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MSU ME 221 - Lecture 08

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PowerPoint PresentationHomework #3Homework #4Quiz #4Slide 5Centroid of Composite BodiesArea CentroidsMay Also Use SubtractionComposite Centroid of an AreaComposite Centroid of a VolumeExamplesSlide 12BeamsEquivalent Load LocationExampleSlide 16ME221 Lecture 8 1ME 221 StaticsLecture #8Section 4.5-4.6ME221 Lecture 8 2Homework #3•Chapter 3 problems:–48, 55, 57, 61, 62, 65 & 72•Chapter 4 problems–2, 4, 10, 11, 18, 24, 39 & 43–Due TodayME221 Lecture 8 3Homework #4•Chapter 4 problems:–52 & 54•Chapter 9 problems–2, 11 & 32–Due Monday, June 14•MatLab Group Problems–4.13 – plot as a function of R with 0º < α < 45º–4.51 – plot as a function of l–4.60 – plot the equivalent force and point of action–Due Monday, June 14ME221 Lecture 8 4Quiz #4•TodayQuiz #5•Wednesday, June 16ME221 Lecture 8 5Last Lecture:•Centroids of Areas & VolumesME221 Lecture 8 6Centroid of Composite Bodies•Basic shapes are added together to get the composite centroid–We look these up in Table 4.2–This table will be supplied on future exams for shapes other than rectangles, circles and trianglesME221 Lecture 8 7Area CentroidsThis case is also representative of line and volume centroids.Divide total area into simple shapes (rectangles, semi-circles)Add simple shapesxyxcyc+ +=x3y3A3y2x2A2y1x1A1ME221 Lecture 8 8May Also Use Subtractionxyxcyc=-y2x2A2y1x1A1ME221 Lecture 8 9Composite Centroid of an Area•Geometric center of the area–Summation of the pieces (holes are negative)–Where:iiic AxAx1iiic AyAy1iiAAME221 Lecture 8 10Composite Centroid of a Volume•Geometric center of the volume–Average of the first moment over entire volume–Where:iiicVxVx1iiicVyVy1iiVViiic VzVz1ME221 Lecture 8 11ExamplesME221 Lecture 8 12Distributed Loads•Distributed loads on beams–Application of equivalent loadME221 Lecture 8 13BeamsBeams can be loaded by a point load or a distributed loadPw(x)Replace the distributed load with an equivalent concentrated force.xdxLThe equivalent force is the sum of all the forces. 0LW w x dxME221 Lecture 8 14Equivalent Load LocationThe equivalent load is placed at the centroid of the distributed load.w(x)xcL 01Lcx x w x dxWTo find reaction loads: replace distributed load with equivalent load at centroidWME221 Lecture 8 15ExampleME221 Lecture 8 16Quiz


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