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The video introduces the concepts of consolidation settlement calculations by first examining stresses on a bar. The stress-strain relationship is explored, assuming a linear elastic relationship with the modulus of elasticity (E). Stress is equal to the modulus of elasticity multiplied by the strain, and strain is equal to the change in length over the original length. For a more complex case, the video analyzes a bar with initial length L naught and applies stress to determine the changes in length.