Structural Modelling
Mathematical calculation of the deformation of a beam accounts for both bending moments and transverse shear strain. In the paper industry, timoshenko beam theory is applied to understand the stiffness and deflection of corrugated board and heavy laminates. Accuracy improves here.
This model is preferred for substrates where thickness is a substantial fraction of the span.
Engineering Principle
This approach assumes that the cross section of the beam remains plane but not necessarily perpendicular to the neutral axis after deformation. By including the shear effect, timoshenko beam theory predicts a larger deflection than the simpler euler bernoulli model. Such a distinction is relevant for sandwich structures like fluted board used in shipping boxes.
The shear deformation in the medium significantly contributes to the overall displacement of the panel.
Design Application
Packaging designers use these equations to determine the load bearing capacity of a container. It allows for the optimization of the flute height and the liner weight to prevent collapse during stacking. Timoshenko beam theory helps in predicting the failure point of a carton under vertical compression.
This prevents over engineering, which saves material and reduces transportation costs. The model is a staple in the software used to certify the performance of corrugated packaging.
