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APOSTILA DE ESTRUTURA METÁLICA

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−××××== WxfM yn
 
kNmM n 1910=
 
 
[ ]
8,13379,0
1910;8,1337;5,1644;6,13689,0
×=
=
dr
dr
M
mínM
 
kNmM dr 1204=
 
 
kNmMMMMMM BBdrBBdr 8604,1
1204
4,1
4,1 =∴=∴=∴=
 
Determinação de P: 
 
 
 
 
 
 
 
PVPVPV
PPPV
M
AAA
A
C
2
3
16
2402416
0481216
0
=∴=∴=−
=×−×−×−×
=∑
 
8608
8412
48
2
3
48
=
=−=
×−×=
×−×=
P
PPPM
PPM
PVM
B
B
AB
 
107,5kN=P
 
 
P P P 
4,0m 4,0m 4,0m 4,0m 
A 
B 
C 
VA VC 
Prof. Glauco J. O. Rodrigues. 
Notas de Aula de Estruturas Metálicas 61 
Exemplo 6.3: 
Verificar a viga abaixo, utilizando perfil VS 550x88. Considerar que existe travamento da viga nos 
pontos B e D. Considerar o peso próprio da viga (0,9kN/m). Adotar MR 250 (E=205GPa; 
fy=250MPa). 
 
 
Como esta viga é dotada de cargas permanetes e cargas acidentais, será feita a obtenção dos 
momentos individualmente, conforme a natureza da solicitação. 
 
DMF para cargas acidentais (q): 
 
 
 
DMF para cargas permanentes (g): 
 
 
d=550mm bf=250mm 
tf=16mm tw=6.3mm 
h=518mm A=112,6cm2 
Ix=64345cm4 Iy=4168cm4 
Wx=2340cm3 Wy=333cm3 
rx=23,9cm ry=6,08cm 
Zx=2559cm3 Zy=505,1cm3 
rt=6,77cm It=72,7cm4 
Prof. Glauco J. O. Rodrigues. 
Notas de Aula de Estruturas Metálicas 62 
( )( )36 10250102559 ××=
=
−
pl
yxpl
M
fZM
 
kNmM pl 75,639= 
 
Trecho CD: 
FLM: ( )88,10;16,24 == pr λλ 
p
f
f
t
b λλλ <∴=
×
== 81,7
162
250
2
(Seção compacta) 
kNmM n 75,639= 
 
FLA: ( )2,100;4,160 == pr λλ 
p
wt
h λλλ <∴=== 22,82
3,6
518 (Seção compacta) 
kNmM n 75,639= 
 
FLT: 
( ) mf
E
rL
y
yp 05,310250
102051008,675,175,1 3
6
2
=
×
×
×== − 
( ) ( ) ( ) ( )( ) 325,2101625,0
105501077,61011510250
102050,1
75,4075,40
2
3
32
33
6
2
=





××
×××
×−×
××
=








−=
−
−−
f
t
ry
b A
drff
EC
X
( ) ( )
mX
X
A
d
r
L f
t
r 14,10325,211325,2
101610250
105501077,69,19
11
9,19
2
33
3
22
2
2
=++






×××
×
××
=++








=
−−
−
−
 
Lp=3,05m<Lb=6,40m<Lr=10,14m (Seção não compacta) 
( ) ( ) kNmMffWM ryrxr 90,3151011510250102340 336 =∴×−××=−= − 
( )
( ) ( ) ( )05,340,605,314,10
90,31575,63975,639 −
−
−
−=∴−
−
−
−= npb
pr
rpl
pln MLLLL
MM
MM 
kNmM n 73,86= 
 
Flechas: 
63 1023401025025,125,1 −××××== WxfM yn 
kNmM n 25,731= 
 
[ ]
73,4869,0
25,731;73,486;75,639;75,6399,0
×=
=
dr
dr
M
mínM
 
kNmM dr 06,438= 
 
A partir da análise do diagrama de momentos fletores, temos que: 
Prof. Glauco J. O. Rodrigues. 
Notas de Aula de Estruturas Metálicas 63 
kNmM
kNmM
g
q
4,18
288
=
=
 
( ) ( ) kNmMMM gqd 16,4274,183,12884,13,14,1 =×+×=+= 
kNmMM ddr 16,42706,438 =>= (perfil atende) 
 
Trecho BC: 
(FLM, FLA e Flechas, idem ao vão CD). 
 
FLT: 
mLp 05,3= (idem ao vão CD) 
( ) ( )
( ) ( ) kNmM
kNmM
24,4164,193,13,2794,1
16,4274,183,12884,1
1
2
=×+×=
=×+×=
 
3,23,206,3
16,427
24,4163,0
16,427
24,41605,175,1
2
=∴>=





+





+= bb CC 
( ) ( ) ( ) ( )( ) 011,1101625,0
105501077,61011510250
102053,2
75,4075,40
2
3
32
33
6
2
=





××
×××
×−×
××
=








−=
−
−−
f
t
ry
b A
drff
EC
X
( ) ( )
mX
X
A
d
r
L f
t
r 31,19011,111011,1
101610250
105501077,69,19
11
9,19
2
33
3
22
2
2
=++






×××
×
××
=++








=
−−
−
−
 
Lp=3,05m<Lb=8,5m<Lr=19,31m (Seção não compacta) 
kNmM r 90,315= (idem ao vão CD) 
( )
( ) ( ) ( )05,35,805,331,19
90,31575,63975,639 −
−
−
−=∴−
−
−
−= npb
pr
rpl
pln MLLLL
MM
MM 
kNmM n 20,531= 
 
