Stress Trajectories


Stress trajectories, or more accurately principal stress trajectories or even principal stress resultant trajectories, provide a useful way in which engineers can visualise stress fields which are, by dint of them being second order tensors, somewhat complicated to visualise in a single image. The usual way of presenting stress fields in a graphical fashion is through contour plots of a particular component, principal quantity or equivalent stress like the von Mises stress, or through principal stress vectors or crosses emanating from particular points in a model.

Principal stress trajectories may be considered as a more complete form of a principal stress vector plot in that a series of mutually parallel or orthogonal lines are produced representing the directions of the principal stresses at a particular point in the model. The magnitude of the stress can be indicated in a number of ways, e.g., by colour, by line thickness or by distance above the surface. Of course, all three methods could be combined.

In engineering, particularly structural engineering with reinforced concrete structures, the design of reinforcement is greatly aided by presenting the stress field in the form of principal stress trajectories. For plate membrane problems, trajectories can be used to help identify strut and tie forms of reinforcement and for plate bending problem the principal moment trajectories are of great value in determining an optimal reinforcement layout.


Angus Ramsay
Edward Maunder

Plate Membrane Trajectories

Principal stress trajectories for plate membrane problems enable design engineers to form appropriate strut and tie models and therefore design suitable reinforcement for a reinforced concrete structure.

Plate Bending Trajectories

Principal moment trajectories for plate bending problems offer engineers insight into the reinforcement required for a reinforced concrete slab and, therefore, the ability to perform either manual, or automatic, optimisation of the reinforcement layout.

Useful Links

Publication: Visualisation of stress fields - from stress trajectories to strut and tie models.
Wikipedia: Stress-Strain Analysis