Deriving Moment & Elastic Curve Equations for Incomplete Triangular Load on Beam

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Discussion Overview

The discussion focuses on deriving the moment and elastic curve equations for a beam subjected to an incomplete triangular load, specifically with a pin support at one end and a roller support at the midpoint. The scope includes theoretical derivation and mathematical reasoning related to beam deflection under specific loading conditions.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about the derivation process for moment and elastic curve equations under an incomplete triangular load.
  • Another participant clarifies the definition of the triangular load as a distributed load that starts at zero at the left end and increases linearly to the roller at L/2.
  • A third participant presents a formula for deflection based on known variables for a simply supported beam with a triangular load, indicating different expressions for deflection depending on the position along the beam.

Areas of Agreement / Disagreement

Participants generally agree on the nature of the triangular load and its application, but the discussion remains unresolved regarding the specific derivation of the moment and elastic curve equations.

Contextual Notes

The discussion does not provide explicit assumptions or details on the derivation steps, which may limit understanding of the proposed formulas.

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I was wondering how you would derive the moment and elastic curve equations for an incomplete triangular load. Say you have a pin at the left end of the beam and a roller at L/2 from the left, and a triangular load that goes from the pin and ends at the roller. I know you have to do some kind of extension, but how do you come up with the formula.
 
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When you say "triangular load", you mean a distributed load that's zero at the left end and increases linearly to the roller at L/2?
 
If you know Δ(x) and θ2 for a simply supported beam as a function of L' = L/2 with a triangular load then the deflection would be:

Δ = Δ(x) for x=<L/2
= θ2*(x-L/2) for x>=L/2
 
Last edited:
@timthereaper yes
 

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