Reaction forces on simple 2 strut truss

[James C]

Homework Statement

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

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

 

[CWatters]

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

 

[SteamKing]

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.

 

[James C]

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?

 

[James C]

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

 

[SteamKing]

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.

 

[James C]

I see, thank you for your response!