Capacity of a deep beam 2

You're analyzing "a design" what's the difference? From the photo it looks like the distance from the fascia to face of column is greater than the cap depth, beam theory should be OK.

From experience, it may not be worth repairing.

BTW- is this bridge in NY? The shape of the column and sage green paint made me wonder.

Someone is even thinking about not replacing that deteriorated mess ?!?

OP said:

But that’s for design. We are doing analysis here, not design.

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Disagree. You're doing forensic member design which is mostly the same as new build member design. We generally think of analysis as being the computational work associated with determining the actions that individual members are subject to.

OP said:

I think Sectional method is less accurate for deep beams, but is more conservative (lower bound) in determining capacities.

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That will be an erroneous assumption in many cases. One of the reasons that STM exists is to address the situation with deep beams where sectional theory underestimates the depth of the compression block and, therefore, underestimates the amount of flexural reinforcing required.

OP said:

If we use Sectional method to determine moment and shear capacity of this pier cap, will that be acceptable?

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I don't feel that it will. A common criterion is to use STM when shear spans are 2.0 or less.

@bridgebuster:
North of the border, we require STM when a/d < 2.0.


@SWcomposites:
Until they are replaced, we need to make sure they are able to carry the load. Hence the need for evaluation.

@KootK:
Thanks for pointing out the flexure part. I was mainly thinking about shear. As researchers indicate, Sectional Method underpredicts shear capacity for deep beams, like the following curve.
When these bridges were designed in the 1960s, STM did not exist. So I thought using STM for analysis would be comparing apples to oranges.

How old is this bridge? Was strut and tie method in existence when it was built? Does it make sense to apply a design methodology from the current code for a bridge that was designed years before it was added to the code?

I would definitely consider encasing that pier in 6" to 8" of concrete assuming it doesn't have a capacity issue.

Looks like a candidate for shotcrete...

Likely repair method will be:
1. Chipping concrete a little bit (50 mm) to expose the outside steel.
2. Doweling staple shaped bars to replace heavily corroded stirrups.
3. Adding Cathodic Corrosion Protection to mitigate future corrosion. These are zinc bars that form an electrical circuit allowing sacrificial corrosion of zinc in lieu of steel.
4. Form and patch 100 mm self-consolidating concrete.

Shotcrete will not likely be considered as it might damage the corrosion protection system by impact.

Just chiming in to say that I think using STM would be appropriate, even if the pier was designed before STM was even a thing.

OP said:

As researchers indicate, Sectional Method underpredicts shear capacity for deep beams, like the following curve.

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Neat. May I ask which publication that comes from?

KootK said:

Neat. May I ask which publication that comes from?

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Original research was done by Professor Kani at the University of Toronto. Subsequently, other researchers quoteed him. As an example, here is a paper that includes Kani's graph.

OSUCivlEng said:

How old is this bridge? Was strut and tie method in existence when it was built? Does it make sense to apply a design methodology from the current code for a bridge that was designed years before it was added to the code?

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I find this thinking completely backwards. And somewhat scary.

We are engineers, we design suitable structures according to good science. The laws of physics haven't changed. The code is a distant second to the primary goal of good engineering design!

Does anyone know how deep beams under concentrated load were analyzed before STM came to prominence?

How long ago are you asking about?

Basic versions of Strut Tie were being used when I started in the mid 1970's.

tmalik3156 said:

Does anyone know how deep beams under concentrated load were analyzed before STM came to prominence?

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In some respects, I feel as though there is no such thing as "before strut and tie". The terminology is new and the method has been refined but the notion of detailing reinforced concrete based on compression fields and the assumption of shear cracked concrete goes waaaaay back. At least as far back as working stress design methods.

Consider some examples of sectional method detailing that are, and always were, informed by strut and tie principles applied to disturbed regions:

1) Tension lag in flexural reinforcement for bar cutoff detailing.

2) Anchorage of positive moment bottom steel.

3) Hanger reinforcement where beams tie into the sides of supporting girders.

3) The entire concept of stirrups for shear and torsion reinforcing which is based on truss models.

....on and on.

At the risk of sounding pretentious, I feel as though any concrete designer worthy of that description ought to be capable of producing a sectional method design that would mostly satisfy STM principles. With a few exceptions, the results should not be that different when both methods are applied skillfully.

When you look at an estabilished firm's typical detailing, almost all of that will:

a) Have been developed prior to formal strut and tie yet;

b) Be utterly informed by strut and tie principles.

Skilled sectional design in concrete is "STM adjacent" in my opinion.

This is one of the reasons why I don't see an inconsistency when it comes to checking a pre-STM design with modern STM methods. One the one hand, you've got this structure that you know a fair bit about. On the other hand, you've got a suite of modern methods to assess capacity, one of which is STM. Unless you're gunning for some kind of grandfathering pitch, go with whatever tool feels appropriate and lets the structure present its best self.

It's not apples and oranges; it's gala apples vs honey crisp.

@rapt, that's good to know. I had a misconception that the modern STM was theorized in the 80's by Schlaich et al. But of course, truss models for beams were there before.
@ KootK, Thanks for the Park and Paulay book. I have seen this 'internal lever arm method' applied to footing designs.

Prior to the 13th Ed. of AASHTO shear strength was underestimated. In the late 20th C we would design this as a cantilever beam.