C5; Concrete Buildings Assessment – Appendix C5D Diaphragms Grillage Modelling  

This query is specifically with reference to Appendix C5D, of the C5 engineering assessment guidelines for concrete buildings.

Specifically with regards to the modified Hrenikoff model analysis methodology documented therein including recommendation for section sizes to obtain an elastic solution of forces in the diaphragm elements.

It is my understanding that this methodology / Appendix has been published in the assessment guidelines prior to Amendment 3 (August 2017) of the NZS 3101:2006, at a time when reinforcement with a lower ductility class than E was allowed to be used for some reinforcement.

This methodology / Appendix has also been in place historically prior to the recommendations in the assessment guidelines to ignore cold-drawn steel mesh (often, the major typical reinforcement content in some historical buildings).

While the methodology detailed in Appendix C5D references a paper by Holmes (2015) it is listed as unpublished in the references list. (I have not found this paper in my own searches).

The majority of the content of the Holmes paper was included in Appendix C5D.

I am making an educated interpretation or guess that the adaption of the Hrenikoff analysis methodology by Holmes had the purpose of estimating forces at relatively small yields in order to make use of historical reinforcement such as cold-drawn welded mesh for example. Thus it is technically not a strut-&-tie analysis.

Two comments:

1. No – the Hrenikoff method was not used to allow cold-drawn wire mesh to be used.
   • Even prior to 2010, it was recommended that cold drawn wire mesh could not be relied upon for tension is diaphragms.
2. The Hrenikoff method (1941) is an elastic method that forming a square grillage that replicates the in-plane stiffness of a plate. And as we do not want to yield a diaphragm (other than what we have to accept this, say at the corners where beam elongation destroys the diaphragm plate).  So, an elastic plate models would serve this purpose. 
   • The Hrenikoff model is not a strut and tie method in the sense of “Strut and Tie” Appendix A , NZS 3101. It was not proposed as a “Strut and Tie” method.
   • I am aware of some designers using the member sizes of the Hrenikoff grillage and checking the compressive stresses using Appendix A – this is in error.

The issue I am finding is that predominantly engineers in the industry including peer reviewers and territorial authorities have adopted the interpretation that the elastic solution only to the modified Hrenikoff model is the definitive methodology for all Strut-&-Tie models (as per Appendix A of NZS3101) only including new designs with ductility class E steel.

The Hrenikoff model is like a “poor man’s finite element analysis”.  It is an elastic tool to indicate the distribution of forces in and out of the floor plate (columns or walls) and across the floor plates.  The designer should use these nodal forces and the flow of forces across the floor plate to develop an actual “Strut and Tie” solution.  Finding where the ties and struts are located and checking strut stresses and nodal stresses using Appendix A requirements. 

At the recent, 2024, SESOC / HERA seminar titled “Seismic Design of Diaphragms in Steel Frame Structures” this interpretation was essentially reinforced as this method was described as equivalent to the Strut-&-Tie method. I believe this is a little misleading as it really is potentially only one of an infinite number of exact solutions since Strut-&-Tie is a plastic analysis methodology based on the lower bound theorem. My understanding is that well detailed and carried out, with appropriate materials (e.g. ductility class E reinforcement) a Strut-&-Tie solution as per Appendix A of NZS3101 already should provide a conservative and safe design or assessment solution.  Yes

The aim is to develop a grillage that models (within reason) the stiffness of a plate of the same thickness and plan dimensions.  Hrenikoff and Gardiner (UoC) confirmed that a grillage of 1 metre spacings produced consistent results as the pure flat plate.  The large grillage solution was tested during the PhD studies by Alizadeh (UoC) with positive outcomes.  I prefer the 1 metre grillage because it easier to apply to floors with stair and lift penetrations, re-entrant corners and variable floor shapes (other than rectangular or “L” shaped). 

As stated earlier, I believe the grillage analysis should be used to inform use of a best/likely Strut and Tie solution, and the use of the forces found in the elements of the Hrenikoff grillage needs to be done with caution.  The grillage is good at showing where the forces accumulate, the general distribution of forces (including magnitudes) and aspects like “Shear lag” can be seen with a 1 metre density, for example),    

It also appears to me that in some situations the limitations of the elastic solution in the modified Hrenikoff model may be both unduly conservative and unrealistic given that in a squat element, “D” region, such as a floor plate diaphragm or squat reinforced concrete wall one would expect some in-elastic behaviour at ULS and MCE scenarios and this is OK. In the context of diaphragm design and/or analysis for new design or assessment of existing floor plates we are already typically using design loads for the diaphragm factored up by the building over-strength (pESA) method, which is ensuring adequacy of design for the diaphragm floor plate.

I am not sure I understand nor agree with your comments that “the limitations of the elastic solution in the modified Hrenikoff model may be both unduly conservative and unrealistic given that in a squat element, “D” region, such as a floor plate diaphragm or squat reinforced concrete wall one would expect some in-elastic behaviour at ULS and MCE scenarios”.

Of course, often a floor plate is just one big “D” zone?

Inelasticity in diaphragms is perilous.  In order that the vertical lateral force resisting structures deform and attract forces as per how we model them (within accepted limitations) the diaphragms need to remain elastic.  Otherwise, the distribution of forces to the VLFR is indeterminable once plasticity is permitted over a substantially area of a floor plate. 

I understand I have missed the opportunity for public consultation for the proposed revision of non-epb seismic assessment guidelines.

However, I am wondering whether it may be taken into considerations that in future revisions of the seismic assessment guidelines, Appendix C5D may add some background from the original authors on the original intention of the methodology e.g. was it intended for assessment purposes of diaphragms with lower strain capacity reinforcement, very low target crack widths and/or with addition of retrofit solutions with limited strain capacity?

If a designer was attempting to get down to that level of detail – strain predictions aiming to confirm that brittle materials are not overloaded or those of low plastic capacity can survive – this is thwart with risk.  Possibly, non-linear finite element model, accounting for creep, shrinkage, strain history during its life, and the strain history of the seismic event. It is unlikely that the effort and inherent uncertainties would justify use of a non-linear FEM. 

Because of the unknowns, the relatively coarse method of Hrenikoff and overlaying a Strut and Tie solution  for the diaphragm is appropriate, (the means of demonstrating compliance – Cl. 13.3.2 – NZS 3101 – which says diaphragms shall be analysed using Strut and Tie (Appendix A)).  Being appropriate, while accepting that designers recognise the limitations of the coarse method.  

Also some guidance on what is the relationship of the modified Hrenikoff analysis method to Strut-&-Tie method in Appendix A of NZS3101 would be helpful (since it is now being commonly adopted as the definitive interpretation of strut-&-tie in the NZ structural engineering industry).

Concrete NZ – Learned Society  has a seminar (Video) on its website that provides reasonable explanations on how Hrenikoff and Appendix A can be employed. 

Who would I contact with regards to the non-epb seismic assessment guideline revisions, with regards to this?

Des Bull  –  Holmes NZ LP

desb@holmesgroup.com