[ ]
20,5319,0
25,731;20,531;75,639;75,6399,0
×=
=
dr
dr
M
mínM
 
kNmM dr 08,478= 
 
A partir da análise do diagrama de momentos fletores, temos que: 
 
kNmM
kNmM
g
q
4,18
288
=
=
 
( ) ( ) kNmMMM gqd 16,4274,183,12884,13,14,1 =×+×=+= (idem ao vão CD) 
kNmMM ddr 16,42708,478 =>= (perfil atende) 
 
Prof. Glauco J. O. Rodrigues. 
Notas de Aula de Estruturas Metálicas 64 
Trecho AB: 
(FLM, FLA e Flechas, idem ao vão CD). 
 
FLT: 
mLp 05,3= (idem ao vão CD) 
75,101 =∴= bCM 
( ) ( ) ( ) ( )( ) 329,1101625,0
105501077,61011510250
1020575,1
75,4075,40
2
3
32
33
6
2
=





××
×××
×−×
××
=








−=
−
−−
f
t
ry
b A
drff
EC
X
( ) ( )
mX
X
A
d
r
L f
t
r 40,15329,111329,1
101610250
105501077,69,19
11
9,19
2
33
3
22
2
2
=++






×××
×
××
=++








=
−−
−
−
 
Lp=3,05m<Lb=7,30m<Lr=15,40m (Seção não compacta) 
kNmM r 90,315= (idem ao vão CD) 
( )
( ) ( ) ( )05,330,705,340,15
90,31575,63975,639 −
−
−
−=∴−
−
−
−= npb
pr
rpl
pln MLLLL
MM
MM 
kNmM n 30,528= 
 
[ ]
30,5289,0
25,731;30,528;75,639;75,6399,0
×=
=
dr
dr
M
mínM
 
kNmM dr 47,475= 
 
A partir da análise do diagrama de momentos fletores, temos que: 
 
kNmM
kNmM
g
q
4,19
3,279
=
=
 
( ) ( ) kNmMMM gqd 24,4164,193,13,2794,13,14,1 =×+×=+= (idem ao vão CD) 
kNmMM ddr 24,41647,475 =>= (perfil atende) 
 
Prof. Glauco J. O. Rodrigues. 
Notas de Aula de Estruturas Metálicas 65 
7 CARACTERÍSTICAS MECÂNICAS DE PERFIS “I” SOLDADOS DA USIMINAS 
PERFIS SOLDADOS - SÉRIE VS
DIMENSÕES (mm) EIXO X-X EIXO Y-Y
PERFIL A W Ix Wx rx Zx Iy Wy ry Zy Cw IT rT
d bf tf tw h (cm2) (kg/m) (cm4) (cm3) (cm) (cm3) (cm4) (cm3) (cm) (cm3) (cm6) (cm4) (cm4)
VS 550 x 71 550 250 9.50 8.00 531.0 90.0 70.6 44,677 1,624.6 22.3 1,847.6 2,476 198.1 5.2 305.4 1,808,512 23.01 6.34
VS 550 x 82 550 250 12.50 8.00 525.0 104.5 82.0 54,797 1,992.6 22.9 2,230.9 3,257 260.6 5.6 399.0 2,352,743 40.49 6.53
VS 550 x 92 550 300 12.50 8.00 525.0 117.0 91.8 63,827 2,321.0 23.4 2,566.9 5,627 375.1 6.9 570.9 4,064,362 47.00 7.95
VS 550 x 102 550 350 12.50 8.00 525.0 129.5 101.7 72,857 2,649.3 23.7 2,902.8 8,935 510.5 8.3 774.0 6,453,105 53.51 9.38
VS 600 x 98 600 250 16.00 8.00 568.0 125.4 98.5 80,445 2,681.5 25.3 2,981.2 4,169 333.5 5.8 509.1 3,554,733 75.21 6.62
VS 600 x 111 600 300 16.00 8.00 568.0 141.4 111.0 94,091 3,136.4 25.8 3,448.4 7,202 480.2 7.1 729.1 6,141,074 88.86 8.05
VS 600 x 124 600 350 16.00 8.00 568.0 157.4 123.6 107,736 3,591.2 26.2 3,915.6 11,436 653.5 8.5 989.1 9,750,584 102.51 9.48
VS 600 x 140 600 300 22.40 8.00 555.2 178.8 140.4 123,562 4,118.7 26.3 4,498.0 10,082 672.2 7.5 1,016.9 8,409,244 223.69 8.22
VS 650 x 98 650 300 12.50 8.00 625.0 125.0 98.1 92,487 2,845.8 27.2 3,171.9 5,628 375.2 6.7 572.5 5,717,797 48.70 7.84
VS 650 x 102 650 250 16.00 8.00 618.0 129.4 101.6 96,144 2,958.3 27.3 3,299.8 4,169 333.5 5.7 509.9 4,189,691 76.06 6.57
VS 650 x 114 650 300 16.00 8.00 618.0 145.4 114.2 112,225 3,453.1 27.8 3,807.0 7,203 480.2 7.0 729.9 7,237,858 89.71 8.00
VS 650 x 155 650 300 25.00 8.00 600.0 198.0 155.4 160,963 4,952.7 28.5 5,407.5 11,253 750.2 7.5 1,134.6 10,988,828 306.33 8.23

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