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The video tutorial introduces the concept of consolidation settlement and how to calculate it by first examining the stresses on a bar. The stress-strain relationship assumes a linear elastic relationship, with stress equal to the modulus of elasticity times strain. The strain is also equal to the change in length over the initial length, so the change in length can be calculated as the initial length times the ratio of stress over the modulus of elasticity. This relationship is then applied to a more complex case involving a bar.