Column Statics Help

[asalisbury]

Hi,

I am working to develop a free body diagram of a column but running into some issues here specifically with the moments. I have a 1m long solid cylindrical column that has a fixed base, and goes through a set of plates with holes at 0.2 and 0.8m. There are two distributed forces action on the rod at 0.75m in the +x direction and 0.25m in the +y direction or into the page. See the attached images for a diagram and what I have so far.

Because the plates are not pinning the rod, they are acting as roller supports and do not resist a moment, but they do interact with the rod resulting in x and y reaction forces. I am wondering where exactly the moments are on this FBD?

 

[rb1957]

why do there have to be moments in your FBD ?

wouldn't the two holes be simple supports, intentionally designed that way ?

 

[asalisbury]

I suppose there would just be a resultant moment at the base from the fixed support resisting the induced moment.

 

[Stick.]

At each boundary condition (support or applied force/displacement), you can potentially have 3 force and 3 moment components (x, y, z). They're either applied or reactions, depending on the boundary condition. You need to go through each boundary condition and determine which of the 6 you are requiring to be zero (based on boundary condition type). For your fixed base (if it's truly fixed), all 6 have the potential to be non-zero. The other are less clear since I'm a little confused by your description and diagrams. Your initial post has a set of axes drawn that seems to indicate that the Y axis is the long axis of the column, but then your reaction force nomenclature indicates that Z is the column long axis (since X and Y are both transverse to the column long axis). Also, I'm not clear what Rn is.

Having said that, your second post looks more reasonable, assuming the base is fixed, each plate hole is a roller support (can only provide reaction forces transverse to the column axis and nothing else), and the applied forces are pure 1 dimensional forces. It does look like you're missing a reaction force along the column long axis at the fixed support though.

 

[rb1957]

There is a moment reaction at the base if there is structure to provide it, like the base of the column in sunk into a hole (or socket)such tha the column can transmit a moment to the supporting structure. You don't assume a moment incase the lateral forces get out of balance.

In your later post, why wouldn't the two blue loads (onto the buckling guides) balance the applied red load ?