EXERCÍCIOS SELECIONADOS Aulas 13 14 e 15

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Mecânica I – 2015/2 Universidade Federal do Amazonas 1 
 
Prof. Winston Zumaeta Aulas 13, 14 e 15 20/10/2015 
 
2
A
E
B
C
D
3,
0 
m
3,
0 
m
4,0 m 4,0 m
4,
0 
m
8,0 m
100
 
kN
/m
100
 kN/m
100
 kN/m10
0 
kN
/m
3
150
kN/m
A D
B C
4,0 m 6,0 m 4,0 m
14,0 m
3,
0 
m 50 
kN
/m
50
kN/m
50
 kN/m
4
A E
B
4,0 m 4,0 m 4,0 m
14,0 m
3,
0 
m
C D
2,0 m
100
 
kN
/m
100 kN/m
100
 kN/m
300 kN
400 kN.m
1
3,0 m
7,0 m 2,0 m
4,
0 
m
A
B C D
E
4,0 m
200 kN/m
20
0 k
N/
m
300 kN 400 kN
800 kN.m
 
 EXERCÍCIOS SOBRE REAÇÕES DE APOIO EM PÓRTICOS PLANOS 
 
Calcular as reações de apoio e fazer a verificação em um ponto de sua preferência para 
todos os pórticos. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Mecânica I – 2015/2 Universidade Federal do Amazonas 2 
 
Prof. Winston Zumaeta Aulas 13, 14 e 15 20/10/2015 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
5
A
E
B
C
D
3,
2 
m
4,
0 
m
3,2 m 3,2 m
2,
4 
m
6,4 m
200
 
kN
/m 200
 kN/m
200
 kN/m20
0 
kN
/m
8A
G
F
B C D
E
2,
0 
m
1,5 m 6,0 m 2,0 m
3,
0 
m
4,
0 
m
100 kN/m
80 kN
100 kN
100
kN/m
200
kN/m
4,0 m
6,0 m
C
3,0 m
100
kN/m
10
0
kN
/m
20
0
kN
/m
300
kN/m
A
4,0 m
400 kN.m
F
B D E
73,
0 
m
4,
0 
m
200
 kN/m
200
 
kN
/m 200
 kN/m
A
E
B
C
D
3,
2 
m
4,
0 
m
20
0 
kN
/m
640 kN.m
3,2 m 3,2 m
2,
4 
m
6,4 m
600 kN
6
Mecânica I – 2015/2 Universidade Federal do Amazonas 3 
 
Prof. Winston Zumaeta Aulas 13, 14 e 15 20/10/2015 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
10
4,0 m 4,0 m
2,
0 
m
2,
0 
m
80 kN
60 kN
3,
0 
m 100
 
kN
/m
100
 
kN
/m
2,0 m
100 kN
A
H
G
B C
D
E
F
I
2,0 m
11
50 kN
200 kN/m
200
 
kN
/m
200
 kN/m
4,0 m 4,0 m 2,0 m
3,
0 
m
2,
0 
m
4,
0 
m
3,0 m
2,
25
 
m
1,0
A
B
C D E F
H
G
I
3,0 m
9 3,
0 
m
100
kN/m
200
kN/m
A
H
G
B C D E
F
2,
0 
m
1,5 m 6,0 m 2,0 m 2,0 m 2,0 m
4,
0 
m
100 kN/m
80 kN
100 kN
Mecânica I – 2015/2 Universidade Federal do Amazonas 4 
 
Prof. Winston Zumaeta Aulas 13, 14 e 15 20/10/2015 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
14
4,0 m
400
kN/m
G
200
 
kN
/m
200
 kN/m
200 kN/m
200
kN/m
2,0 m 2,0 m 4,0 m
3,
0 
m
3,
0 
m
A
B C D
E
F
100 kN/m
50 kN/m
3,0 m 4,0 m 4,0 m
4,
0 
m
2,
0 
m
1,
5
2,0 m
A
BC D
E F
G13
12
100 kN/m
50 kN/m
3,0 m 4,0 m 4,0 m
4,
0 
m
2,
0 
m
1,
5
2,0 m
A
BC D
E F
G
Mecânica I – 2015/2 Universidade Federal do Amazonas 5 
 
