Flexural behaviour and bending capacities of reinforced concrete members like beams and slabs depend on reinforcement and concrete strength properties. In flexural analysis, tensile resistance of concrete [ which is low (about 10 %) as compared to compressive strength of concrete] is generally neglected. In bending, mostly tension and compression actions on opposite sides of cross section of member occur. The effect of shear being less, normally neglected in bending analysis. The cracks in tension side during bending make concrete ineffective in taking shear in tension zone. In compression zone, concrete remains in compression and intact. This makes easy to apply bending beam theory to analysis of reinforced concrete flexure members like beams and slabs assuming concrete as homogeneous material.

In case of shear analysis of reinforced concrete beams or slabs, complex behaviour of load transfer through various ingredients of concrete and also dowel action and geometric parameters associated with reinforcement and cross section of member, make difficulty in quantifying contribution of each parameter towards shear strength. The uncertainties of these parameters is the reason for not having unified shear model in determination of shear capacity of reinforced or un-reinforced concrete members.

Thank you for your reply, Ishwar. You are right about both flexural and shear behaviour of reinforced concrete members when mentioned the uncertainty of influencing parameters.

For calculating bending capacity we need only fc, (Ec), fy, (Es) and the failure mode is clear understood (compression failure of concrete or tension failure of reinforcement).

In case of shear strength we may need all of information of material and geometry of the reinforced concrete member. In most cases, we consider only some of them, which are assumed to be the most influencing parameters. The shear parts are considered with different opinions. Some researchers believe that the dowel action is decisive. Some other suppose that the largest shear strength part is from concrete compression zone. Others think shear strength due to aggregate interlock should be the most shear strength part of RC members without shear reinforcement,....

We do the research on shear strength like the blind men and an elephant.This story can be found in the following link:

https://en.wikipedia.org/wiki/Blind_men_and_an_elephant

A typical approach to overcome this above mentioned problem is that we calculate the shear strength Vc as the sum of all shear strength parts. For example:

Vc = Vcc + Vct + Vc,d

where, Vc - the total shear strength

Vcc - the shear strength in the compression zone

Vct - the shear strength in the tension zone

Vc,d - the shear strength due to dowel action

However, what is the (typical) mistake in this calculation?

Best regards,

Good question.. Please share me the best answer might you get...

Regards…

Good question.. Please share me the best answer might you get.

Good question. In my opinion, the mechanical behavior of bending failure can be described at the sectional level. However, the diagonal cracking of shear failure breaks the description of mechanical behavior at the sectional level. The mechanical behavior of shear failure has to be described at the member level. From the sectional level to the member level, more information is needed and the interaction of each influencing factor becomes more complicated. This is also why we need to study the constitutive relationship at the material level. The smaller the scale, the more stable it is.

Ning Chao-Lie : "The smaller the scale, the more stable it is." I really dont understand this statement. Could you give me a more detailed explanation or proof for it?

"This is also why we need to study the constitutive relationship at the material level". Could you give me an example of the consideration of constitutive relationship at the material level. Thanks.

Regards,

Ngoc Linh Tran

Maybe I can reply to some extent for Chao-Lie. Ning Chao-Lie

Both flexure and shear are mechanical behaviors at the member level (scale), which involves several factors like geometric dimensions, material properties, etc. In general, we use the three fundamental equations to solve the member scale problems, e.g., equilibrium, constitutive model, and compatibility. Obviously, constitutive model bridges the member scale and material scale, and is the most complex part, since the damage, plasticity etc. are all represented in this part. So if we solve the constitutive relationship, the member scale problems can be solved readily.

"The smaller the scale, the more stable it is." means (as far as I understand) for small scale (material scale), we need only to focus on the constitutive relationship, so the problem won't be affected by other parameters like geometric dimensions and external loads.

Back to the original question, why flexure models are accurate but not the case for shear models. In my opinion, flexural behavior mostly relates to the uni-axial properties (purely tension or compression state) of the material point, while shear behavior mostly relates to the bi-axial properties (tension-compression state) of the material point. Evidently, bi-axial properties is more complicated than the uni-axial properties in both the experimental and theoretical viewpoint. It is easy for most of researchers around the world to perform the un-aixal test of concrete but rarely can perform the bi-axial (shear) test of concrete. The experimental equipment and measurement, ect. are difficult to develop. Pioneers in this field, e.g., MCFT by Vecchio et al. from Toronto and STM by Hsu et al from Houston, both started from the experimental investigations of the bi-axial (shear) behavior of a unit concrete panel. Unfortunately, although 40 years past, problems still remain. We didn't even experimentally find out the precise mechanism of shear, how can we propose an accurate analytical model?

De-Cheng Feng: thank you for the reply.

"The smaller the scale, the more stable it is." By formulating a constitutive relationship of material behaviour, the properties of material (here concrete) need to be used. However, the mechanical properties such as concrete compressive strength fc and tensile strength fct depend on the geometries (of samples like cubic or cylinder). Because concrete is not homogeneous material but strongly brittle, it shows a size effect. This means the concrete properties in relation to the sample size should be correctly taken into account. The natural variability of concrete properties is stronger on the small scale, which may lead to a larger scatter of analysis result. It is therefore difficult to say about the stability of the behaviour of concrete material on the small scale.

