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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.

  Submitted by Bractals    
Rating: 3.0000 (1 votes)
Solution: (Hide)
Label the joints from A to B as A=J1, J3, J5, ... ,J2n+1=B.
Label the joints from D to C as D=J2, J4, J6, ... ,J2n+2=C.

If we look at the joints in the order J1, J2, J3, ... ,J2n we can easily calculate
the forces as
     Strut           Force         Type

     J2k-1J2k+1        (2k-1)S       Compression
     J2k-1J2k          2S            Tension
     J2kJ2k+1          2S            Compression
     J2kJ2k+2          2kS           Tension

     where S = W√3/3 and k = 1, 2, 3, ... , n.
The largest compression and tension forces are in the horizontal struts nearest the wall.
Therefore, for these to fail at the same time, we must have
     C = (2n-1)S  and  T = 2nS

                or

     C/T = (2n-1)/(2n)
Thus, for n = 25, C/T = 0.98

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: Am interested in learningKenny M2010-02-28 21:21:46
SolutionHarry2010-02-28 00:01:00
Am interested in learningDej Mar2010-02-27 21:07:48
SolutionBractals is correctKenny M2010-02-27 16:53:11
re: Soultion (spoiler)Bractals2010-02-27 06:35:01
SolutionSoultion (spoiler)Kenny M2010-02-26 22:39:04
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