FormularioFINAL

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UNIDERP - ANHANGUERA

0

Jacquicelle Gomes

16/10/2019

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qk0qqjkj0k1qqgkggkgd F)FF(FFF   
 (ELU - Normal) 
qk0qjkj0k1qgkgkfund,d F)FF(FFF   
 (Fundações) 
   
min,sqsjkj0k1qnkgnnd
dskgssd
ndsd
Q)QQ(GF
RGF
FSFS




 (ELU - Equilíbrio) 
 
 
 
 













 



MPa50f
400
50f
8,0
MPa50f8,0
ck
ck
ck
 













 



MPa50f
200
50f
185,0
MPa50f85,0
ck
ck
ck
c 
kfd FF 
 
c
ck
cd
f
f


 
s
yk
yd
f
f


 
yd
s
s
f


 
yd
'
s'
s
f


 
sc
c
x
d
x



 
xy
d
y

 
xz 5,01
d
z

 
 xxczxcc 5,01 
 











max
h
d2,1
cm2
maxa 
 











max
v
d5,0
cm2
maxa 
 
 
 
 
s 
encurtamentos 
c 
5 
4 
2 
1 
c2 cu 
d’ 
alongamentos 
yd 
4a 
3 
d 
As 
a 
b 
A’s 
h 
10‰ 
 
vigas de seção retangular sem armadura de compressão 






















Sd
sup,ctk0
Sd
min,d
Rd
M
fW8,0
max
M
M
maxM
 
 
6
hb
W
2
w
0 
 
 
 








MPa50ff11,01ln756,2
MPa50ff0,39
f
ckck
ck
3 2
ck
supctk,
 
 









s
z
x
cd
2
w
Rd
c tab
fdb
M 








MPa50f350,0
MPa50f450,0
ck
ck
dtlx,x
 
 









cmax,s
cmin,s
ydsz
Rd
s
A%4A
A%15,0A
fd
M
A
 
 
x
yds
cdwc
s
fA
fdb








 

 
 
hbA wc 
 
 
Concreto ≤ C50 
Aço CA-50 s = 1,15 
x y z c s 
 
x y z c s 
0,010 0,008 0,996 0,007 1,000 
 
0,260 0,208 0,896 0,158 1,000 
0,020 0,016 0,992 0,013 1,000 
 
0,270 0,216 0,892 0,164 1,000 
0,030 0,024 0,988 0,020 1,000 
 
0,280 0,224 0,888 0,169 1,000 
0,040 0,032 0,984 0,027 1,000 
 
0,290 0,232 0,884 0,174 1,000 
0,050 0,040 0,980 0,033 1,000 
 
0,300 0,240 0,880 0,180 1,000 
0,060 0,048 0,976 0,040 1,000 
 
0,310 0,248 0,876 0,185 1,000 
0,070 0,056 0,972 0,046 1,000 
 
0,320 0,256 0,872 0,190 1,000 
0,080 0,064 0,968 0,053 1,000 
 
0,330 0,264 0,868 0,195 1,000 
0,090 0,072 0,964 0,059 1,000 
 
0,340 0,272 0,864 0,200 1,000 
0,100 0,080 0,960 0,065 1,000 
 
0,350 0,280 0,860 0,205 1,000 
0,110 0,088 0,956 0,072 1,000 
 
0,360 0,288 0,856 0,210 1,000 
0,120 0,096 0,952 0,078 1,000 
 
0,370 0,296 0,852 0,214 1,000 
0,130 0,104 0,948 0,084 1,000 
 
0,380 0,304 0,848 0,219 1,000 
0,140 0,112 0,944 0,090 1,000 
 
0,390 0,312 0,844 0,224 1,000 
0,150 0,120 0,940 0,096 1,000 
 
0,400 0,320 0,840 0,228 1,000 
0,160 0,128 0,936 0,102 1,000 
 
0,410 0,328 0,836 0,233 1,000 
0,170 0,136 0,932 0,108 1,000 
 
0,420 0,336 0,832 0,238 1,000 
0,180 0,144 0,928 0,114 1,000 
 
0,430 0,344 0,828 0,242 1,000 
0,190 0,152 0,924 0,119 1,000 
 
0,440 0,352 0,824 0,247 1,000 
0,200 0,160 0,920 0,125 1,000 
 
x,dtl 0,360 0,820 0,251 1,000 
0,210 0,168 0,916 0,131 1,000 
 
0,460 0,368 0,816 0,255 1,000 
0,220 0,176 0,912 0,136 1,000 
 
0,470 0,376 0,812 0,260 1,000 
0,230 0,184 0,908 0,142 1,000 
 
0,480 0,384 0,808 0,264 1,000 
0,240 0,192 0,904 0,148 1,000 
 
0,490 0,392 0,804 0,268 1,000 
0,250 0,200 0,900 0,153 1,000 
 
0,500 0,400 0,800 0,272 1,000 
 
 
 










 



MPa50f
400
50f
8,0
MPa50f8,0
ck
ck
ck 










 



MPa50f
200
50f
185,0
MPa50f85,0
ck
ck
ck
c
 
kfd FF 
 
c
ck
cd
f
f


 
s
yk
yd
f
f


 
yd
s
s
f


 
yd
'
s'
s
f


 
sc
c
x
d
x



 
xy
d
y

 
xz 5,01
d
z

 
 xxczxcc 5,01 
 











max
h
d2,1
cm2
maxa 
 











max
v
d5,0
cm2
maxa 
 












00,2
60,0
75,0
00,1
a 












4
3
2
1
b
a1,0
b
b5,0
a1,0
b
 
 
 
 
vigas de seção retangular com armadura de compressão 
 

















































MPa50f350,0
MPa50f450,0
tab
fdb
M
MPa50ff11,01ln756,2
MPa50ff0,39
f
6
hb
W
M
fW8,0
max
M
M
maxM
ck
ck
dtlx,x
s
z
x
cd
2
w
Rd
c
ckck
ck
3 2
ck
supctk,
2
w
0
Sd
sup,ctk0
Sd
min,d
Rd
 
