Moments Forces Help

1. Jan 4, 2015

smr101

How do I determine the support reactions at A & E in this example?

Help is much appreciated.

2. Jan 4, 2015

SteamKing

Staff Emeritus
Have you tried writing equations of static equilibrium for this frame?

3. Jan 4, 2015

How?

4. Jan 4, 2015

SteamKing

Staff Emeritus
Have you written equations of static equilibrium for any structure before?

5. Jan 4, 2015

smr101

Right I've worked it out.

I've got E vertical as 50kN.

A horizontal as -30kN, vertical as -50kN.

Only problem is the answers have them listed as these values but I have all of the signs wrong.

6. Jan 4, 2015

SteamKing

Staff Emeritus
This indicates that the direction in which you assumed the reactions are acting is opposite of the direction in which they act.

7. Jan 4, 2015

smr101

Yeah, I get that, I'm unsure why the answer is in correct.

Here's my working for vertical E:

∑M = (10 x 3) + (20 x 6) - (E x 3)
= 150 - 3E
Ev = 50

The correct answer is - 50

Any idea where I've gone wrong?

Thanks.

8. Jan 4, 2015

SteamKing

Staff Emeritus
If you don't set up a convention for what constitutes a positive direction for forces and a positive orientation for moments, your equilibrium equations often will give you incorrect signs in the results.

It helps to write both equilibrium equations. There should be an equation for the forces such that ∑F = 0, just as there is one for the moments, ∑M = 0.

9. Jan 5, 2015

CWatters

What SteamKing said. Its much better to write...

I define clockwise as +ve and then

(+10 x 3) + (+20 x 6) + (?E x 3) = 0

Note: I have explicitly written the sign in front of the 10 and 20N. The "+" sign before the E is because I am summing the moments, it is NOT because I have assumed E has any particular direction. To further clarify I have put a ? indicating the sign of E is unknown. I wouldn't normally put a ? mark but you can if it helps.

Rearrange

?E = - {(+10 x 3) + (+20 x 6)} / 3

?E = - 50

So the unknown sign of E is -ve. That means E acts anticlockwise (eg downwards).

Last edited: Jan 5, 2015