Solving for VA and VB: Support Reaction Homework Solution

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Discussion Overview

The discussion revolves around solving for the support reactions VA and VB in a mechanics problem involving loads and moments. Participants are analyzing the equations and calculations presented in the homework statement, focusing on the derivation of these reactions based on given forces and distances.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents their calculations for VA and VB, arriving at VA = 7333N and VB = 9667N, but questions the provided answers of VA = 8000N and VB = 9000N.
  • Another participant seeks clarification on the equation VA + VB = 1000(6) = 5000 + 0.5(400x3), questioning the meaning of the terms and the origin of the numbers involved.
  • A subsequent post corrects the equation to VA + VB = 1000(6) + 5000 + 0.5(4000x3) = 17000N, indicating a potential miscalculation in the original statement.
  • Participants discuss the significance of the value '6' in the context of the problem, with one clarifying that it represents the length associated with a 1000 N/m load.
  • Another participant points out a correction regarding the center of mass of a triangular load, suggesting it should be 1/3rd of the base from the left edge instead of 2/3rds, which affects the moment calculations.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the calculations and interpretations of the problem. There is no consensus on the correct values for VA and VB, and multiple viewpoints on the equations and their components remain unresolved.

Contextual Notes

Participants highlight potential errors in the original calculations and assumptions, particularly regarding the center of mass and the interpretation of the load distribution. The discussion reflects a need for clarity on the definitions and values used in the equations.

chetzread
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Homework Statement


I'm asked to find the VA and VB in this question .

Homework Equations

The Attempt at a Solution


Here's my working :
VA +VB =1000(6) =5000+0.5(400x3)
VA +VB = 11600

total moment about A = 0 , sum of moment about A = 5000(6) -9000 + (4000/2)(9 +3(2/3) ) -VB(9) =0
hence VB = 9667N pointed upwards

total moment about B = 0 , sum of moment about B = 1000(6)(9) -VA(9) +9000+5000(3)-4000(3/2)(2) = 0
VA = 7333N (upwards)

But , the ans provided is VA = 8000N , VB = 9000N , which part i did wrongly ?

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chetzread said:
VA +VB =1000(6) =5000+0.5(400x3)

Is that meant to read VA + VB = 1000(6) + 5000 + 0.5(400*3) ?

If so then..
Where does the 6 come from?
Where does the 400 come from?
 
CWatters said:
Is that meant to read VA + VB = 1000(6) + 5000 + 0.5(400*3) ?

If so then..
Where does the 6 come from?
Where does the 400 come from?
sorry , i made a mistake , it should be VA + VB = 1000(6) + 5000 + 0.5(4000x 3) =17000N ...
 
and the 6?
 
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CWatters said:
and the 6?
The 1000 N /m has 6 m
 
Ok yes I agree. 1000N/M for 6m.
 
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Ill try and have a look at the rest tomorrow.
 
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chetzread said:
total moment about A = 0 , sum of moment about A = 5000(6) -9000 + (4000/2)(9 +3(2/3) ) -VB(9) =0

The centre of mass of the "triangular load" is 1/3rd of the base from it's left hand edge not 2/3rds so it should be..

5000(6) -9000 + (4000/2)(9 +3(1/3) ) -VB(9) = 0
 
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