S11 = σ x = -4343,86

S22 = σ y = -11759,805

S12 = τ xy = 14216,797

C = σx+σy2 =

(−4343.86 )+(−11759.81)2

= -8051.83

R = √( σx−σy2 )2

+σ2 xy = √( (−4343.86 )−(−11759.81)2 )

2

+(14216.797)2

= 14692,39

σ max=C+R = -8051.83 + 14692,39 = 6640,56

σ min=C−R = -8051.83 - 14692,39 = -22744,22

2 p = arctanx 2x τ xyx− y = arctanx

2 x (14216.797)(−4343.86 )−(−11759.81)

2 p = 75.38⁰ = 180⁰ - 75.38⁰ = -104.62⁰

2 s = - arctanx x− y2x τ xy = - arctanx

(−4343.86 )−(−11759.81)2 x (14216.797)

2 s =-14.62⁰ = 180⁰ -14.62⁰ = 165.38⁰

σ n=C+Rcosβ = -8051.83 + 14692,39 cos 75.38⁰ = -4343.86

τ nt=Rsinβ = 14692,39 sin 75.38⁰= 14216.80

S11 = σ x = 11161,323

S22 = σ y = 1266.522

S12 = τ xy = -4374,253

C = σx+σy2 =

(11161,323 )+(1266.522)2

= 6213,92

R = √( σx−σy2 )2

+σ2 xy = √( (11161,323 )−(1266.522)2 )

2

+(−4374,253)2

= 6603,85

σ max=C+R = 6213,92 + 6603,85= 12817,77

σ min=C−R = 6213,92- 6603,85= -389,93

2 p = arctanx 2x τ xyx− y = arctanx

2 x (−4374,253)(11161,323 )−(1266.522)

2 p = -41.48⁰ = 180⁰ -41.48⁰ = -138.52⁰

2 s = - arctanx x− y2x τ xy = - arctanx

(11161,323 )−(1266.522)2 x (−4374,253)

2 s =-131.48⁰ = 180⁰ -131.48⁰ = 48.52⁰

σ n=C+Rcosβ = 6213,92 + 6603,85 cos 41.48⁰ = 11161.32

τ nt=−Rsinβ = -6603,85 sin 41.48⁰= -4374.25

S11 = σ x = 56859,21

S22 = σ y = 1555,47

S12 = τ xy = -77,772

C = σx+σy2 =

(56859,21 )+(1555,47)2

= 29207.34

R = √( σx−σy2 )2

+σ2 xy = √( (56859,21 )−(1555,47)2 )

2

+(−77,772)2

= 27651.98

σ max=C+R = 29207.34 + 27651.98= 56859.32

σ min=C−R = 29207.34 - 27651.98= 1555.36

2 p = arctanx 2x τ xyx− y = arctanx

2 x (−77,772)(56859,21 )−(1555,47)

2 p = -0.16⁰ = 180⁰ -0.16⁰ = 179.84⁰

2 s = - arctanx x− y2x τ xy = - arctanx

(56859,21 )−(1555,47)2 x (−77,772)

2 s =-90.16⁰ = 180⁰ -90.16⁰ = 89.84⁰

σ n=C+Rcosβ = 29207.34 + 27651.98 cos 0.16⁰ = 56859.21

τ nt=−Rsinβ = -27651.98 sin 0.16⁰= -77.77