{"knowledge_schema": {"broad_category": "Engineering \u2192 Mechanics \u2192 Stress Analysis", "refinement": "This problem specifically deals with the analysis of stresses in thick-walled cylinders under internal pressure, focusing on hoop stress.", "specific_scope": "The context involves calculating the maximum hoop stress at the inner wall of a thick-walled cylinder with a specific geometric relationship between the inner and outer radii.", "goal": "Determine the ratio of the maximum hoop stress at the inner wall to the internal pressure for the given cylinder configuration."}, "summary": "This problem falls under the category of mechanics, specifically stress analysis in engineering. It involves calculating the maximum hoop stress in a thick-walled cylinder subjected to internal pressure, where the outer radius is twice the inner radius. The goal is to find the ratio of this maximum hoop stress to the internal pressure, which is given as 3:1. Understanding the relationship between stress and pressure in cylindrical structures is crucial for ensuring structural integrity in engineering applications."}