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## Yield Line Analysis calculation example

Question
State MN
Description Text

As we discussed in our meeting last Thursday, attached is a concrete barrier detail for you review. As a reminder, we would like to know what your design methodology is (assumptions and process) and what recommendations you might have for both the interior and end regions of the barrier. The steel reinforcing is 60 ksi, and the minimum concrete strength is 4 ksi

**Deflection joints were a concept that was supposed to allow the rail to rotate and expand more freely as the bridge moves under live load and expands with temperature. It was an attempt to limit cracking in our barriers. They don’t work and we no longer use them. I forgot that we haven’t changed the standard yet. You can ignore them, we have moved to a tooled joint 10 ft were the rebar runs right through the joint.

Keywords
• Permanent Concrete Barriers
Other Keywords yield line
Date April 6, 2013

Response
Response I conducted a full Yield Line analysis on one of the bridge rails you sent, and I tried to list / show all of the assumptions that I made.  I attempted to be as detailed as possible in order to show every step.  Take a look at the attached file.  Is this what you were looking for in regards to methodology of calculating barrier strength?
Date April 18, 2013
Attachment MN bridge rail Fig 5-394 117 Analysis.pdf

Response
Response

Joe's questions are below, answered in RED

Again, thank you for helping us with our barrier design.  We appreciate your time and expertise in this matter. After reviewing the design you provided, I had some questions concerning some of your assumptions.

First, the design assumes that the rebar in the barrier yields both longitudinally and vertically, front and back.  Because the bars are so close to the compression face, shouldn’t a yield check be performed to make sure the bars yield as assumed?

I use an Excel spreadsheet program to calculate the bending strength of reinforced concrete cross sections.  It calculates the strain distribution throughout the entire cross section and relates that to the estimated stress in the steel (assumes elastic, perfectly plastic behavior).  Thus, the program should have checked for yielding and calculated all stresses according to strain at each depth.

Second, the hook on the dowel into the deck does not appear to be fully developed, should this be accounted for when calculating Mc for both the interior and exterior regions?

I assumed adequate anchorage to develop the yield strength of each bar.  Yield Line Theory requires that the barrier deflects/bends/yields to absorb energy and balance out the energy of the impact.  If no yielding occurs, the analysis procedure would not be valid.

If a dowel will not develop full yield strength, I would recommend altering the bar / hook details.  Of course, the development lengths found in ACI 318 are conservative in nature and designed for static loading.  Under dynamic loading, failure stresses are typically increased.  Thus, often times we can rely on field proven or crash tested embedment/anchorage designs.

Third, a f of 0.90 was used to modify the barrier resistance, where does this value come from?  As I read AASHTO f is equal to 1.0 for extreme event cases.

The 0.9 factor comes from ACI 318 for bending strength.  We typically use it to give some safety factor to designs, but you may elect not to.

Last, We have always assumed that the longitudinal bars need to be fully developed on both sides of the yield line.  Some of the longitudinal bars in the barrier are underdeveloped for the end region by this assumption, should this be considered when calculating the capacity of the end region?

My answer here will mirror what was said above… yield line requires the full yield strength of the reinforcement.  Thus, it’s easier to just extend longitudinal bars to obtain the proper development length.  When designing end section reinforcement, we specify longitudinal bar lengths that span the critical length, an additional foot or two for conservatism, and the required development length (or splice length if being splice to interior section reinforcement).