Structural similitude and scaling laws for sandwich beams

Abstract

Problems associated primarily with structural similitude as applied to sandwich beams and columns are investigated. Similitude theory is employed to develop the necessary similarity conditions or scaling laws. Scaling laws provide the relationship between a full-scale structure (prototype) and its scaled down model. These relationships can be used to design the small-scale model and to extrapolate the experimental data of the model to predict the behavior of the large prototype. Note that scaled down models are inexpensive and easily tested. The developed methodology is demonstrated through analysis of the bending of sandwich beams subjected to transverse loads, and it is totally analytical. A small model is designed and theoretically analyzed. The theoretically obtained responsepredictions are treated as if they wereexperimentally obtained (from model testing ). Then, scaling laws are used with the model data to predict the behavior of the large prototype. Finally, these predictions are compared to the theoretically obtained response of the prototype to test the validity of the method. Predicted and theoretical response is very close, and therefore, the demonstration is successful. Both complete (satisfaction of all similarity conditions) and partial similarity are discussed. Nomenclature bwk = width of panel ck = thickness of the core dtk;dbk = thickness of the upper and the lower skin, respectively EAtk;EAbk = longitudinal rigidities of the upper and the lower face, respectively Eck; Gck = vertical modulus of elasticity of the core and its shear modulus, respectively EIk = e exural rigidity of beam EItk;EIbk = e exural rigidities of upper and lower faces, respectively k = p or m, where p refers to the prototype and m to the model