Forces and Moments: Solving Homework Equations

[jwtp45]

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

 

[jwtp45]

it should read

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

 

[PhanthomJay]

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?