8aex. Stress Transformation Examples • Ex. 8a.1 • Ex. 8a.2 
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Step 2. The Stress Transformation Equations are: Here, s_{y} and t_{xy} are both zero, so the equations simplify to: s_{x'} = 0.5 s_{x}(1+cos2q)
= stress normal to weld Or, the normal and shear stresses acting on the weld are: s_{w} = 3.75 MPa, t_{w} = 2.17 MPa 

s_{x'} + s_{y'} = s_{x} + s_{y} = 3.75 MPa + 1.25 MPa = 5.00 MPa 
s_{x'} = 13.2 ksi, s_{y'} = 16.8 ksi, t_{x'y'} = 6.83 ksi 

Step 2. Principal Stresses and Principal Angles. The Principal Stresses are:
and occur at angles rotated byq_{p}: For the element: s_{I} = 22.1 ksi at q_{I} = 67.5° s_{II} = 7.93 ksi at q_{II} = 113°  
Step 3. Maximum Shear Stress. The Maximum InPlane Shear Stress is: and act on element faces that have outward pointing vectors rotated by q_{s} from the xaxis: Thus: t_{max,1} = 7.07 ksi on face: q_{s,1} = 22.5° t_{max,2} = –7.07 ksi on face: q_{s,2} = 113° s_{s,x} = _{ }s_{s,y } = _{ }s_{ave } = 15 ksi A positive t_{max} means the shear stress causes a counterclockwise rotation on the face defined by q_{s}. ... the shear stress on the x_{s} face is positive. A negative t_{max} means the shear stress causes a clockwise rotation on the face defined by q_{s}... the shear stress on the x_{s} face is negative. 

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