Recall the formulas that describe flexure and shear stresses in beams.
We will use these to determine the stress state at various locations in a beam. The next step will be to determine the principal stresses and maximum shear stresses at these locations.
These stresses are used to design against failure.
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principal-stress trajectory plots
show directions of the principal stresses
Do these look familiar?
Is there a similarity to plant growth?
stress contour plots
show curves of equal principal-stress magnitudes
Normal Stress Shear Stress 
σ = My/I
τ = VQ/Ib
Principal 1 Principal 2 Max Shear 1 Max Shear 2 Max Shear 3
Average Normal Stress Mises Stress 
