Atps resmat2 etapa 1 a 3

ATPS- Resistência dos Materiais
Etapa 1. σx = 40 Mpa σy = 0 σxy = 30 Mpa
Passo1.

σx = -40 Mpa σy = 80 Mpa σxy = 60 Mpa σx’ = (σx + σy/2) + (σx - σy/2)* cos 2*θ + Txy * sen 2*θ σx’ = (40 + 0/2) + (40 - 0/2)* cos 2*40 + 30 * sen 2*40 σx’ = 53,0171 Mpa
Tx’y’ = (σx - σy/2)* sen 2*θ + Txy* cos 2*θ
Tx’y’ = (40 - 0/2)* sen 2*40 + 30* cos 2*40
Tx’y’ = 24,90 Mpa

Passo 2,3 e 4.

X’
50°

σx’ = (σx + σy/2) + (σx - σy/2)* cos 2*θ + Txy * sen 2*θ σx’ = (-40 + 80/2) + (-40 - 80/2)* cos 2*(-30) + 60 * sen 2*(-30) σx’ = -61,96 Mpa
Tx’y’ = (σx - σy/2)* sen 2*θ + Txy* cos 2*θ
Tx’y’ = (-40 - 80/2)* sen 2*(-30) + 60* cos 2*(-30)
Tx’y’ = -21,96 Mpa

-61,96 Mpa
-21,96 Mpa

30°
X’

Etapa 2 : σx = -80 Mpa σy = -110 Mpa τxy = 70 Mpa

Passo 1 σmax/min = σx+σy2 ± √ (σx- σy2)2 + τxy2 σmax/min = -80+(-110)2 ± √ (-80-(-110)2)2 + 702 σmax = -95 + 71,58 ► -23,41 Mpa σmin = -95 – 71,58 ► -166,58 Mpa

Tg 2 θp = 2*τxyσx-σy
Tg 2 θp = 2*70-80-(-110)
Tg 2 θp = 140 / 30
2 θp = 77,90̊
.θp = 38,95̊
.θp = 38,95̊ + 90̊ = 128,95̊

Passo 2, Passo 3
Tg 2 θc = σx- σy2*τxy
Tg 2 θc = -80-(-110)2*70
2 θp = -12,09
.θp = -6,047̊
.θp = -6,047̊ + 90̊ = 83,95̊

τmax = √ (σx- σy2)2 + τxy2 τmax = √ (-80-(-110)2)2 + 702 τmax = 71,58 Mpa σmed = σx+σy2+σx- σy2*cos2θ+τxy*sen2θ σmed = -80+(-110)2+-80-(-110)2*cos-12,095+70*sen*(-12,095) σmed = -95 Mpa

Passo 3
Passo 4

Passo 4 σmax τ y σ x σmin τmin τmax X = (σx ,τxy) ► (-80 , 70)
Y = (σy ,τxy) ►(-110 , 70)
C = (σx+σy2 , 0) ► (-80+(-110)2 , 0)►(-95 , 0)
R = (-80-(-95))2+ 702► 76,16 Mpa σmax = σmed + R ► -95 + 71,58 ► -23,42 Mpa σmin = σmed – R ► -95 – 71,58 ► -166,58 Mpa σ = σmed ►-95 Mpa

σx = -150 Mpa σy = 30 Mpa τxy = -80 Mpa

σmax/min = σx+σy2 ± √ (σx- σy2)2 + τxy2 σmax/min = 150+302 ± √ (150-302)2 + (-80)2 σmax = 90 + 100 ► 190 Mpa σmin = 90 – 100 ► -10 Mpa

Tg 2 θp = 2*τxyσx-σy
Tg 2 θp =