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 Cantilever Structure (Posted on 2010-02-26)

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 learning Kenny M 2010-02-28 21:21:46 Solution Harry 2010-02-28 00:01:00 Am interested in learning Dej Mar 2010-02-27 21:07:48 Bractals is correct Kenny M 2010-02-27 16:53:11 re: Soultion (spoiler) Bractals 2010-02-27 06:35:01 Soultion (spoiler) Kenny M 2010-02-26 22:39:04
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