Identifying Stress in Three Rods: A Practical Approach

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Homework Help Overview

The discussion revolves around identifying stress in three rods under a load, focusing on the deformation and load distribution among the rods. The subject area includes mechanics of materials and structural analysis.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore different methods to calculate the load and stress in the rods, questioning the assumptions about load distribution and deflection. Some suggest calculating the load for a specific deflection and analyzing the strain in each column based on displacement.

Discussion Status

The discussion is active, with participants sharing various approaches and confirming the effectiveness of one suggested method. There is a collaborative atmosphere as participants build on each other's ideas without reaching a definitive conclusion.

Contextual Notes

Participants note the importance of understanding the load distribution and the implications of deflection on stress calculations. There is mention of specific deflection values that influence the analysis.

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Homework Statement



See attached - not the yellow engineering paper.


Homework Equations



PL/AE = deformation


The Attempt at a Solution



See attached


I can't figure out what the heck I'm doing wrong - my work is a little scattered because I was kind of thinking while doing it...
 

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Looks like the outside columns equally support the portion of the load up to the point where their deflections equal 0.3 mm. Calculate what that load is for that deflection, and the stress in the outside columns (no stress or deflection in the interior column) under that load. Then the remainder of the load will be divided equally amongst the 3 columns.
 
Another way of doing it is to let the displacement of the top cap be x downwards.

Then assuming all the columns take some load, the strain in the end posts is x/125 and the strain in the middle post is (x-0.3)/125. Find the force in each column corresponding to the strain, and get an equation for x by saying the forces in the 3 columns sum to the total load.

If x comes out as less than 0.3, then the middle column did not take any load, in which case finding the load in the two end columns is easy!
 
I did it the way PhantomJay said and it worked like a charm! Thanks you guys!
 

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