Eds 5 semestre Engenharia Mecânica

ED 1 - Alternativa E

EFV = 0

– VA – 10 + VB – 40=0

VB = VA + 50

VB = RA cos (30º) + 50 (Equação I)

EFH = 0

HA + 10 – HB + 15 = 0

HB = HA + 25 (Equação II)

MA = 0

– 5 + 2 * HB + 2 * VB – 40 * 30 – 15 * 2 = 0

2HB + 2VB – 155=0

2 * (RA sen (30º) +25) + 2 * (RA cos (30º) + 50) = 155

RA + 50 + 1,73 * RA + 100 = 155

2,73 * RA = 155-150

RA = 5 / 2,73

RA = 1,83 kN

Em I: VB = 51,58 kN

Em II: HB = 25,92 kN

ED 2 - Alternativa A

EFH = 0

RH = -5 kN

EFV = 0

RV = 4 kN

EM =0

MR+4-4*1+5*2 = 0

MR = -10 kNm

S1

N = -5 Kn

V = -2*1,2 V = -2,4 Kn

M = -2,4*0,6 M= 1,44 kNm (TC)

S2

N = -5 Kn

V = -2,4 + ( -2* 0,8) V = - 4 kN

M = - 1,44 – 4 * 2,8 M= 12 kNm (TC)

S3

N = -4kN

V = 5kN

M = -4 * 3 + 4 M= 8 kNm (TD)

S4

N = 5kN

V = 4kN

M = -8 + 10 M = 2 kNm (TC)

ED 3 – ALT C

M5,6=0

V1x2-5+40-10x2+10x2=0 => v1= -17,5 KN

S1:

FV=0 FH=0 M=0

-N-17,5=0=>N=-17,5 KN V+10=0 => V=-10 KN M=0

S2:

FV=0 FH=0 M=0

-17,5-N=0 =>N=-17,5 KN V+10=0 => V=-10 KN 10x1,2=12 KN.m

S3:

FV=0 FH=0 M=0

-N-17,5=0 => N=-17,5 KN 10-V=0 => V=-10 KN 10x2=20 KN.m

S4:

FV=0 FH=0 M=0

V-17,5=0 => V=17,5 KN N+10=0 => N=-10 KN 10x2-5=15KN.m

S5:

FV=0 FH=0 M=0

V-40-17,5=0 =>V=-12,5 KN N+10=0 => N=-10 KN 40-5+17,5=20KN.m

ED 4 – ALT B

F= 20 * 2 = 40 KN

X = 2/2 = 1m

MA = 0

(10*4) – (2*A) + (40 *1) – (10*2) = 0

A= 30kN

ΣFy = 0

A + By -10-10- 40 = 0

By = 30 kN

(S1)

ΣFx = 0

N = 0

ΣFy = 0

-10 – V = 0 => V = -10

ΣM. = 0

M = 0

(S2)

ΣFx = 0

N = 0

ΣFy = 0

-10 –V = 0 => V=-10

ΣM. = 0

M – (10*2) = 0 => M = 20

(S3)

ΣFx = 0

N =0

ΣFy = 0

-V – 10 + 30 = 0 => V =20

ΣM. = 0

M – (10*2) = 0 => M=20

(S4)

ΣFx = 0

N = 0

ΣFy = 0

V=0

ΣM. = 0

M = (40*1) – 30 = 10

(S5)

ΣFx = 0

N = 0

ΣFy = 0

V – 10 + 30 -30 = 0

V = 10

ΣM. = 0

M= 10*2 = 20

(S6)

ΣFx = 0

N = 0

ΣFy = 0

-V = -10 => V=10

ΣM. = 0

M=0

ED 5 – ALT A

Somatória de forças na horizontal:

10+15-HB=0

HB=25KN

Somatória de forças na vertical:

VA+ VB-40-10=0

VA+VB=50KN

Somatória de momentos:

10*2-5-40*1+VB*2-40=0

20-5-40-40+VB*2=0

VB=(-20+5+40+40)/2

VB=32,5KN

VA=50-VB

VA=50-32,5

VA=17,5KN

CALCULOS

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