How to Determine Reactions at Points in Beam Analysis?

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Discussion Overview

The discussion focuses on determining the reactions at points in beam analysis, specifically for a beam with a pulley. Participants are analyzing the shear and bending moment diagrams and addressing the challenges of identifying unknown reactions and forces in the system.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • The initial approach suggested involves calculating the reactions at points A and C, but there is uncertainty due to having four unknowns and only three equations.
  • One participant asserts that it is the correct first step to find the reactions, indicating that there are three equations and three unknowns.
  • A question is raised about the direction of the reaction at point C, with a participant expressing confusion over whether pin connections always have an unknown direction for reactions.
  • Another participant clarifies that since member CD is pinned at both ends and has no internal transverse applied load, the reaction at C will align with the line segment CD.
  • There is a reiteration that pin connections generally have reactions with initially unknown directions, but this can change under specific conditions related to the member's constraints and loads.

Areas of Agreement / Disagreement

Participants generally agree on the approach to find the reactions, but there is some debate regarding the nature of pin connections and the conditions under which reactions can be determined. The discussion remains unresolved regarding the implications of these conditions on the analysis.

Contextual Notes

There are limitations regarding the assumptions made about the member connections and the loads applied, which may affect the analysis. The discussion does not resolve these assumptions or their implications.

zzinfinity
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Homework Statement



Neglecting the size of the pulley at G, draw the shear and bending moment diagrams for beam AB.



Homework Equations


Fxnet=0
Fynet=0
Netmoment=0


The Attempt at a Solution

\

What I want to do first is figure out the reactions at A and C, however I'm not sure how to do that since there seem to be four unknowns and only three equations. Is this the correct first step, or should I try it another way? Thanks!
 

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zzinfinity: Yes, that is the correct first step. No, there are three equations and three unknowns. Hint 1: Is member CD a so-called truss (axial force) member? Give it a try.
 
So does that mean the reaction at c is in the direction of cd? I thought pin connections always had a reaction with unknown direction. Is this not always the case?
 
Since member CD is apparently pinned at both ends, the reaction at C will be in line with the line segment CD.
 
zzinfinity said:
So does that mean the reaction at c is in the direction of cd?
Yes.
zzinfinity said:
I thought pin connections always had a reaction with unknown direction. Is this not always the case?
zzinfinity: You are correct. Pin connections generally have a reaction force with (initially) unknown direction. However, this is not the case if a member is (1) pinned at both ends, and (2) has no internal transverse applied load. (Notice, there is no load applied to member CD between points C and D. It thus meets both conditions 1 and 2, making it a truss member.)

Meeting condition 1, alone, does not define a truss (axial force) member.
 

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