Isostatic lines define the directions of principal stress to visualize the stress trajectories in beams and other elements. Isostatic lines can be defined by experimentally by photo-elastic model simulation or graphically by Mohr’s circle.
1 Simple beam with a square marked for investigation
2 Free-body of square marked on beam with shear stress arrows
3 Free-body square with shear arrows divided into pairs of equal effect
4 Free-body square with principal stress arrows (resultant shear stress vectors)
5 Free-body square rotated 45 degrees in direction of principal stress
6 Beam with isostatic lines (thick compression lines and thin tension lines)
Under gravity load beam shear increases from zero at mid-span to maximum at supports. Beam compression and tension, caused by bending stress, increase from zero at both supports to maximum at mid-span. The isostatic lines reflect this stress pattern; vertical orientation dominated by shear at both supports and horizontal orientation dominated by normal stress at mid-span. Isostaic lines appear as approximate tension “cables” and compression “arches”.