Forces and Moments: Solving Homework Equations

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SUMMARY

The discussion focuses on solving equilibrium equations for a triangular plate attached to a wall by pins A and B, subjected to a force F at point C. Key equations include the sum of moments and the sum of forces, which must equal zero for the system to be in equilibrium. The initial attempt at solving the problem contained inaccuracies in the moment equations and force components, specifically regarding the use of F_ax and F_by instead of Fa and Fb. The correct approach involves summing moments about point B to derive the correct expressions for the forces.

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Homework Statement


A triangular plate is attached to a wall by two pins A and B. It is loaded at point C by A force F

View attachment diagram.bmp

Homework Equations


Sum of Moments = 0
Sum of Forces = 0

The Attempt at a Solution



Moments act around bottom of plate
F*L1=L2*Fa+L3*Fb

Vertical Forces
F=Fa+Fb
Fb=F-Fa
Horizontal Forces
F=0

So vertical forces into moments
F*L1=L2*Fa+L3*(F-Fa)

Fa= F (L1-L3)
-------------
L2 - L3


It doesn't feel right can someone tell me if I've done it right cheers
 
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it should read

Fa = (F (L1 - L3))/(L2-L3)
 
jwtp45 said:

Homework Statement


A triangular plate is attached to a wall by two pins A and B. It is loaded at point C by A force F

View attachment 32117

Homework Equations


Sum of Moments = 0
Sum of Forces = 0

The Attempt at a Solution



Moments act around bottom of plate
Moments act about any point you choose, not just the bottom of the plate. For objects in equilibrium, the sum of moments about any point is zero.
F*L1=L2*Fa+L3*Fb
This moment equation about the bottom of the plate is not correct. You first need to use F_ax and F_bx, not Fa and Fb, And your moment arm from F_ax to the bottom of the plate is wrong. It is easier to sum moments about B to solve for F_ax.
Vertical Forces
F=Fa+Fb
Fb=F-Fa
Again, here it should be F_by = F - F_ay, and you can assume that F_ay and F_by are equal.
Horizontal Forces
F=0
You mean F_netx = 0?
So vertical forces into moments
what do you mean by this?
F*L1=L2*Fa+L3*(F-Fa)

Fa= F (L1-L3)
-------------
L2 - L3


It doesn't feel right can someone tell me if I've done it right cheers
Try again summing moments about B. What is the problem asking?
 

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