Reaction forces on simple 2 strut truss

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Discussion Overview

The discussion revolves around calculating the reaction forces (R1x, R1y, R2x, R2y) in a simple two-strut truss subjected to a 100N load. Participants explore the application of static equilibrium equations and the implications of fixed supports on the analysis.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • The original poster (OP) presents equations for static equilibrium, including force and moment equations, and expresses difficulty in solving them using matrices.
  • Some participants question the accuracy of the OP's moment equations, suggesting a possible error in the terms used.
  • There is a discussion about the nature of the supports, with one participant noting that the OP's equations assume pinned connections, which cannot develop moment reactions.
  • Another participant points out that if the supports are fixed, the system becomes statically indeterminate, requiring additional equations based on member deflections to solve for the reactions.

Areas of Agreement / Disagreement

Participants generally agree that the supports should be treated as fixed rather than pinned, but there remains uncertainty about how to proceed with solving for the reaction forces given the number of unknowns and equations.

Contextual Notes

Participants note that the OP's equations may not account for the fixed nature of the supports, leading to a potential misapplication of static equilibrium principles. The discussion highlights the need for additional considerations when dealing with statically indeterminate structures.

James C
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Homework Statement


Calculate reaction forces R1x, R1y, R2x, R2y. Load of 100N. Node 1 and 2 are fixed. Distances listed on image.

6X8ka4i.jpg


Homework Equations

[/B]
I have:
∑Fx = 0 = R1x + R2x
∑Fy = 100 = R1y + R2y

∑M2 = 0 = (-100 x 0.1) + R1 x 0.06 + R1y x 0.02
∑M1 = 0 = (-100 x 0.04) + (-R2x x 0.06) + (-R2y x 0.02)

The Attempt at a Solution


Using this equations I have tried to solve using matrices but I get a number error in Excel. Could someone please help clarify if I've made a mistake or why this can't be solved?

Thank you
 
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Perhaps too obvious to be the problem but I assume you mean...

∑M2 = 0 = (-100 x 0.1) + R1x x 0.06 + R1y x 0.02
 
James C said:

Homework Statement


Calculate reaction forces R1x, R1y, R2x, R2y. Load of 100N. Node 1 and 2 are fixed. Distances listed on image.

{See image in OP.}

Homework Equations

[/B]
I have:
∑Fx = 0 = R1x + R2x
∑Fy = 100 = R1y + R2y

∑M2 = 0 = (-100 x 0.1) + R1 x 0.06 + R1y x 0.02
∑M1 = 0 = (-100 x 0.04) + (-R2x x 0.06) + (-R2y x 0.02)

The Attempt at a Solution


Using this equations I have tried to solve using matrices but I get a number error in Excel. Could someone please help clarify if I've made a mistake or why this can't be solved?

Thank you
For static equilibrium, you can write one force equation and one moment equation. You should pick either support #1 or support #2 as the reference for you moment equation and solve for the remaining unknowns.

The OP said the connections at support Nos. 1 and 2 were "fixed", but your equations assume each is a pinned connection, which cannot develop a moment reaction.
 
SteamKing said:
For static equilibrium, you can write one force equation and one moment equation. You should pick either support #1 or support #2 as the reference for you moment equation and solve for the remaining unknowns.

The OP said the connections at support Nos. 1 and 2 were "fixed", but your equations assume each is a pinned connection, which cannot develop a moment reaction.

Thank you for your response SteamKing. You are correct that the supports should be fixed instead of pinned. How could I go about solving the 4 variables in this instance? You're saying I can write one force and one moment but then I have 4 unknowns and 2 equations don't I?
 
CWatters said:
Perhaps too obvious to be the problem but I assume you mean...

∑M2 = 0 = (-100 x 0.1) + R1x x 0.06 + R1y x 0.02

Haha yes sorry it should be R1x
 
James C said:
Thank you for your response SteamKing. You are correct that the supports should be fixed instead of pinned. How could I go about solving the 4 variables in this instance? You're saying I can write one force and one moment but then I have 4 unknowns and 2 equations don't I?

If the two supports are indeed fixed, then the struts are statically indeterminate, and the equilibrium equations alone are insufficient to determine the reactions. You have to develop additional equations based on the deflections of the members.
 
I see, thank you for your response!
 

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