Tuberias

Problema 2
f'c=210 kgcm2
fy=2800 kgcm2
An°9=6.45 cm2
d=h-rec-∅est-∅var=45 cm-4 cm-0.95 cm-2.87 cm=37.18 cm
S= b-2rec-2∅est-3∅var2=25 cm-24 cm-20.95 cm-32.87 cm2=3.25 cm
3.25 >2.5 ok
Cc=Ts
0.85f'cab=fyAs
0.85210 kgcm2a25 cm= 2800 kgcm238.70 cm2
4462.5a=108360
a=24.28 cm
c=a0.85=24.28 cm0.85=28.57 cm
εs= εcu(d-c)c= 0.003(37.18 cm-28.57 cm)28.57 cm=0.0009041
0.0009041<εy
Cc=Ts0.85f'c0.85cb=As×εcu(d-c)c×Es
0.85210 kgcm20.85c25 cm= 0.00337.18 cm-cc×2.03×10638.70 cm2
3793.125c2=235683(37.18-c)
c=26.16 cm
a=0.85c=0.8526.16=22.24 cm
εs= εcu(d-c)c= 0.003(37.18 cm-26.16 cm)26.16 cm=0.00126
0.00126<εy La sección no es ductil
Mn=0.85f'cab(d-a2)
Mn=0.85(210 kgcm2)22.24 cm25 cm(37.18 cm-22.24 cm2)
Mn=2586350.76 kg-cm=25.86 t-m
∅=0.65 ya que la viga se encuentra acompresión.
Mu=∅Mn
Mu=0.6525.86 t-m=16.81 T-cm
45
25

Problema 4
f'c=280 kgcm2
fy=2800 kgcm2
As=21.98 cm2=3.96 cm2
S'=h-2rec-2∅rec-N∅varEspacio=45 cm-24 cm-20.95 cm-4(1.59 cm)3=9.58 cm
S=b-2rec-2∅rec-N∅varEspacio=25 cm-24 cm-20.95 cm-2(1.59 cm)1=11.92 cm
S y S'>2.5 cm ok
d=h-rec-∅est-∅var
d1=4 cm+0.95 cm+1.59 cm2=5.745 cm
d2=4 cm+0.95 cm+1.59 cm+9.58 cm+1.59 cm2=16.915 cmd3=45 cm-4 cm-0.95 cm-1.59 cm-9.58 cm-1.59 cm2=28.085 cm
d4=45 cm-4 cm-0.95 cm-1.59 cm2=39.255 cm
Cc+Cs1=Ts2+Ts3+Ts4
0.85f'cab+Asfy=Asfy+Asfy+Asfy
0.85280 kgcm2a25 cm+3.96 cm22800 kgcm2=3.96 cm22800 kgcm2+3.96 cm22800 kgcm2+3.96 cm22800 kgcm2
5950a=22176
a=3.73 cm
c=a0.85=3.73 cm0.85=4.38 cm
εs= εcud-cc
εs1=0.003(4.38 cm-5.745 cm)4.38 cm=-0.0009349
εs2=0.003(16.915 cm-4.38 cm)4.38cm=0.0085856
εs3=0.003(28.085 cm-4.38 cm)4.38 cm=0.016236
εs4=0.003(39.255 cm-4.38 cm)4.38 cm=0.0238869
εs2=εs3=εs4>0.005
Cc=Ts1+Ts2+Ts3+Ts4
0.85f'cab=Asεcud-ccEs+Asfy+Asfy+Asfy
0.85280 kgcm20.85c25 cm=3.96 cm20.003(5.745-c)c2.03×106+3.96 cm22800 kgcm2+3.96 cm22800 kgcm2+3.96 cm22800 kgcm2
5057.5c2=24116.45.745-c+33264c
c=6.22 cm
a=0.85c=0.856.22 cm=5.29 cm
εs= εcud-cc
εs1=0.003(5.745 cm-6.22cm)6.22 cm=-0.000229
εs2=0.003(16.915 cm-6.22 cm)6.22 cm=0.00515
εs3=0.003(28.085 cm-6.22 cm)6.22 cm=0.010546
εs4=0.003(39.255 cm-6.22 cm)6.22 cm=0.015933

Cc+Cs1=Ts2+Ts3+Ts4
0.85f'cab+Asεcuc-d'cEs=Asfy+Asfy+Asfy
0.85280 kgcm20.85c25 cm+3.96 cm20.003(c-5.745 cm)c2.03×106=3.96 cm22800 kgcm2+3.96 cm22800 kgcm2+3.96 cm22800 kgcm2
5057.5c2+24116.4c-5.745=33264c
c=6.22 cm
a=0.85c=0.856.22cm=5.29 cm
εs= εcud-cc
εs1=0.003(6.22 cm-5.745 cm)6.22 cm=0.000229
εs2=0.003(16.915 cm-6.22 cm)6.22 cm=0.00515
εs3=0.003(28.085 cm-6.22 cm)6.22 cm=0.010546
εs4=0.003(39.255 cm-6.22 cm)6.22 cm=0.015933
εs2=εs3=εs4>0.005
∅=0.9
f's1=εs1Es=0.0002292.03×106=464.87 kgcm2
As12=As×f's1fy=3.96 cm2464.87 kgcm22800kgcm2=0.667 cm2
As11=11.88 cm2-0.667 cm2=11.22 cm2
A's2=A's3=A's4=11.22 cm23=3.74cm2
Mn= Ccd1-a2+Ts2d2-d1+Ts3d3-d1+Ts4d4-d1
Mn=0.85f'cabd1-a2+A's2fyd2-d1+A's3fyd3-d1+A's4fyd4-d1
Mn=0.85280 kgcm25.29 cm25 cm5.745 cm-5.29 cm2+3.74 cm22800 kgcm216.915 cm-5.745 cm+3.74 cm22800 kgcm228.085 cm-5.745 cm+3.74 cm22800 kgcm239.255 cm-5.745 cm
Mn=799407.49 kg-cm
Mn=7.99 T-m
Mu=∅Mn=0.97.99 T-m=7.19 T-m

45 cm
25 cm

Problema 6
f'c=280 kgcm2
fy=3500 kgcm2
As=23.88 cm2=7.76cm2
d=h-rec-∅est-∅var2=50 cm-4 cm-0.95 cm-2.22 cm2 cm=43.94 cm
Ac=b'a+12b-b'a
50 cm
25 cm
a
b’

b'25 cm= 50 cm-a50 cm
b'= 1250 cm-a
Ac=1250-aa+12b-1250-aa
Cc=Ts
0.85f'cAc=fyAs
0.85210 kgcm212a50 cm-a+12a25 cm-1250 cm-a= 3500 kgcm27.76 cm2
178.512a50 cm-a+12a25 cm-1250 cm-a= 27160
a=6.51 cm
c=a0.85=6.51 cm0.85=7.66 cm
εs= εcud-cc
εs=0.003(43.94 cm-7.66 cm)7.66 cm=0.01420.0142>0.005
∅=0.9
Ac=1250-aa+12b-1250-aa
Ac=1250 cm-6.51 cm6.51 cm+1225 cm-1250 cm-6.51 cm6.51 cm
Ac=152.15 cm2
Cc=0.85f'cAc
Cc=0.85210 kgcm2152.15 cm2=27159.56 kg

y
50 cm
25 cm
a




Ac=b'a+12b-b'a
152.15 cm2=6.51 cmb'+1225 cm-b'6.51 cm
b'=21.74 cm

Área | y | Ay |
21.74 cm6.51 cm=141.53 cm2 | 126.51 cm=3.255 cm | 141.53...