I think the important result of the bi-axial shear tests is that the potential shear strength of cracked concrete is large. We have not so many experimental results, but I think enough to describe the behaviour of concrete also in bi-axial state. If a shear model (e.g. using experimental results of the pure shear tests like MCFT) is not valid for all members, its approach is probably not good enough and should be modified.

Ngoc Linh Tran

Maybe there are some misunderstandings.

The stable here may not refer to the 'stability properties' of concrete. Here Dr. Ning means (I guess) the concentration of the problem (focus on constitutive relations only).

All in all, the word stable may not be suitable.

You write: "The flexural behaviour and bending capacity of reinforced concrete members is clearly explained and can be determined with very high accuracy.".

Nevertheless, even this is not true. Thanks God, flexural capacity is very unsensitive to concrete strength, hence the negative influence of our assumption of perfect bond vanishes unless we apply relatively thick rebars. In that case when the relative depth of compression zone is beyond ~0.2, the calculated ultimate bending moment is on tthe unsafe side!

The fundamental source of the problems with shear theory was the decision at the end of the XIX century, that for bending the flanges, and for shear the web are "responsible".

See my attached quite recent paper.

The "concrete contribution" to shear load-bearing capacity Comes from the concrete compression Zone. Aggregate interlock does not exist, does not contribute at all.

Best regards

Andor Windisch

To Mr. Windisch: thanks for the reply.

Actually, I dont really understand your statement, that the calculated ultimate bending moment is on the unsafe side, when the relative depth of compression zone is small, e.g. 0.2.

About the shear strength of reinforced concrete, your statement regarding the effect of aggregate interlock may be true for the case of RC members with shear reinforcement or for short beams. In this case, the contribution of aggregate interlock in shear is quite small compared to other effects and can thus be neglected. However, when we considere RC members without shear reinforcement, many shear tests show that the aggregate interlock has strong influence on the shear strength, especially for slender members with small depth.

About your paper: many strong statements again existing theories are given without confirmation of experimental results. It may be due to the limitation of page number and I hope that you can support more detailed explanations for your conclusions.

By the way, in Section 2.5 you explain the "size effect" with an example of a constant flexural force as well as a constant longitudinal tensile reinforcement. This is not suitable, because we should considere the effect of size when all geometrical parameters are kept with the same ratios (only scalling).

Best regards,

Ngoc Linh Tran

Thanks for the interesting re-questions.

At calculation of the flexural capacity we assume perfect bond. Nevertheless, we admit that a Ø8 rebar yields at smaller crack than a Ø28 rebar does. A wider crack is longer than a smaller one. Applying only Ø8 or only Ø28 rebars in a say 200 mm deep cross section than the cracks are different Long and if the rate of reinforcement (i.e. the relative depth of compression Zone) as high that the crack extends into the compression Zone (they are incompatible to each other) then the cross section fails below the calculated moment. I drew this conclusion evaluating test results of Kordina and Nilsson on opening Corners. You can find the relevant figures in my paper on efficiency factor of inclined rebars (rebars which are not in trajectory direction (see RG). Opening Corners: Increasing the rate of reinforcement the Ratio of measured to calculated failure load decreases. The test does not mistake, only our calculation model. I dealt with many Tests concerning brackets. The authors arrived at max. sensible rate of reinforcement: all at about 0.2!! We engineers neglect to consider and fulfil compatibility.

Aggregate interlock: in order to activate ai a relative parallel shift of the crack faces and small crack widths are necessary. Muttoni and Völgyi et al. measured the relative movements of real crack faces: either there are no parrallel shifts of the crack widths are big! We engineers neglect to consider crack face kinematics. The crack face kinematics are identical either without or with shear reinforcement.

In the Tests of Walraven whe relative movements of the crack faces were produced without obeying any real crack face kinematics: no compression zones influenced the movements. Consider please the paper of Völgyi et al. in Structural Concrete about innecessity of Aggregate interlock.

You are completely right: the limits in words and pages constrict a deeper support of the theses.

My first paper on this issue was published in BuStb. in 1988. You can find my other relevant papers in RG.

Size effect: further Explanation will follow.

If you agree, we should continue our discussion.

Kind regards and good success in your research.

Andor Windisch

Dear Dr. Windisch,

thank you for the reply. Yes, I am willing to continue our discussion. The main points in your reply can be summarised as follows:

1. With the same longitudinal reinforcement ratio, the member with a larger diameter of reinforcing bar can fail by a moment smaller than the calculated bending capacity.

2. If there are some reinforcement in compression zone, concrete members also fail with smaller moment than that of calculated bending capacity.

3. Also the same trend, when the relative compression zone is smaller than 0.2.

Note that, in all above case, the failure due to the yielding of the tensile reinforcement is assumed.

*******************************

First of all, the phenomenon you described is very interesting. Thanks for giving us this information. In what follows I will explain/comment your findings.

