The experimental results may be different as compared to theoretical results which can be obtained from the available equations in different codes. The size effect of beam specimen , percentage of longitudinal reinforcement and compressive strength of concrete are most important variables. In addition to characteristics of aggregates is need to consider. All these factors directs need of empirical factor.

For additional study , Please refer " A Comparative Study of the Shear Strength Prediction for Reinforced Concrete Beams without Shear Reinforcement " by

Leandro Mouta Trautwein, Luiz Carlos de Almeida, Ricardo Gaspar

Dear Ishwar,

thank you for the reply. You are right about the existing shear models, in which many empirical factors are used.

Actually, in my question the shear model is assumed to be perfect. All the required input parameters are experimentally determined, also the characteristics of aggregates. This is a theoretical question. If the answer is YES, that means at least one empirical factor is required, then we can feel comfortable to formulate a shear model without much thinking about a model with no empirical factor.

Regards,

Linh

The shear resisting capacity of reinforced concrete without shear reinforcement is predicted based on shear resisted by compression zone of concrete, aggregate interlocking property and dowel action of reinforcement. Many codes have have given these properties in relation to the percentage of steel and grade of concrete.

In one of the article by Evan C. Bentz, Frank J. Vecchio, and Michael P. Collins they presented Modified Compression field theory for shear design and they included size effect as one parameter assuming the crack spacing but still these tests were conducted on panels and in case of beams how the aggregate interlocking will be taken in to account in resisting shear is to be modeled empirically.

Looking to the complexity of this behavior it seems that empirical factor is needed to predict the the shear resisting capacity.

Dear Mr. Chahangani,

thank you for the comment.

The shear equations in codes are often results of the simplication of shear models. For the design purpose, the complexity should be reduced as much as possible. Therefore, the codes cannot say much about the shear behaviour of concrete members. For the code empirical factors are required to fit the simplified equations to the experimental results.

What I want to know is that if there is a convinced reason/explanation that empirical factors are also required for a mechanical model (not code equations) in case of shear capacity.

Regards,

Linh

I think no if this model considers all effective factors.

Dear Mohannad Husain,

the key problem is how to consider the influencing parameters. Or in other words, how to formulate the model.

For example, which values of material parameters should be used in the model? The mean value, fractile value or in between (such as quantile value) ?

Regards,

Linh

The uncertainty that lies at the basis of needing a factor usually are a combination of modeling uncertainties, geometric, and material uncertainties. So, even when the model itself is "perfect" you would still have geometric and material uncertainties.

@ Eva Lantsoght: We may separate the model uncertainty and parameter uncertainty in evaluation of a shear model. Geometric and material uncertainties can be reduced if we use all measured parameters, described above as experimentally determined. What I want to discuss is the core of the model. For example, how to consider the size effect in a shear model. Can we take it into account by a pure mathematical formulation without emprical factors? If we cannot then why?

Dear Mr. Tran,

I think your interesting question raises some general issues that we need to be aware of. Unlike philosophy or mathematics, all ‘natural’ science including engineering is by definition an empirical science which relies on observing the external world. Our knowledge of laws of nature is produced exclusively a posteriori by observation and experiment.

With regards to shear failure, we can formulate simple mathematical formulas as strength predictors (“empirical formulas”) based on experiment. The more complex the formula, the better the predictions. Our model of shear failure is then of purely semantic nature, describing ‘what happens’ during shear failure. The formulae themselves do not represent any of the internal mechanisms of physical principles.

A step further would be to introduce physical boundary conditions as a hypothesis as a means to predict shear failure in a more general manner. Such conditions could be equilibrium of forces, strain compatibility, geometric compatibility, conservation of energy and so on. We would then require laws of material for concrete (uniaxial, biaxial, or triaxial) and steel, and laws for mechanisms like doweling action, aggregate interlock or fracture process zone. Note that all of these laws are derived purely empirically. We now have a synthetic model of shear failure in which single components of shear transfer are described mathematically. Phenomena like size effect do not need to be included as an additional factor but are a direct result of the model. Such a model is surely a step forward, but still relies at its core on empirical observation. In fact many presuppositions are made that do not represent reality but are good enough for us and serve their purpose (presuppositions as Newtonian physics in general, homogenous materials, Bernoulli hypothesis if applied, rigid bodies for geometric compatibility if applied and so on).

