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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

     
   
 
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