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SOAL No 5 September 2011
σ 1 = σ x = 70 MPaσ
2 = σ y = 65 MPaσ
3 = σ z = 55 MPa
Determine the Six Cartesian Component of stress Relatives
x y z rad x y zx' π /3 π /3 π /4 x' 1.0472 1.0472 0.7854
y'3π /4 π /4 π /2
y' 2.35619 0.7854 1.5708z' π /3 π /3 3 π /4 z' 1.0472 1.0472
2.35619
x y z x y zx' ℓ1 m1 n1 x' 0.5 0.5 0.70711y' ℓ2 m2 n2 y' -0.7071
0.70711 0z' ℓ3 m3 n3 z' 0.5 0.5 -0.7071
σ x' = σ x.ℓ 12 + σ y.m 12 + σ z.n12
+ 2τ xy. (ℓ 1.m 1) + 2 τ yz .(m 1.n1) + 2 τ xz.(ℓ 1.n1)
σ x' = 70x0.5^2 + 65x0.5^2 + 55x0.707^2
+ 0 + 0 + 061.25 MPa [ 1 ]
σ y' = σ x.ℓ 22 + σ y.m 22 + σ z.n22
+ 2τ xy. (ℓ 2.m 2) + 2 τ yz .(m 2.n2) + 2 τ xz.(ℓ 2.n2)
σ y' = 70x-0.707^2 + 65x0.707^2 + 55x0^2
+ 0 + 0 + 0
67.5 MPa [ 2 ]
TUGAS :MEKANIKA MATERIAL LANJUT
Nama : Toni Hartono BagioNIM : 3111301009
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SOAL No 5 September 2011
TUGAS :MEKANIKA MATERIAL LANJUT
Nama : Toni Hartono BagioNIM : 3111301009
σ z' = σ x.ℓ 32
+ σ y.m 32 + σ z.n3
2
+ 2τ xy. (ℓ 3.m 3) + 2 τ yz .(m 3.n3) + 2 τ xz.(ℓ 3.n3)
σ z' = 70x0.5^2 + 65x0.5^2 + 55x-0.707^2
+ 0 + 0 + 061.25 MPa [ 3 ]
τ x'y' = σ x.ℓ 1.ℓ 2 + σ y.m 1.m 2 + σ z.n1.n2
+ τ xy. (ℓ 1.m 2 + ℓ 2.m1) + τ yz .(m 1.n2 + m 2.n1) + τ xz.(ℓ
1.n2 + ℓ 2.n1)
τ x'y' = 70x0.5x-0.707 + 65x0.5x0.707 + 55x0.707x0
+ 0 + 0 + 0-1.7678 MPa [ 4 ]
τx'z' =
σx.
ℓ1.
ℓ3 +
σy.m 1.m 3 +
σz.n1.n3
+ τ xy. (ℓ 1.m 3 + ℓ 3.m1) + τ yz .(m 1.n3 + m 3.n1) + τ xz.(ℓ
1.n3 + ℓ 3.n1)
τ x'z' = 70x0.5x0.5 + 65x0.5x0.5 + 55x0.707x-0.707
+ 0 + 0 + 06.25 Mpa [ 5 ]
τ y'z' = σ x.ℓ 2.ℓ 3 + σ y.m 2.m 3 + σ z.n2.n3
+ τ xy. (ℓ 2.m 3 + ℓ 3.m2) + τ yz .(m 2.n3 + m 3.n2) + τ xz.(ℓ
2.n3 + ℓ 3.n2)
τ y'z' = 70x-0.707x0.5 + 65x0.707x0.5 + 55x0x-0.707
+ 0 + 0 + 0-1.7678 Mpa [ 6 ]
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TUGAS :MEKANIKA MATERIAL LANJUT
Nama : Toni Hartono BagioNIM : 3111301009
RESULT 61.25 -1.7678 6.25
σ ij = -1.7678 67.5 -1.7678
6.25 -1.7678 61.25
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