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Stress and Strain

6 tools in the Structures area.

Mohr's Circle

Mohr's circle for plane stress, plane strain and a general three-dimensional stress state: the centre and radius, the principal stresses or strains with both principal directions, the maximum in-plane shear with its planes and the average normal stress on them, the absolute maximum shear from the three circles (the free-surface stress is zero in plane stress, the out-of-plane strain is zero in plane strain), the components on an element rotated through an entered angle by the transformation equations written out with the substituted numbers, and the von Mises and Tresca equivalent stresses. The three-dimensional case gives the stress invariants, the characteristic cubic solved in closed form and by Jacobi iteration, the principal direction cosines, the three circles and the octahedral stresses. Mohr's circle and the given and rotated elements are drawn to scale. The default case is Example 9.3 of Hibbeler's Mechanics of Materials (σx = −20 MPa, σy = 90 MPa, τxy = 60 MPa), whose printed principal stresses and directions the page reproduces.

1 worked example reproduced, listed on the tool page.

Strain Transformation 2D

Calculates the engineering and principal strain values and directions given the strain components and rotation angle. Also outputs stresses if moduli are known.

Strain Gage to Strain State

Calculates the engineering and principal strain values and directions given the strain values of a rossete strain gage. Also outputs stresses if moduli are known.

Stress to Strain 3D

Calculates the engineering and principal strain values and directions given the three-dimensional stress components.

Strain to Stress 3D

Calculates the stress components and principal stress values given the three-dimensional strain components measured in microstrain.

Linear to True Stress

The following analysis produces an estimated local stress and strain from an elastic point stress using the Neuber and Glinka methods and a weighted Unified Estimate between them. This is useful in predicting a peak stress and strain in a high gradient area from a linear finite element (FE) analysis. This method allows an estimate of an true stress and strain at a stress concentration without having to run a material nonlinear FE analysis.

Other Structures sections

Materials · Composites · Frames and Trusses · Beams · Loads and Dynamics · Joints · Stability · Plates and Shells · Thin-Walled Structures · Contact · Stress Concentrations · Fatigue · Damage Tolerance