Simple (relatively) Beam Supports, pinned or not

[djw2k3]

Hi All,

Have been toying around in my head for a day or so now a problem that can be simplified to that as shown here;

http://www.mytempdir.com/868898

(note - drawn in 3rd Angle) With a load at G.

My question is;

If I am to model this with fixed ends that support a moment Mz by placing a pinned restraint at points A & C and D & F (note D & F would be realeased in x direction).

This would create a moment couple between the attachment points, as I moved them closer together the reactions at say points A & C would become very large although in opposite directions *the beam is realively stiff). But if I were to place one pinned restraint at A & F then there would be no moment and the reaction at each point would be realatively low.

Now when designing the beam would an assumption that the ends are pinned be okay?

When designing the bolted joint, if I am to support the moment couple the prying loads for an anchor could become quite massive.

Should I look at a way to design the anchoring at point C (and D) to be flexible enough in y direction so the beam can displace and a much smaller moment couple produced? Have no idea how I might go about this using a rigorous approach.

Any help / comments would be much appreciated.

Dave

 

[desertfox]

Hi djw2k3

I tried your link but it doesn't seem to work for me.
Could perphaps describe your problem in words or is it to complicated.

regards desertfox

 

[corus]

The link works fine, if you wait a minute.

For the beam strength then you'd assume that you had pinned ends. For the design of the bolts and spacing then you'd assume each bolt was pinned, effectively applying built-in ends. This assumes, of course that the ground is relatively rigid. From the drawing it looks as if the beam has to be welded to the support plates. You'll also have to check the welds for the direct load and bending moment that they'll see.

If the ground isn't rigid then you'd expect that the moment seen by the bolts would reduce and the beam ends would be able to rotate. Look at beams on elastic foundations in Timoshenko for a theoretical solution. It'd be generalyl better to assume the ground is rigid though and just use bigger bolts or a wider spacing/more bolts to cope with the reaction forces and moments at the ends.

corus

 

[rb1957]

yeah, the link works ... you have to find the file name on the page to download.

as drawn, you have a constant section, so the simply supported case causes the highest moments in the beam and so it is conservative to design the beam with this. if you varied the section, the simply supported design would be unconservative near the fixed ends, but that is another story.

before worrying about the bolt loads, you have to worry about the welds, as corus points out ... these are the load path from the beam to the bolts, if they don't work then nobody works !

you asked a queston about bolt loads, and as corus says it depends on the rigidity of the ground. what happens is the bolts (weld willing) will react as much load as they can. as the load is applied, the support reacts as much moment as the ground permits (assume fully fixed). as more load is applied, eventually the most highly loaded bolts will start to yield, limiting the moment reaction, the limiting condition would be (IMHO) all 6 bolts working at ultimate strength. part of the point to having a uniform section is that the moment at the fixed end support is less than the maximum moment for the simply supported beam (so you won't over load the beam).

if you wanted to, you could consider the beam simply supported at the outer bolts (A and F) and treat the other bolts as redundancies (how much deflection does the simply supported assumption imply at the the bolts ? how much bolt load is required to counter-act this deflection ?)

 

[JAE]

Why don't you just put some horizontal slots in one end and make it be simple span?

 

[desertfox]

Hi djw2k3

I would approach this using the "simply supported beam theory" for the beam itself, as this would give the worst case for beam deflection, in reality of course your probably somewhere between simply supported and built in ends.
For the loads in the bolts assuming that the ground is rigid
and there is no distortion of the plates welded to the beam I would proceed as follows:-
split the beam in half and using half the total load say (P/2) acting at G take the moments from the extreme end of the beam (ie where the welded plate for the bolts D,E,F ends) and equate them as follows:-

3000*P/2 = 2*u*(Lf)^2 + 2*u*(Le)^2 + 2*u*(Ld)^2

where u=tensile force on the bolt at a unit distance from
the far righthand side of the beam.

(Lf)= the distance from the far righthand side of the
beam to the bolt line F

(Le)= the distance from the far righthand side of
the beam to the bolt line E

(Ld)= the distance from the far righthand side of
the beam to the bolt line D

the constant 2 in the above equation is because you
have 2 bolts in the line of D,E,F.

Transpose the equation and solve for u:-


(3000*P/2)/(2*((Lf)^2+ (Le)^2+(Ld)^2)=u

to get the tensile load in each bolt at positions D,E,F simply multiply "u" by (Lf),(Le),(Lf) clearly the bolts at position D will see maximum load.
However this maximum load is only due to the prying action the maximum total load will need to have the proportion of the direct load (P/2)/6 (six being total number of bolts at right hand end of beam)

therefore max bolt load = u*(Ld)+ ((P/2)/6)

regards

desertfox