Bending Moments and max deflection

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SUMMARY

The discussion centers on calculating the maximum deflection and bending moments for a simply supported beam. The user correctly identifies the maximum bending moment as M=PL/4 but struggles with the maximum deflection equation, mistakenly deriving it as δ=(PL3)/(24EI) instead of the correct δ=(PL3)/(48EI). The confusion arises from boundary conditions, which are critical in structural analysis. Clarification on these conditions is essential for accurate calculations.

PREREQUISITES
  • Understanding of beam theory and mechanics of materials
  • Familiarity with the concepts of bending moments and deflection
  • Knowledge of boundary conditions in structural analysis
  • Proficiency in using equations for deflection and moment calculations
NEXT STEPS
  • Review the derivation of the maximum deflection formula δ=(PL3)/(48EI)
  • Study the effects of different boundary conditions on beam deflection
  • Learn about the application of the moment-area method in beam analysis
  • Explore software tools for structural analysis, such as SAP2000 or ANSYS
USEFUL FOR

Structural engineers, civil engineering students, and anyone involved in beam design and analysis will benefit from this discussion.

Brooks18
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Please could some help me get around this problem I know the derived formulas are all over the internet, but I wanted to prove it out myself. Its for a supported beam 2 end beam, worked out the max bending moment is M=PL/4. However I just can't seem to get the max deflection equation of δ=(PL3)/(48EI) and dv/dx. I keep getting δ=(PL3)/(24EI), I know its probably a stupid mistake I'm making to do with the boundary conditions. If anyone can help point out where I'm going wrong that would be great.
 
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Brooks18 said:
Please could some help me get around this problem I know the derived formulas are all over the internet, but I wanted to prove it out myself. Its for a supported beam 2 end beam, worked out the max bending moment is M=PL/4. However I just can't seem to get the max deflection equation of δ=(PL3)/(48EI) and dv/dx. I keep getting δ=(PL3)/(24EI), I know its probably a stupid mistake I'm making to do with the boundary conditions. If anyone can help point out where I'm going wrong that would be great.
Welcome to the PF.

Could you post a diagram about the scenario? This sounds like more of a studying task rather than an assigned homework problem, right? :sorry:
 

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