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The normal and shear stresses

  • Thread starter Zouatine
  • Start date
14
0
Homework Statement
Calcul of stresses
Homework Equations
1- σ'x=σx*cos(β)^2+σy*sin(β)^2+2*τxy*cos(β)*sin(β)

2- σ'y=σx*sin(β)^2+σy*cos(β)^2-2*τxy*cos(β)*sin(β)

3- τxy'=-σx*sin(β)*cos(β)+σy*sin(β)*cos(β)+τxy*(cos(β)^2-sin(β)^2)
Hi! i have this exercise and solution :

Exercise:
steel plate given in figure (a) is joined by an inclined butt weld ,the plate is subjected to tensile stresses in both x and y directions, σ(x)=54 N/mm^2 and σ(y)=38 N/mm^2 ,
1) Determine the normal and shear stresses of the butt weld.
1.PNG


this is transformation matrices :
2.PNG


2)second question :
in which direction the stress normal will be maximum ?

3.PNG


My problem: is τxy ( why in first we made it 0 in transformation matrice (and why it's 0) and in second question it's calculed .
 

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