The Strain menu
Figure 1. The Strain
commands
To visualize the strain field over the cross-section of a beam, the following steps must be completed first.
- Load the problem you want to run and perform the finite element analysis, and
- Select a static loading case.
Once these steps are completed, you are ready to visualize the strain field. Select the menu Strain, to reveal the options shown in fig. 1. If you prefer to list the components of the strain tensor for one single element of the model, use the commands under the Element menu.
The strain field
The strain field comprises six strain components, which can be divided into two groups.
- The out-of-plane strain components. The axial strain component, ε_{11} (x_{2}, x_{3}), the two transverse shear strain components, γ_{12} (x_{2}, x_{3}) and γ_{13} (x_{2}, x_{3}).
- The in-plane strain components. The two in-plane direct strain components ε_{22} (x_{2}, x_{3}) and ε_{33} (x_{2}, x_{3}), and the in-plane shear strain component γ_{23} (x_{2}, x_{3}).
The usual sign conventions are used for these various strain components. Note that in Euler-Bernoulli beam theory, all strain components are assumed to vanish, except for the axial strain component, ε_{11}, which is assumed to vary linearly over the cross-section. Timoshenko beam theory relaxes these assumptions by allowing non-vanishing values for the two transverse shear strain components, γ_{12} and γ_{13}, that are uniformly distributed over the cross-section.
Visualization of the axial strain field (Strain→Axial strain)
Command Strain→Axial strain represents the axial strain field, ε_{11}(x_{2}, x_{3}), by a set of vectors pointing in the direction normal to the plane of the cross-section. The length of each vector is proportional to the magnitude of the axial strain component, ε_{11}, at that point. This option depicts the axial strain component only; the other strain components are ignored.
Figure 1. Distribution of axial strain over an L-sectionFigure 2. Distribution of axial strain over a T-section
Figure 1 shows the distribution of axial strain, ε_{11}, over an L-section subjected to a bending moment M_{2}. Figure 2 shows the distribution of axial strain, ε_{11}, over a T-section subjected to a bending moment M_{3}. Because the axial strain vector acts in the direction normal to the plane of the cross-section, it was necessary, in both cases, to rotate the cross-section using the Graphics→Rotate commands.
If the lengths of the strain vectors are too long or too short, use the Graphics→Data size + or Graphics→Data size - commands to adjust their length appropriately.
Visualization of the shear strain field (Strain→Shear strain)
Command Strain→Shear strain represents the transverse shear strain vector field, γ_{12} b_{2} + γ_{13} b_{3}, by a set of vectors pointing in the plane of the cross-section. The length of each vector is proportional to the magnitude of the transverse shear strain vector, √ γ_{12}^{2} + γ_{13}^{2}, at that point. This option depicts the transverse shear strain components only; the other strain components are ignored.
Figure 3. Distribution of shear strain over an I-sectionFigure 4. Distribution of shear strain over a triangular section
Figure 3 shows the distribution of transverse shear strain, γ_{12} b_{2} + γ_{13} b_{3}, over an I-section subjected to a torque M_{1}. Figure 4 shows the distribution of axial strain, γ_{12} b_{2} + γ_{13} b_{3}, over a triangular section subjected to a torque M_{1}. Because the transverse shear strain vector acts in the plane of the cross-section, it was not necessary, in either cases, to rotate the cross-section.
If the lengths of the strain vectors are too long or too short, use the Graphics→Data size + or Graphics→Data size - commands to adjust their length appropriately.
Visualization of individual strain components
Individual strain components of the strain field, ε_{11}, ε_{22}, ε_{33}, γ_{23}, γ_{13}, and γ_{12} can be visualized by invoking commands Strain→Epsilon_11, Strain→Epsilon_22, Strain→Epsilon_33, Strain→Gamma_23, Strain→Gamma_13, and Strain→Gamma_12, respectively.
When visualizing individual strain components, the strain field is represented through color mapping: the magnitude of the strain components is associated with a given color select from a color palette. This representation depicts one strain component only; all other strain components are ignored.
Figure 5. Shear strain component γ_{13} over a rectangular sectionFigure 6. Shear strain component γ_{13} over a circular tube with fins
Figure 5 shows the distribution of strain component γ_{13} over a rectangular section subjected to a shear force F_{3}. Figure 4 shows the distribution of strain component γ_{13} over a circular tube with fins subjected to a shear force F_{3}.