Distributed LoadingWhat is a Distributed Load? • A load applied across a length or area instead of at one pointAnalyzing Distributed Loads • A distributed load can be equated with a concentrated load applied at a specific point along the barGeometry Method • The magnitude of the resultant force is equivalent to the area under the curve of the distributed load 10 kN/m 1 m 3 m 2 m kNFmmkNhbFrr303*10*Geometry Method • The location of the resultant force is at the center of mass of the distributed load. 10 kN/m 1 m 3 m 2 m mxmmbxx5.23*2112102.5 m 30 kNGeometry Method – Example • For a triangular distributed load, the magnitude of the resultant force is the area of the triangle, ½*b*h 5 kN/m kNFmmkNhbFrr104*5*5.*214 m 4 mGeometry Method – Example • For a triangular distributed load, the location of the resultant force is 1/3 of the length of the load, from the larger end 5 kN/m 4 m 4 m mxmmbxx344*3103101.33 m 10 kNIntegral Method • The magnitude of the resultant force is given by the integral of the curve defining the force, w(x) 5 m 2 m kNFxFdxxdxxwFrmrmxmxr45.7][32)(5023502/15021)( xxw Integral Method • The location of the resultant force is given by the centroid of the area under the curve 5 m 2 m mkNxxw /)(21mxxxdxxdxxwxdxxwxmmLL0.3][45.7*5245.7)()(50255023007.45 kN 3 mIntegral Method – Example • For a vertical bar, simply integrate with respect to y instead of x mkNyyw /)(25 m 2 m kNFyFdyydyywFrmrmymyr7.41][31)(50350250Integral Method – Example • For a vertical bar, simply integrate with respect to y instead of x 3.75 m myyydyydyywydyywymmLL75.3][7.41*417.41)()(5045030041.7 kNReferences • Vector Mechanics for Engineers: Statics (Beer, 9th ed) • Distributed Load on Beams • www.engr.uky.edu/statics/Content/Chapter.../Chapter%205%20D.doc • Resolving Distributed Loads • http://pages.uoregon.edu/struct/courseware/461/461_lectures/461_lecture20/461_lecture20.html • Distributed Load on a Beam (Centroid) •
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