So in the end I think we should consider three things when thinking about models:

1) We can (and should) always dig deeper to find more general solutions for failure mechanisms and behavior of structures to gain more realistic and precise models. However, we must not forget that as part of natural sciences all of our research is of empirical nature (it would be useless otherwise).

2) In my opinion there is also a threshold for the beneficiary effect of more and more complicated models as the repeatability of our experiments is really somewhat limited due to various uncertainties (i.e. relatively high variance if the same test is repeated over and over).

3) All our models should help us actually building or preserving structures (i.e. serve a purpose). After all we are engineers not philosophers.

Certainly there can not be perfect models (which probably means a perfect mathematical representation of reality?) as we have no means to actually perceive reality directly but can only observe ‘what happens’ in experiments and draw our conclusion from these observation.

That being said I thank you again for starting an interesting discussion!

BR Martin

Dear Mr. Herbrand,

thank you very much for the reply with valued information, especially in the last hours of the year 2018. I aggree with all the points of your answer.

According to "empirical science" as presented in your reply, it can be concluded that empirical factors are included also in mechanical models. They are required for describing the physical boundary conditions. The question is, which level should be considered as basic elements of mechanical rules. For example, the new proposed EC2 shear model is based on the assumption of shear strength Tau_c of cracked concrete (also including uncrack part) as square root of fc and this is dirrectly applied in the final shear strength equation. This point is clearly empricial. It is noted that the new shear equation of EC2 is very good in terms of prediction accuracy. Another approach is that with the basis of existing mechanical rules (obtained from experimental works) such as aggregate interlock the shear model is step by step formulated. To complete the final shear equation, an additional factor may be required to fit to the experimental results (of shear strength). This factor is also an empirical factor. Both approaches also require certain assumptions, which are empirically formulated.

Therefore, by considering shear models a practical question is, which model is valid for many cases (more general solution). This criterion should be considered by evaluating shear models. If a model has to be modified in core of formulation when considering new members (e.g. new concrete or reinforcement), it may not present a general solution.

About point 2) and 3) of yours: in my opinion, we even dont need a perfect model, which shows a scatter is equal to scatter due to random field effect (as the same as "repeat effect" of experiments). By the way, according to my analysis, the natural variation coefficient of shear strength of RC members without shear reinforcement is about 9%. The precise of a prediction should be set in relation to the parameter uncertainty and model uncertainty. For example, for the design we often have only the compressive strength of concrete fc, with this we cannot expect to have a model with a variation coefficient of total uncertainty smaller than about 12%.

Thank you again for the interesting reply.

Best regards,

Linh

Dear Mr. Tran,

Sorry to come into the conversation this late, but it's a very interesting one and something not so common for engineering discussions. Mr Herbrand raised a lot of interesting points.

Personally, I think it can be misguided to think of models in terms of 'mathematical purity' to which we are often guided by the 'unreasonable effectiveness of mathematics'.

For any model in 'natural sciences', as Mr Herbrand said, empirical observation is at its heart. So too will it be for shear.

For example, E=mc2 is the conversion between mass and energy. It's a perfect model but still requires a 'conversion rate' - c2, and c had to be empirically observed.

Or closer to engineering, e.g. the strength of concrete in compression N = Acfc can be thought of as a conversion between compressive strength and axial load of a cross-section. The conversion 'rate' is 1xAc (even 1 is an empirical factor).

Best regards,

Nikola

I would like to introduce you to one of the shear models, which are very strict with empirical factors.

Article A mechanical model for the shear capacity of slender reinfor...

I hope you all enjoy reading this paper and would welcome your feedback on it.

Best regards

Ngoc Linh Tran