Elastic tension of non-planar strips with asymmetric out-of-flatness for the biquadratic law of stress distribution over the width

The dependencies establishing the relationship between the tensile stresses, maximum stresses, and parameters of asymmetric out-of-flatness of strips during elastic tension for the biquadratic law of stress distribution over the width have been obtained. A comparative analysis of the obtained dependences with those known for the quadratic law of stress distribution is performed. The obtained dependencies allow the stresses and parameters of out-of-flatness to be calculated more accurately in case of partial concealment of a defect in the stretched strip and, accordingly, its treatment modes to be adjusted (for example, during drawing, hot-dip galvanizing, and continuous annealing). A more accurate calculation of the maximum stresses along the width, taking into account the asymmetry of the defect, makes it possible to reduce the probability of strip breakage and stabilize the technology of their production. The obtained dependencies can be applied in automatic flatness control systems for the production of cold-rolled strips.