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# Differential Deflections and Intermediate Diaphragms

## Differential Deflections and Intermediate Diaphragms

(OP)
I have a question about designing intermediate diaphragms when there are differential deflections of adjacent steel girders.  Typically, intermedate diaphragms are designed to transfer wind loads and to meet all applicable slenderness and minimum material thickness requirements.  This is appropriate for tangent bridges with small skew angles.  However, as the skew angle increases, the differential deflections between girders increase.  What procedure is generally used to determine the force effects from differential deflection?  A computer model (STAAD, GTSTRUDL, etc.) could be used, but this is time consuming to generate and check.  How large does the differential deflection between adjacent girders have to be before this type of analysis is required?  NCDOT requires a more refined method of computing deflections due to the weight of the slab when the deflections between adjacent girders differ by more than 1 inch.  The analysis method chosen must take into account the effect of the diaphragms on the stiffness and relative deflection of the girders.  Other states require oversize or slotted holes for the diaphragm connections when the differential girder deflections are greater than 1/2 inch.  Is this a common solution?  Large differential deflections can generate large forces in the diaphragms.

How small does the differential deflection have to be to ignore the force effects on the diaphragms?  Do these forces cause problems if the diaphragms are designed for wind forces only?  What methods are typically used to calculate these force effects?  Any suggestions would be greatly appreciated!

### RE: Differential Deflections and Intermediate Diaphragms

(OP)
One of my reference books states that for skew angles not exceeding 30 degrees for slab-on-beam bridges, bridges can be safely designed as right or normal bridges by simplified methods.  However, for larger skew angles, the torsional moments, which are not calculated directly in simplified analyses, are large and would invalidate the results from the simplified analyses.

In Ohio, the erection bolt holes in the cross frame members are detailed as slotted holes in order to accommodate differential dead load deflections of adjacent girders that exceed 1/2 inch at any cross frame location.  Hole dimensions are 1/16" wider than the nominal bolt diameter and 3/4" longer than the nominal bolt diameter.  Holes in the stiffeners are 3/16" larger than the diameter of the erection bolts.  Final bolting and welding are not completed until after the deck concrete has been placed.

I'm thinking about using the following procedure.  If the skew angle is 30 degrees or under, I'll ignore the effects of differential deflection.  If the dead load differential deflection exceeds 1/2 inch, I'll detail slots in the cross frame members.  If the skew exceeds 45 degrees or the differential dead load deflection exceeds 1 inch, I'll perform a more refined STAAD analysis of the bridge to determine force effects and more accurate camber values.  Does this approach seem reasonable?  I'm curious how others approach the design of skewed bridges.

### RE: Differential Deflections and Intermediate Diaphragms

bridgeman8,

Try this, skew the diaphragms. To answer your question though, do your bracing analysis using spring supports equivalent to its position along the bridge, no need for a full blown fe analysis.

Regards

VOD

### RE: Differential Deflections and Intermediate Diaphragms

A few years ago we designed a pair of single span steel bridges. The abutment skews varied from 53 to 59 degrees; girder lengths ranged from 125' to 150'.

We provided slotted holes in the cross-frame connections; the bolts were tightened after the deck set. Everything went well; no problems.

The frames were normal to the girders; made life a little easier for the detailer.

### RE: Differential Deflections and Intermediate Diaphragms

(OP)
VOD,

Skewing the diaphragms is a good option.  AASHTO limits this to 20 degrees however.  For skews larger than 20 degrees, the diaphragms must be normal to the main members.  Another option would be to stagger the intermediate diaphragms.

Could you give me a little more detail about doing the bracing analysis using spring supports?  Thanks.

Hg,

Thanks for this link.  This is a very good article.  The article states that if girders with large differential deflections are plumb under their own weight when erected and crossframes are fully connected in this condition, the girders will be out-of-plumb after the deck is poured.  It is not desirable to have out-of-plumb girders, so I think slotted holes in the diaphragm connections is a good solution.  Even if the diaphragm and connection are designed to resist the effects of the differential deflection, the web is probably going to be pushed out-of-plumb when the deck is poured.  Stiffer diaphragms will attract more load and become primary members (similar to curved girder design).  The girders could be erected out-of-plumb before the deck is poured so that they will be plumb after the pour.  I think this would be difficult for the contractor to build.

bridgebuster,

I think slotted holes is the best solution to the differential deflection issue.  The bolts are tighted after the deck is set.  Although it may be more expensive and time consuming, the diaphragms will not have to resist the effects of the dead load differential deflection and the girder will remain plumb.  Is this a common solution to this problem?  Have others had good results using slotted holes in the cross-frame connections and tightening the bolts after the deck is set?

bridgeman8

### RE: Differential Deflections and Intermediate Diaphragms

I Am Told (I Am Not A Designer) that usually the distance by which the girders will be out of plumb is not enough to worry about, and that it greatly simplifies design, detailing, and erection to have them plumb at erection (steel dead load) and out plumb thereafter.

I think there was something about this at the most recent World Steel Bridge Symposium, or maybe it was the Transportation Research Board, but I don't have my proceedings or notes with me at the moment.  It also may be that what I'm thinking of has to do with curved rather than skewed bridges.

Hg

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### RE: Differential Deflections and Intermediate Diaphragms

Hi bridgeman8,

Use a unit udl loading about the xx and yy axes to determine displacement per unit loading along your structure, then invert to determine stiffnesses.  You will still need to do a 2d frame analysis with spring supports to come up with frame forces.

HTH

VOD

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