 Ch 7. Centroid/Distributed Loads/Inertia Multimedia Engineering Statics Centroid: Line Area Vol Centroid: Composite Distributed Loads Area Moment of Inertia
 Chapter 1. Basics 2. Vectors 3. Forces 4. Moments 5. Rigid Bodies 6. Structures 7. Centroids/Inertia 8. Internal Loads 9. Friction 10. Work & Energy Appendix Basic Math Units Sections Search eBooks Dynamics Statics Mechanics Fluids Thermodynamics Math Author(s): Kurt Gramoll ©Kurt Gramoll STATICS - CASE STUDY SOLUTION Rail Subparts Rail Dimensions The beam cross section can be broken into 4 composite parts consisting of 3 rectangles and a triangle as shown. Orient an axis system as shown, so that the cross section lies entirely in the x-y plane. Since the thickness is constant for all the parts, the centroid can be found using the area equations, Composite Part 1 Part 1 Part 1 is a rectangle with an area of      A1 = (2)(3) = 6 cm2 The centroid of a rectangle lies at half its width and half its height, so for part 1 Composite Part 2 Part 2 Part 2 is a rectangle with an area of      A2 = (16)(2) = 32 cm2 Its centroid is located at Composite Part 3 Part 3 Part 3 is a rectangle with an area of      A3 = (2)(10) = 20 cm2 Its centroid is located at Composite Part 4 Part 4 Part 4 is a triangle with an area of      A4 = (0.5)(4)(4) = 8 cm2 The centroid of a right triangle is located two-thirds of the distance from the vertex to the other end; therefore, for part 4 Centroid of Total System Total System With these results, find the total area of the system is Substituting the areas and centroid locations for each of the individual parts into the first two equations gives  Practice Homework and Test problems now available in the 'Eng Statics' mobile app
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