Cantilever Beam Deflection with Concentrated Loads

AI Thread Summary
The discussion focuses on calculating the deflection of a cantilever beam subjected to concentrated loads at its midpoint and tip. The user seeks to derive the deflection equation as a function of distance from the fixed end and to establish the flexibility matrix for the system. A key inquiry involves the relationship between the second derivative of deflection and the bending moment acting on the beam. Understanding these concepts is essential for solving problems related to cantilever beam mechanics. The conversation highlights the importance of grasping beam theory fundamentals for accurate analysis.
parmz_11
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hi guys was doing one of the questions sort of stuck as i don't know much about cantilever beams. I've got this question here:

Consider a cantilever beam of length L carrying concentrated masses at both of its mid-lenght and at its tip. the cantilever may be assumed to have negligible mass:
find the equation of cantilever deflection solely under a concentrated load applied at its tip as a function of a positive variable measured relative to the fixed end and also the flexibility matrix of a cantilever system equation abpve, matrix element 1,1 1,2 2,1 2,2

thanks guys
 
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What's the relation between the second derivative of deflection and the moment?
 

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