Meriam, Kraige & Bolton — Statics of Particles: Problem 2_111

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/111 The steel H-beam is being designed as a column to support the two vertical forces shown. Replace these forces by a single equivalent force along the vertical centerline of the column and a couple M. Problem 2/111 1. Analysis of Forces and Position Vectors First, we define a right-handed coordinate system based on the diagram provided. The -axis is the vertical centerline of the H-beam column, with the positive direction pointing upwards. The -axis lies in the plane of the web, and the -axis is perpendicular to the web. The origin is located at the center of the beam's cross-section. The two given vertical forces are: acting downwards. In vector form: . acting downwards. In vector form: . Based on the dimensions given in the figure: Force is applied at a point from the -axis in the negative -direction and from the -axis in the positive -direction. Its position vector is: Force is applied at a point from the -axis in the positive -direction and from the -axis in the negative -direction. Its position vector is: 2. Calculate the Resultant Force The single equivalent force acting along the vertical centerline is the vector sum of the individual forces: ● Calculation Process 1. Final Formula: z xy O F = 1 100 kipsF = 1 −100k kips F = 2 150 kipsF = 2 −150k kips F 1 6 in.yx 3 in.xy r = 1 −6i+3j in. F 2 6 in.yx 6 in.xy r = 2 6i−6j in. R R=F=∑F + 1 F 2 2. Substitute Values: 3. Final Calculation: The resultant force is acting verticall