Lecture Notes
Page 1 of 3
Maximum Stresses in Beams
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.
principal-stress trajectory plots
show directions of the principal stresses
Do these look familiar?
Is there a similarity to plant growth?
https://classes.mst.edu/civeng2210/concepts/12/principal/maximum/index.html
12/04/2021
Lecture Notes
Page 2 of 3
stress contour plots
show curves of equal principal-stress magnitudes
Normal Stress
Shear Stress
σ = My/I
Principal 1
Principal 2
Max Shear 1
Max Shear 2
Average Normal Stress
Mises Stress
τ = VQ/Ib
Max Shear 3
https://classes.mst.edu/civeng2210/concepts/12/principal/maximum/index.html
12/04/2021
Lecture Notes
Page 3 of 3
https://classes.mst.edu/civeng2210/concepts/12/principal/maximum/index.html
12/04/2021