torsion on bridge girder

[dison]

Please give me your opinions on what exactly is going on with the following situation:

- short simple span bridge
- two concrete slab girders side by side
- bearing at each end on one or more elastomeric pads
- no positive connection holding the girder down
to the substructure (gravity only)
- no transverse connection of the girders
(no tie rods & no cast-in-place concrete deck)
- eccentric live load toward center of bridge
- live loads are large compared to dead load

Under the eccentric load does torsion develop? Is sufficient restraint provided at the ends of the girder to prevent rotation and develop torsion? If so, how would you quantify it? Obviously, the reaction on the elastomeric pads would follow a distribution greatest at the center of the bridge and least at the outsides. Would this cause rotation of the whole girder toward the center of the bridge (however small), thereby preventing torsion?

If not, how would you consider the eccentric loading? Would there be transverse bending of some sort? Would you look at only the loaded portion of the girder to be effective in resisting the loads? (i.e. ignore the outer portion of the slab for normal flexure and shear calculations) or some type of shear transfer between longitudinal sections? ~dison

 

[flamby]

I think torsion is inevitable in this case. However, there is a limit to it. If the eccentric loading keeps on incresing, the torsion keeps on increasing till the beam overturns about its edge. So you have to check the amount of torsion against the resisting moment due to self weight of the beam.

 

[ishvaaag]

The eccentricity respect the axis of the bridge signifies torsion that needs to be met. Since no tie-down anchors, only the standing connected integral weight can be counted to cause the torsion be equilibrated in a complete load path. If, sasy, the deck is of planks alone and loaded in cantilever, toppling is a risk. In any case, 1st, is a non redundant system, 2nd even if allowed to such bridge build, one would locate the girders as separate as to prevent any possibility of toppling for the standing construction.

3d, torsin there is but normally one first looks the main vertical loads equilibrium, that is, one beam gets more loaded than the other by the eccentrical loads. If both beams and reactions are OK, rarely special considerations of torsion will be being made, even if there is some.

A proper modeling of the supports, bridge and deck can bracket the amount of torsion that occurs in the beams themselves, and then be used for design. More likely will be irrelevant execept that say the deck would only be attached to one beam and not the other acting as counterweight.

 

[dison]

flame & ishvaag,

Thanks for the responses. I also believe that torsion is present based on the restraint provided by the dead load of the bridge. However, there may be something I am overlooking or not looking at correctly.

Just to clarify a few things:

- there is no bridge deck, the top of the slab girder acts
as the bridge surface (the slab is wide compared to its
depth)
- I agree that normally vertical flexure and shear control
the design of bridge girders, but in this case I need to
evaluate the additional effects of torsion (or whatever
else is going on)

ishvaag,

When you say that proper modeling of the supports and bridge can bracket the amount of torsion in the beam, how do you determine proper? From initially taking torsion as the eccentric load times the eccentricity (P*e) where P is the amount of eccentric reaction at the support, I get torsion in the girder that is too great. How do I account for the reduction in torsion that occurs due to deflection of the bearing pads? or is there any? For instance, if I do a finite element analysis I can easily model elastic behavior of the girder itself thereby getting the effects of torsion on the girder indirectly (by indirectly, I mean no applied torsion and no torsion on individual elements), but how do you model the elastomeric bearing pads and substructure with proper supports?
~dison

 

[ishvaaag]

OK sorry by my beams etc reasoning, always running took as stringer bridge etc.

Well, how to model the bearing supports?

Normally as compression only springs, for vertical action. For horizontal we can also derive spring stiffness from the shear modulus.

You can pass the loads to the spring through rigid links for an initial test, later with more commensurate stiffness to the present status. Were the springs not only compression, you could convert them to torsional springs respect torsional restriction, with TC only not so.


Anyway, there is something here a bit off the mark in that slab bridges have been practiced in some ranges and so seem to successfully overcome any structural requirements that presently may be apparent.


I suggest as an alternative model the slab-bridge with thick plate or shell elements. Bending action will prevail at most parts of the bridge and so it is not much difficult then to derive proper reinforcements from the found sresses, and the effect of the deflection of the pads and torsion will be immediately visible in the stresses' patterns.


