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Evaluate the stiffness matrix for the CST element shown below. Co-ordinates are given in mm. Assume plane stress condition. Thickness 10mm, E = 200 GPa nd v = 0.3


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E=200GPa, v=0.3, t=10mm
Now x1,y1=10,20
x2,y2=70,20
x3,y3=40,60

β1=y2y3=2060=40
β2=y3y1=6020=40
β3=y1y2=2000=0

γ1=(x2x3)=(7040)=30
γ2=(x3x1)=(4010)=30
γ3=(x1x2)=(1070)=60

2A=|1x1y11x2y21x3y3|=|110201702014060|

=1(70604020)10(6020)+20(4070)
=3400400+(600)
2A=2400mm2

[B]=12A[β10β20β300γ10γ20γ3γ1β1γ2β2γ3β3]

[B]=12400[4004000003003006030403040600]

[B]=[0.016700.016700000.012500.012500.0250.01250.01670.01250.01670.0250]

[B]T=[0.016700.012500.01250.01670.016700.012500.01250.0167000.02500.0250]

Plane-Stress condition,
[D]=E1v2[1v0v10001v2]

E=200GPa=2103N/mm2,v=0.3

[D]=210310.32[10.300.3100010.32]

[D]=1.99103[10.300.310000.35]

v=tA=1024002=12000mm2

Stiffness matrix [K] is given by,

[K]=[B]T[D][B]tA

[K]=1.991031200[0.016700.012500.01250.01670.016700.012500.01250.0167000.02500.0250][10.300.310000.35][0.016700.016700000.012500.012500.0250.01250.01670.01250.01670.0250]

[K]=106[0.8768000000.35710.668500000.58840.02750.87680000.02750.15570.35710.6685000.28850.38460.28850.38460.576900.32970.82420.37970.824201.6464]

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