Solve Cantilever Beam: End Load 20kN, EI=40KNm^2, Length 0.25m

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Discussion Overview

The discussion revolves around solving a problem related to a cantilever beam subjected to an end load of 20kN. Participants are exploring how to determine the slope at the free end of the beam using integration, given the beam's length of 0.25m and an EI value of 40 KNm². The focus is on applying the fundamental equation of beam deflection.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant presents the problem statement and the relevant equation, indicating a need for assistance in applying integration to find the slope.
  • Another participant clarifies that the slope refers to the first derivative, which represents the rotation of the beam's cross-section.
  • A different participant expresses uncertainty about the integration process and the number of times integration is required.
  • Another participant suggests reviewing the mechanics of materials book to understand the meaning of 'y' in the differential equation, implying that this understanding is crucial for progressing in the problem.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the integration process or the interpretation of the variables involved, indicating that multiple viewpoints and uncertainties remain in the discussion.

Contextual Notes

There are limitations regarding the clarity of the integration steps and the definitions of variables in the differential equation, which are not fully resolved in the discussion.

johnboy14
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Homework Statement



A cantilever beam carriers an end load of 20kN and has an EI value of 40 KNm^2. If the beam is 0.25m long, use intergration to determine

the slope at the free end of the beam?



Homework Equations



I know from a handout I have that the fudamental equation to use is

d^2y/dx^2 = M/EI

when I substitute this I get EI X d^2y/dx^2 = WU(l - x)

This is where I am stuck? Any help much appricated
 
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Hint: the slope means 'first derivative', i.e. the rotation of the cross section of the beam.
 
Not with you? I think you have to intergrate it but Not sure how many times though.
 
Do you know what the y means in that differential equation? open up your mechanics of materials book and look it up, then you'll understand what radou said.
 

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