- Oct 18, 2003
- Saline Michigan
This is just the first part of doing composites, and it is a useful exercise to go through and learn from, but it can give big errors in strength.Useful video
Let's discuss the limitations of this simplified version:
When you convert the width of the various materials to correct for E in them, you are correcting for E perpendicular to the cross section. In steel and concrete, that is OK because the E changes the same in all directions. In wood and in unidrectional composites, that is WAY OFF, and significant errors will result in actual strains and FOS;
There is no attempt in this method to calculate or account for strain induced perpendicular to the long axis of the beam (in the plane of the cross section), and it matters, as that also loads the lamina (steel caps here) and the wooden core and the bond lline between them, which will also be subject to failure;
The large widths compared to thicknesses also produced some other fundemental errors in strain state and stresses, even in a homogenous plate. Plate and shell theories were developed to take into account the attemps by the materials to change width when length is changed under loads. This model does not attempt to consider the plate theory issues;
In fiber and matrix composites, the E's of the materials in the plane of the cross section are generally hugely different from the E's perpendicular to the cross section, and so would have to corrected differently. These differences in on-axis strain and perpendicular-axis strain generally further strains the lamina and increases the shear stresses both within and between the lamina;
These failures of simple composite theory to adequately model fiber and matrix composites and to model plates were significant - things were not behaving as modeled and were failing at lower loads than expected. This provided the incentive to develop plate theory and composite plate theory.
I have an intro coming, still editing. It will have its own thread.