Re-reading your 1st entry...

Of course if you load eccentrically one double tee the pads simply have not widht enough to deliver centering, hence torsion I see less de problem than toppling. Providing connection through flanges or diaphragms will cause stability to be more feasible.

In any case, you can model the pad itself as an array of springs of the above described kind, that will take the efforts they can, but never to the extent of overcoming inestability itself.

 

[dison]

Now I am getting a little frustrated.

A colleague of mine adamantly insists that NO torsion is present in this girder. He believes that the only effect of the eccentric load is that the reactions at the bearings will also be eccentric and that only vertical shear is present if you took a transverse cross-section through the girder. He claims that this vertical shear varies in magnitude across the section such that the resultant lines up with the applied eccentric load. So, no horizontal shear is present across the section as there would be with torsion. Furthermore, he believes that a good deal of transverse bending may be occurring at the supports due to the differing distribution of reaction vs. applied loads.

I don't disagree that the reactions at the bearings will also be eccentric to the same degree as the applied load, BUT, if you load the girder with a vertical load eccentrically, by statics, an equivalent force system is a vertical load of the same magnitude through the shear center of the girder combined with a torsional moment equal to the vertical load times the eccentricity from the shear center. Does this translate to torsion on the girder? I think so. How much does the magnitude depend on end restraint? I don't know, but I'd like to find out.

Just for further information, the loads and girder geometry look like the following (dead load is an evenly distributed load):
\|/ or /|\ = loads
****** = bearing pads

eccentric liveload
_____________________
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
\|/ \|/ \|/ \|/ \|/ \|/ \|/ \|/
---------------------------------------------------
| |
| concrete slab girder |
| + <--shear center |
| |
| |
---------------------------------------------------
******* ******* *******
/|\ /|\ /|\ /|\ /|\ /|\ /|\ /|\ /| | | | | | | | |
| | | | | | |
| | | | | |
| | | | |
| | | |
| | |
| |
|
reaction ~dison

 

[dlew]

dison,

I think that your statement on the third paragraph of your second message is correct. Independently of the shape of the girder, if the resultant of the loads does not coincide with the shear center, there is torsion in the girder. The torsional moment acting along the length of the girder is the magnitude of the loads time the eccentricity of the resultant from the shear center.

As you described the bridge, it seems that the only restraint at the ends of the girder are the bearing pads. Thus, the torsional moment modifies the reactions on the bearing pads, as you described.

You have not mentioned any lateral load. Lateral loads could add or sustract to the
torsion in the girder and to the torsional moment at the ends in a similar way to the gravity loads. In addition, lateral loads would introduce a horizontal reaction on the top of the bearing pads.

AEF

 

[sven]

Dison,

There is no question that the eccentric load will produce a torque on the beam. This torque will twist the beam. For design, we usually consider the interaction of shear and torsion in the beam. Where torsion is significant, this usually results in additional ligatures and additional longitudinal reinforcement.

The bearing pads will allow the beam to twist. A rigid end will not allow twist, but will not reduce the torsion in the beam either. If the beam end is &quot;cast-in&quot; but the end is not properly designed, it is the restraint that will fail and then the beam can twist. This is often seen in practice where a beam inadvertantly &quot;sticks&quot; to a support due to leakage of concrete slurry during construction and subsequently cracks appear around the support area.

If you have a fully rigid end connection, then you can size the bearings to each carry an equal load, ignoring the torsion. The usual method in bridges is to use an end diaphragm beam to achieve this.

Sven

 

[ishvaaag]

In any case the slab bridge is entirely amenable as thisk plates witth the end pads as compression only springs.

Normally the wide beam is of such capacity that one can see the point of the colleague of Dison, one side being more loaded and the other being even maybe in relative upwards displacement one can see the transverse bending the colleague refers to.

However, straight bending plus the torsion produces as well the same kind of deformation since loading one side and forcing upwards the other.

The flat plate model should discover better what happens in the slab bridge than a stick one.