Finding Reactions In Simply Supported Beams

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Discussion Overview

The discussion revolves around solving a homework problem related to finding reactions in simply supported beams. Participants explore the application of equilibrium principles, specifically focusing on summing moments about reaction points and the correct application of signs in their calculations.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents an initial attempt at calculating reactions, suggesting values for Ra and Rb based on their calculations.
  • Another participant emphasizes the importance of summing moments about a chosen point and correctly applying signs for clockwise and counterclockwise moments.
  • There is a discussion about the correct identification of forces as positive or negative when summing moments, with one participant questioning their understanding of the signs used in their calculations.
  • Further clarification is provided regarding the need to measure perpendicular distances correctly when summing moments, with a suggestion to fill in blanks in the moment equation to solve for Rb.
  • A participant acknowledges a mistake in their earlier approach and corrects their formula, indicating that they had not properly accounted for the direction of forces relative to the reaction point.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct approach to summing moments, as there are differing interpretations of how to apply signs and distances in their calculations. The discussion remains unresolved regarding the final values for Ra and Rb.

Contextual Notes

Participants express uncertainty about the correct application of equilibrium principles and the handling of signs in their moment calculations. There are also indications of reliance on memory rather than a systematic approach to the problem.

Jamesnikko
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Homework Statement


Hope you can access this link for question http://s353.photobucket.com/albums/r387/james_nikko/?action=view&current=img002.jpg

Supports are at 1.5m and 4.5m

Homework Equations


The Attempt at a Solution


Ok so i have attempted the problem using the following
(5x1.5) + (5x3) + (5x6) = (Rb x 4.5)

Therefore giving:
(Rb x 4.5) = 52.5
Rb= 11.67kN

Therefore:
Ra = (5+5+5) - Rb
Ra = 3.33kN
 
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When the beam is in equilibrium, you can sum moments of a force about any point and set the sum equal to zero, but you must compute the moments of each force about that same chosen point, and then watch your plus and minus signs (clockwise vs. counterclockwise). Although you can choose any point, it is convenient to choose a point on the beam at one of the reaction supports. Try again to sum moments about R_a, and watch your plus and minus signs. Note from the symmetry of the loading and beam, the values of the end reactions, as you gain more experrence, should pop right out at you.
 
ok so my first force which is before point Ra on an overhang should be negative whereas the other two forces are positive? assuming i use a negative reaction at b of course. therefore formula would be, -(5x1.5) + (5x3) + (5x6) - (Rbx4.5)?
 
Jamesnikko said:
ok so my first force which is before point Ra on an overhang should be negative whereas the other two forces are positive? assuming i use a negative reaction at b of course. therefore formula would be, -(5x1.5) + (5x3) + (5x6) - (Rbx4.5)?
You are not summing moments correctly. All perpendicular distances must be measured between the force and the point (Ra) about which you are summing moments.

So I'll start you off, it's -(5 x 1.5) + (5 x 1.5) + (5 x ___) -(Rb x ___) = 0. Fill in the blanks and solve for Rb.
 
sorry i was working from memory :) formula should be
-(1.5 x 5) + (5 x 1.5) + (5 x 4.5) - (Rb x 3)
My major problem was that i wasn't using the force to the left of reaction a as a - number.
Thanks.
 

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