.00018fs2=378kgcm2
εs3<εyZ.Efs3=Es*εs3=2.1x106*0.00069fs3=1449kgcm2
εs4<εyZ.Efs4=Es*εs4=2.1x106*0.00137fs4=2877kgcm2εs5>εyZ.Pfs5=fyfs5=4200kgcm2
εs6>εyZ.Pfs6=fyfs6=4200kgcm2
εs7>εyZ.Pfs7=fyfs7=4200kgcm2
Hormigón:
σ=0.85*f'c=0.85*280→σ=238kgcm2
a=β1*c ; f'c=280kgcm2→ β1=0.85
a=0.85*73.75
a=62.688cm

Diagrama de Esfuerzos:

RESULTANTES:

Refuerzos:
Rsi=Asi*fsi
Rs1=As1*fs1=1*4.91*0→Rs1=0kg
Rs2=As2*fs2=2*4.91*378→Rs2=3711.96kg
Rs3=As3*fs3=2*4.91*1449→Rs3=14229.18kgRs4=As4*fs4=2*4.91*2877→Rs4=28252.14kg
Rs5=As5*fs5=2*4.91*4200→Rs5=41244.00kg
Rs6=As6*fs6=2*4.91*4200→Rs6=41244.00kg
Rs7=As7*fs7=1*4.91*4200→Rs7=20622kg

Hormigón:
cc=0.85f'c*AEHC

A1=22.688*9.3972=106.600cm2
A2=22.688*2.319=52.613cm2
A3=28.284*11.7162=165.688cm2
A4=22.688*28.284=641.707cm2
A5=28.284*28.284=799.985cm2
A6=11.716*282842=165.688cm2
A=1932.281cm2
AT=3864.562cm2

ACIR.=πR2
ACIR.=π152=706.858cm2AEHC=AT-ACIR

AEHC=3864.562-706.858
AEHC=3157.704cm2

CC=0.85f'c*AEHC
CC=0.85*280*3157.704
CC=0.85*280*3157.704
CC=751533.552kg

DIAGRAMA DE FUERZAS INTERNAS - EXTERNAS:

Fy=0 ↑
RS2+RS3+RS4+RS5+RS6+RS7+CC-Pn=0
Pn=RS2+RS3+RS4+RS5+RS6+RS7+CC
Pn=3711.96+14229.18+28252.14+41244.00+41244.00+20622+751533.552
Pn=880214.732kg=880.215Ton

Z1=Z7=33.750cm
Z2=Z6=29.228cm
Z3=Z5=19.875cm
Z4=0MCL=0(←)
-RS1*z1-RS2*z2-RS3*z3+RS5*z5+RS6*z6+RS7*z7+CC*zc-Pn*ex=0
ex=-RS1*z1-RS2*z2-RS3*z3+RS5*z5+RS6*z6+RS7*z7+CC*zcPn
ex=-3711.96*29.228-14229.18*19.875+41244.00*19.875+41244.00*29.228+20622*33.750+751533.552*8.656880214.732

Pn*ex=Mn=8835172.939kg.cm=88.35Ton.m

ex=10.038cm=0.10038m

3.- PARA C = h = 80cm

x1=8.750cm
x2=4.228cm
x3=8.125cm
x4=25.00cm
x5=41.875cm
x6=54.228cmx7=58.750cm

εsi=cte*yi
εsi=cte*xi ; cte=εcuc=0.00365

εs1=cte*x1=cte*8.750=0.00040 mm/mm
εs2=cte*x2=cte*4.228=0.00020mmmm
εs3=cte*x3=cte*8.125=0.00038mmmm
εs4=cte*x4=cte*25.00=0.00115mmmm
εs5=cte*x5=cte*41.875=0.00193mmmm
εs6=cte*x6=cte*54.228=0.00250mmmm
εs7=cte*x7=cte*58.750=0.00271mmmm

CALCULO DE ESFUERZOS:

Refuerzos:
εy=fyES=42002.1x106

εy=0.002mmmm
εsi Vs εyiεs1<εyZ.Efs1=Es*εs1=2.1x106*0.00040fs1=840kgcm2
εs2<εyZ.Efs2=Es*εs2=2.1x106*0.00020fs2=420kgcm2
εs3<εyZ.Efs3=Es*εs3=2.1x106*0.00038fs3=798kgcm2
εs4<εyZ.Efs4=Es*εs4=2.1x106*0.00115fs4=2415kgcm2
εs5<εyZ.Efs5=ES*fS5=2.1X106*0.00193fs5=4053kgcm2
εs6>εyZ.Pfs6=fyfs6=4200kgcm2
εs7>εyZ.Pfs7=fyfs7=4200kgcm2

Hormigón:
σ=0.85*f'c=0.85*280→σ=238kgcm2
a=β1*c ; f'c=280kgcm2→...
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