### STRUCTURES - PRINCIPLE STRESS

**Isostatic lines**

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)

**Note:**

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”.

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