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Cantilever Structure (Posted on 2010-02-26) Difficulty: 3 of 5

The cantilever structure shown in the figure consists of 4n-1 struts of the same length plus one that is half that length. Each strut can handle a maximum tension force T before it will snap and a maximum compression force C before it will buckle. The structure is connected to a wall at points B and C. A weight W is attached at point A. The weight W is increased until two struts fail - one from tension and the other from compression.

What is the value of the ratio C/T if n = 25?

Consider the struts as weightless.

See The Solution Submitted by Bractals    
Rating: 3.0000 (1 votes)

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Am interested in learning | Comment 4 of 6 |
As I have had no formal training in engineering I had to do some research.
Of the cantilever structure, a cantilevered truss, the segments along the top chord DC are not struts (segments bearing the compressional forces), but ties (segments bearing the tensile forces). The segments of the bottom chord DC are struts. The members of the webbing, AD and those segments parallel to it would be ties, sharing the force of the tension created by the weight W; with the other members of the webbing being struts.
I do not know how much of the tensile and compressional forces are applied to the the wall to which segment BC spans. Perhaps Bractals will explain, in comment and/or solution, the forces, the values of each of these forces, and the equations used to calculate the values.

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In regards to the first segment along the bottom chord, a question arises. Is it a tie or a strut? That is, due to the angle in which force of the weight W is applied to the cantilever structure, would the force of compression be greater than the tensile force? And, how much compressional force is transferred to the remaining segments along the bottom chord, as these would also have the tensile force leveraged from the weight?

Edited on February 27, 2010, 10:15 pm
  Posted by Dej Mar on 2010-02-27 21:07:48

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