Rigid Frame Bridges 3

[tmalik3156]

Hello
I am looking for guidelines/example calculations of Rigid Frame Bridges. So far I have found only two ancient books (Hayden, PCA). If anyone can name textbooks, or provide links to online resources, I will highly appreciate it.

 

[Enable]

I would like to see that bridgebuster if you dont mind! Quite curious.

 

[tmalik3156]

@bridgebuster, sure that would be awesome.

 

[bridgebuster]

See attached. Here's a picture. The bridge was built in the 1950's. In the 1980's I worked with the gentleman who designed it.

 

[bridgebuster]

Here's another one I found in my files. Unfortunately the copy isn't very clear making the calculations difficult to follow. I remember the gentleman who did the rating used a slide rule, trig tables, and the PCA manual from the 30's "Analysis of Rigid Frame Bridges (Without Higher Mathematics)". That's how I was able to get a Xerox of the manual.

 

[Enable]

Many thanks bridgebuster!

 

[bridgebuster]

Enable, you're welcome; glad I could be of help.

 

[MIKE_311]

Do you only check capacity of the deck ? or the vertical wall too ?
I have a situation where the mid-span capacity exceeds positive moment demand (that's good)
End-span capacity exceeds the negative moment demand (that's good)
But the negative moment demand on top of vertical wall exceeds its capacity there. What do we do in this case ? Any suggestion ?

We check every member, horizontal and vertical, AAHSTO will allow simplification (eg. ignore axial loads) if the axial loads are below 10% or 20%.

For your last point, if the structure isn't showing distress, we have made the assumption that a plastic hinge can form and you end up with a simple span. so if the positive moment rating is adequate (assuming pinned ends), you are good.

 

[tmalik3156]

if the structure isn't showing distress, we have made the assumption that a plastic hinge can form and you end up with a simple span. so if the positive moment rating is adequate (assuming pinned ends), you are good.

That's a very good point. For a simply-supported condition, my positive moment capacity is only slightly below the positive moment demand. I can make it work.

@ bridgebuster

I was reading through your calculations for LIE over Cemetery Rd. I was able to follow it easily until I came to this part. Do you remember how axial load was calculated ? Where did these highlighted numbers come from?

 

[STrctPono]

tmalik/mike,

I agree with the belief in the simply supported span but technically speaking AASHTO only allows you to redistribute a percentage of your moments up to a maximum amount.

 

[BridgeSmith]

Evaluating it as a simple span on walls, is the simple approach, but in order to get there will likely mean cracked concrete at the rear faces of the abutment walls. That would typically not be acceptable, as it would shorten the service life.

If I was doing it, I would limit the capacity of the bridge to the load where the yield capacity of the wall is reached, assuming the maximum reasonable soil resistance, which would probably be something greater than the at-rest pressure, but less than full passive. Where it falls in that range will depend on the backfill material and the expected flexural movement of the wall. My guess is that you'd be just barely above the at-rest pressure, given the small deflections typical for a structure as stiff as I would anticipate it to be, and the relatively large movement required to mobilize full passive pressure for most backfill materials.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[BridgeSmith]

You'll get alot of help from the spreading of the load. The maximum moment will be generated with the truck wheel loads near midspan. You'll engage a much wider portion of the superstructure at the abutments due to lateral spreading of the load from the point of application. Once you include the lateral spreading, I think you'll find the critical loading will be with the maximum number of lanes loaded, and the full width of the wall resisting.

Per AASHTO Std. spec, Article 3.12.1, if you have 3 or more lanes loaded there's a 10% reduction in the live load. In LRFD, the improbability of coincident multiple design vehicles is accounted for by the multiple presence factor (MPF).

Rod Smith, P.E., The artist formerly known as HotRod10

 

[bridgebuster]

@tmalik3156, I didn’t work on the calculations but I looked at the STAAD output for the influence lines. Joint 15 controls, which is Load Case 9. I found two of the coefficients for Member 6 but I need to another look about the third coefficient; I think I know what they did.