'
s
s
'
s
x
yds
cdwc
s
c
'
ss
yd
'
s
'
2Rd'
s
c
yds
'
2Rd
z
1Rd
s
1RdRd2Rd
cd
2
wc1Rd
'
s
s
c
z
'
dtl,xx
A
A
fA
fdb
A%4)AA(
f)dd(
M
A
A%15,0
f
1
)dd(
M
d
M
A
MMM
fdbM
tab
d
d

















 






































 
para vigas de seção retangular sem armadura de compressão, considerar: 
dtlx,x 
 
Rd1Rd MM 
 
0AdM 's
'
s
'
2Rd 
 
 
 
 
 
vigas de seção T sem armadura de compressão - y  hf 






















Sd
sup,ctk0
Sd
min,d
Rd
M
fW8,0
max
M
M
maxM
 
 
  cdfffcmesa,Rd f
2
h
dhbM 






 
 
mesa,RdRd MM 
 
 












s
z
y
x
cd
2
f
Rd
c tab
fdb
M
 








MPa50f350,0
MPa50f450,0
ck
ck
dtlx,x
 
 
fy hdy 
 
 









hb%4A
A%15,0A
fd
M
A
wmax,s
cmin,s
ydsz
Rd
s 
 
x
yds
cdfc
s
fA
fdb








 

 
 
vigas de seção T sem armadura de compressão - y > hf 






















Sd
sup,ctk0
Sd
min,d
Rd
M
fW8,0
max
M
M
maxM
 
 
  cdfffcmesa,Rd f
2
h
dhbM 






 
 
mesa,RdRd MM 
 
 
  cdffwfc3Rd f
2
h
dhbbM 












 
 
3RdRd1Rd MMM 
 












s
z
y
x
cd
2
w
1Rd
c tab
fdb
M
 
 








MPa50f350,0
MPa50f450,0
ck
ck
dtlx,x
 
 
fy hdy 
 
 






























hb%4A
A%15,0A
f
1
2
h
d
M
d
M
A
wmax,s
cmin,s
ydsf
3Rd
z
1Rd
s
 
 
  
















 

yds
cdfwfc
x
yds
cdwc
s
fA
fhbb
fA
fdb
 
 
seção T - W0   fwfwc hbbhbA  
w
w,00
y
I
WW 
 
)]}hh()bb[()hb{[(2
])hh()bb[()hb(
y
fwff
2
fwf
2
f
w



 
2
wc
3
fwf
3
f yA
3
])hh()bb[(hb
I 





 

 
 
 
y > hf 
y  hf 
 
kfd FF 
 
vigas com estribos verticais - modelo I vigas com estribos verticais - modelo II 






3Rd
2Rd
Sd
V
V
V
 
dbf27,0V wcd2v2Rd 
 
MPaemf
250
f
1 ck
ck
2v 
 
swc3Rd VVV 
 
dbf6,0V wctdc 
 
 
















MPa50f
f11,01ln484,1
MPa50f
f21,0
f
ck
c
ck
ck
c
3 2
ck
ctd
 
ywd
sw
sw fd9,0
s
A
V 






 
MPa435
f
f
s
yk
ywd 


 
ywk
m,ct
w
sw
sw
f
f
2,0
sb
A

 
 








MPa50ff11,01ln12,2
MPa50ff3,0
f
ckck
ck
3 2
ck
m,ct
 
MPa500ff ykywk 
 






3Rd
2Rd
Sd
V
V
V
 
 cossendbf54,0V wcd2v2Rd
 
MPaemf
250
f
1 ck
ck
2v 
 
 4530
 
swc3Rd VVV 
 
0c
0c2Rd
Sd2Rd
0cc V
VV
VV
VV 










 
dbf6,0V wctd0c 
 
 
















MPa50f
f11,01ln484,1
MPa50f
f21,0
f
ck
c
ck
ck
c
3 2
ck
ctd
 






 cotfd9,0
s
A
V ywd
sw
sw
 
MPa435
f
f
s
yk
ywd 


 
ywk
m,ct
w
sw
sw
f
f
2,0
sb
A

 
 








MPa50ff11,01ln12,2
MPa50ff3,0
f
ckck
ck
3 2
ck
m,ct
 
MPa500ff ykywk 
 
10
b
mm5 wt 
 











cm30
d6,0
minscm767,0
V
V
2Rd
Sd
 











cm20
d3,0
minscm767,0
V
V
2Rd
Sd
 
deslocamento de diagrama 
vigas com estribos verticais - modelo I vigas com estribos verticais - modelo II 
  
















d
d5,0
VV
V
2
d
a
cmax,Sd
max,Sd

 
cmax,Sd VVda 
 
 gcotd5,0a
 
 4530
 
 
 
 sen cos cot 
30º 0,500 0,866 1,732 
35º 0,574 0,819 1,428 
40º 0,643 0,766 1,192 
45º 0,707 0,707 1,000 
 
d 
a  2d 
d/2 
d 
diagrama VSd para 
cálculo da armadura 
de cisalhamento 
diagrama VSd para 
cálculo da armadura 
de cisalhamento 
VSd 






d2
a
VSd