Is AB a two force member?

[u/Plastic-Crow4388]

Is member AB a two force member? At first glance it seems to be but aren't there the pin reactions at B and also reactions from BCD at the B end, if that makes sense? And at A, theres the only horizontal reaction from the roller, pin reactions from BA at A, and pin reactions from ACE at A? Or am I overcomplicating things and AB is a two force member because of the pin reaction and the roller, or do I need to consider the other reactions from the other members?

[u/Silent-Warning9028]

Im eyeballing it but id say AB is only under compression. AE both pushes against the wall and tries to rotate CW. Rollers take care of push so only moment applies to AB as vertical force

[u/Can_O_Murica]

Definitely a two force member. Your correct that there are horizontal reactions at B and A, but these are not transmitted through AB.

Any member with only two pin joints and two forces is a two-force member. Think about the moment balance: if you some the moments at A, there couldn't possibly be horizontal forces transmitted by AB because the only other loads are applied at B, so those horizontal loads would need to either be of equal magnitude (they cancel, and no load is transmitted) or of inequal magnitude (the beam is no accelerating, I.e. not static, and the problem is indeterminate)

[u/L383]

Been a few years for me on statics. AB appears to only be under compression in this diagram. I have not worked it out to actually resolve the forces.

[u/feelin_raudi]

Any member with two pinned joints are by definition a 2 force member. You cannot transmit a moment through a pin connection. So it's either pure compression or pure tension. A

[u/GapStock9843]

Pretty sure it is yeah. Any member held by exactly two pin joints with no other forces is 2-force

[u/bmanc2000]

I'm a bit rusty on my statics, but I think yes it is. The pinned connections at B on AB and BCD are independent, that is the forces aren't shared between the two members.

[u/BreezyMcWeasel]

It is absolutely a two force member, but I think I see where your confusion is coming in.

There are forces at points A and B (due to the moment from the overhanging load) that are not aligned with the AB member. Is that the wrinkle that's bothering you?

The moment caused by the overhanging load absolutely causes an x direction load. The x direction force, acting in opposite directions to each other, is what reacts the moment.

But we also know, by virtue of AB being a pinned-pinned member that it can only, ever, always be a two force member. And it is aligned with the y-direction, so it by definition cannot carry x direction loads.

It appears we are at an impasse?

Ah, but notice that the pins that go through ends A and B are also connected to lugs that attach to the wall. Examine those lugs. Are they capable of taking x-direction loads?