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1)
32°
Ny
N
58°
Nx 150kn
FORÇA N:
Nx = N . cos 58°
Ny = N . Sen 58°
32°
Vy
150kn
FORÇA V:
Vx = V . cos 32°
Vy = V . Sem 32°
V
Vx
෍
Fx= 0
-Nx + Vx +150=0
- (N . Cos 58°) + (V . Cos 32°) = -150 kn
෍
Fy= 0 + Ny +Vy = 0 
+ N . Sen 58° + V . Sen 32°= 0
V = - sen 58° . N 
Sen 32°
V = 1,60 . N
-( N . Cos 58° ) + ( V . Cos 32°) = - 150kn
- N . 0,53 – 1,60N . 0,85 = - 150 kn
- 0,53N – 1,36N = - 150kn
- 1,89N = -150 .(-1)
N = 150
1,89
N = 79,37 kn
Log V = - 1,60 . (79,37)
V = 127 kn
Calculo de área transversal:
32°
12 mm
A’
D = 12mm
A = 𝜋 . r²
A = 𝜋 . 6²
A = 113,09 mm²
Sen 32° = A
1 A’
A’ = 113,09
0,53
A’ = 213,38 mm²
Tensões:
𝜏
𝜎
= V
A
= N
A
127,00 . 10³
213,38
𝜏 = 595,18 mPa
79,37 . 10³
213,38
𝜎 = 371,97mPa
2)
VC
VA
10 . Sem 52°
10 . Cos 53°
10 . Sen 53° = 7,98 kn
10 . Cos 53° = 6,01 kn
෍
෍
Fx = 0
Fy = 0
VC + VA – 7,98 – 4 = 0
VC + VA = 11,98
෍ MC = 0
- (7,98 . 1,6) – (4 . 2.4) /0,8
- 12,77 – 9,60 /0,8= 0
VA = 22,37
0,8
VA = 27,96 KN
LOG 11,48 – 27,46
VC = - 15,98 KN 
𝜎 RUP = C . S . 𝜎ADM
240 = 1,75 . 15,98 . 10³ N
1 A.BC
ABC = 116,52 MM²
Abc= 𝜋 . r² = 116,32 mm² d = 2 . 6,09 = 12,16 mm
𝜏 = 116,52
𝜋
𝜏 = 37,08 𝜏 = 6,08
D = 12,16mm
3)
45°
FACYFADY
FAD
FAC
𝜃
FADX FACX
෍ FX = 0 (FACX + FADX) = 0
FAC . COS 𝜃 - FAD . COS 45° = 0
෍ FY = 0
350N
(FACY + FADY) = 350N
FAC . SEN 45°=350N
𝜎AC = 1.63 . AD
FAC
Aac
= 1,63 . FAD
Aad
FAC = 1,63 . FAD
𝜋. 3² 𝜋 . 3,75²
FAC . 𝜋 . 3,75² = 1,63 . FAD . 𝜋 . 3²
FAC = 1,63 . 𝜋 . 3² . FAD
𝜋 . 3,75²
FAC = 1,05 FAD
FAC . COS 𝜃 - FAD . COS 45° = 0
1,05 FAD . COS 𝜃 - FAD . COS 45°= 0
COS 𝜃 = FAD . COS 45°
1,05 . FAD
COS = 0,68
LOG : COS ¹ 𝜃 = 0,68
𝜽 = 47,16
SUB. EQ .3
P/ EQ. 2
FAC . SEN + FAD . SEN 45° = 350
1,05 FAD . SEN 47,16 + FAD . SEN 45°= 350
0,77 FAD + 0,71 FAD = 350
1,48 FAD = 350
𝜃
FAD = 236,49 N
𝜎AD = FAD 
Aad
236,49
𝜋. 3,75²
𝜎AD = 5,36 mPa
𝜎AC = FAC 
Aac
248,32
𝜋. 3²
𝜎AC = 8,79 mPa
𝜎AB = FAC 
AaB
350
𝜋. 4,5²
𝜎AB = 5,51 mPa
4)
a) Forças:
෍Fma = 0
( 10. 1,5) + ( 1,5 . 3 ) +(10 . 4,5) + ( 74 .7) /4 = 0
623
4
VB = 138,45 KN
෍FY = 0 - 10 -10 -15 -10 + 138, 45 -74 = 0
VA= -19,45
P/ CHAPA A:
𝜎Adm = VA
1 Aa
A = VA
adm
La² = 19,45 kn
4,8 mPa
La = 63,65mm²
P/ CHAPA B:
AB = VB
adm𝜎
LB = 138,44KN
4,8 mPa
LB = 169,83 mm²
5)
COEFICIENTE DE SEGURANÇA:
A parafuso = . r²𝜋
𝜋 . 9²
A = 254,47 mm²
𝜎 Parafuso = 110 . 10³
254,47
𝜎 parafuso= 432,28 mPa
LOG 𝜎 = 432,28
3
𝜎 = 144,10 mPa
P/ C.S:
C . S : 𝜎RUP
𝜎ADM
360
144,10
C . S = 2,50