Prof. Winston Zumaeta Aulas 13, 14 e 15 20/10/2015 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
15
200
 
kN
/m
200
 kN/m
200 kN/m
200
kN/m
2,0 m 2,0 m 4,0 m
3,
0 
m
3,
0 
m
A
B C D
E
F
4,0 m
400
kN/m
G
16
D F
A I
J
400 kN 200 kN/m
100 kN
40
0
kN
/m
400 kN/m
3,0 m 4,0 m 2,0 m 2,0 m 4,0 m 3,0 m
2,
0 
m
2,
0 
m
2,0 m 2,0 m
3,
0 
m
4,
0 
m
B C E G H
17
3,
0 
m
1,5 m 4,0 m 4,0 m 2,0 m
J
A20
0
kN
/m
100
 kN/m
100
 
kN
/m
400 kN
400 kN
2,
0 
m
2,
0 
m
1 
m
3,
0 
m
1 
m
C
D
E
F
I
B H G
Mecânica I – 2015/2 Universidade Federal do Amazonas 6 
 
Prof. Winston Zumaeta Aulas 13, 14 e 15 20/10/2015 
 
 
 
 
 
 
 
 
Respostas: 
1. �� = 357,14	�� ↑	; 	�� = 800	�� ←	;	�� = 2142,86	�� ↑ 
2. �� = 406,25	�� ↑	; 	�� = 393,75	�� ↑	; �� = 100	�� → 
3. �� = 478,57	�� ↑	; 	�� = 486,90	�� →	;	�� = 521,43	�� ↑	; �� = 486,90	�� ← 
4. �� = 885,71	�� ↑	; 	�� = 954,76	�� →	;	�� = 814,29	�� ↑	; �� = 954,76	�� ← 
5. �� = 256	��.� ↷	;	�� = 640	�� ↑	; 	�� = 240	�� ←	;	�� = 640	�� ↑	; 
�� = 400	�� → 
6. �� = 2176	��.� ↷	;	�� = 540	�� ↑	; 	�� = 360	�� →	;	�� = 740	�� ↑	; 
�� = 400	�� → 
7. �� = 322,06	�� ↑	; 	�� = 179,41	�� →	;	�� = 1477,95	�� ↑	; �� = 629,41	�� ← 
8. �� = 261,33	�� ↑	; 	�� = 562,50	�� ↑	;	�� = 376,17	�� ↑	; �� = 270	�� →	; 
�� = 1080	��.� ↷ 
9. �� = 294,67	�� ↑	; 	�� = 625	�� ↑	; 	�� = 280,33	��	 ↑; �� = 270	�� →	;	 
�� = 1080	��.� ↷ 
10. �� = 792,50	�� ↑	; 	�� = 134,29	�� →;	� = 147,50	�� ↑	; � = 834,29	�� ←	; 
� = 5720	��.� ↶ 
11. �� = 1308,33	�� ↑	;	�� = 1119,44	�� →;	� = 941,67	�� ↑	; � = 919,44	�� ←	;	 
� = 1433,33	��.� ↷ 
12. "� = 146,34	�� ↗	; 	�� = 382,93	�� ↑;	�� = 87,80	�� ←	;	�� = 956,10	��.� ↷ 
13. "� = 187,50	�� ↗	; 	�� = 350	�� ↑;	�� = 112,50	�� ←	;	�� = 606,25	��.� ↷ 
14. �� = 625	�� ↑	;	�� = 475	�� ↑	; �� = 800	�� →	;	�� = 1300	�� ↑	;	�� = 100	�� → 
15. �� = 750	�� ↑	;	�� = 550	�� ↑	; �� = 900	�� →	;	�� = 1100	�� ↑	;	�� = 0 
16. �� = 600	�� ↑	;	� = 1028,57	�� ↑;	�$ = 3171,43	�� ↑	;�$ = 700	�� ←	; 
�$ = 2842,86	��.� ↶ 
17. �� = 391,07	�� ↑	; 	�� = 471,43	�� ←	;	�$ = 408,93	�� ↑	;�$ = 428,57	�� ←	;	 
�$ = 1657,14	��.� ↶ 
18. �� = 1365	�� ↑	; 	�� = 1736,67	�� →	;	�% = 75	�� ↑	; �� = 1200	�� ↑	;	 
�� = 1816,67	�� ← 
100 kN
1,
5 
m
1,
5 
mD
2,0 m
E
4,0 m
200 kN/m
A H
100
 
kN
/m
3,0
 
m
4,0 m 2,0 m 4,0 m
2,0 m 2,0 m
3,
0 
m
B C F G
18
100 kN