1. I agree that with the same reinforcement ratio, a larger reinforcement (e.g. in terms of diameter) leads to a larger crack width. This is true, because the crack width depends on crack spacing, which can be estimated as scr,m = fi/(3.6*roef). However, it should be noted that this is only valid for members with small depth, let's say d < 300 mm. In this case, the primary crack is also the secondary crack in the considered beam.

For a larger beam, which has a primary crack significant larger than the secondary crack (the secondary crack occurs only in the region round of the tensile reinforcement), the crack spacing is not dependent on the diameter of the reinforcing bar any more. According to estimation of Reineck, it is about 0.7*(d-x). In this case, the crack widths in both members (with small and large fi) are nearly the same. Therefore, the load bearing capacities are also the same.

2. It depends on the definition of the bending capacity (calculated strength). If the bending capacity is calculated (as Ft*z) based on a linear distribution of stress in compression zone, the depth of compression zone may be underestimated. If there is reinforcement in the compression zone, this reinforcement may yield (especially in some decades ago, the yielding stress of reinforcement is small, e.g. 290 MPa --> eps,y is about 1.45%o, quite far from eps_c1 of concrete). The yielding of reinforcement in compression zone leads to an increase of compression depth, reducing the distance z. --> reduce the bending capacity.

3. Also if the linear distribution of stress in compression zone is assumed for the determination of the compression zone, the obtained result is underestimated when the reinforcement ratio is small. This is due to the nonlinearity of concrete in compression zone. In this case, I suggeste to use the formular of Martin Zink (2000) to estimate the relative depth of compression zone: x/d = 0.78*(Es/Ec*ro)^(1/3). This will help to partly correct the calculated result.

More details of the explaination regarding the depth of compression zone and the relation to the shear strength is presented in my habilitation thesis:

Thesis Shear strength of slender reinforced concrete members withou...

About aggregate interlock: you said that the relative movements of crack faces are not seen in the test of Muttoni et al. In fact, this does not mean there is no slip between crack faces. The slip is just too small for the mesuarement.

According to many concrete models and many simulation results for reinforced concrete structures, the behaviour of cracked concrete is very important for shear strength calculation. The aggregate interlock is taken into account in most concrete models. This means, the relation between shear stress and crack width and crack slip have to be modelled. Without this consideration, no good result can be obtained in case of shear strength of RC members, especially members without shear reinforcement.

Best regards,

Ngoc Linh Tran

Dear Dr. Tran

Thanks for continuing our interesting discussion.

1. o.K.

2. I did not mention compressive reinforcement, nevertheless, the compatibility issues remain valid. In brackets and opening corners compression reinforcement is seldom used.

3. This will seldomly occur.

1. I dealt deeply with the problems of cracks (was for many years member of TG 2.1 which dealt crack issues). I published a two part paper (which fib did not accept), but you can find it in RG (see there). The more important conclusions: the mean crack distance is not governing the width of the primary crack. (Already in MC2010 instead crack distance the transmission length are involved in the formula.) The primary and secondary cracks must be treated independent form each other, hence the conclusions of data banks (also from Mr. Reineck) must be revised. The secondary cracks restore the compatibility between big steel slips and limited concrete elongation capacity. The development of secondary cracks near to the primary one do not influence the further development of the width of the primary crack (important!!)

📷

Cracks No. 10 and 14 are primary cracks, 9 and 11, and 13 and 15 are secondary ones. Crack widths 10 and 14 continue to open with the same intensity as before.

(This would be the first estimation of Reineck, which is true…). I know him since 33 years…

2. As I wrote: bending capacity is very unsensitive to the concrete data, hence you introduce very different distributions and concrete plasticity and and and. The governing issue is bond. The compression reinforcement is a seldom point. How does it increase the Depth of the compression zone? For the time being I study the 2D and 3D strength of concrete. The modern higher class concretes do not have any plasticity. (Formula with exponents show for me only that the physical basics were not understood.)

Thanks for your habilitation thesis!!!

AI: please read the Völgyi/Windisch paper in Structural Concrete or in RG about the role of AI.

At your model for relation between shear stress and crack width and crack slip did you take into consideration the impact of the uncracked compression zone at the end of the shear crack?

Once more many thansk for the fruitful discussion and best regards

Andor Windisch

Dear Dr. Windisch,

Thanks for the reply.

1. The difference between the crack width developments of primary and secondary cracks is understandable. The experimental results you gave are also very interesting.

2. Actually I am not very interested in the bending capacity of RC members, but the shear capacity. The depth of the compression zone is of my interest, because it is a part of my shear model. You wrote that the relative depth of compression zone, say kx = x/d, smaller than 0.2 is seldom. It is true for members with steel reinforcement. However, when we consider members with reinforcement made of fibre-reinforced polymer (FRP) such as glass fibre or basalt fibre reinforcement, kx can be very small. With an expectation of a modell also for members made of different concrete and reinforcement types I should therefore consider kx carefully.

3. In my shear model, all information of the concrete member is taken into account. As I wrote above, the depth of compression zone is an important part of my model.

Best regards,

Ngoc Linh Tran

Neglect concrete contribution and use reinforcement to get better results.

Concrete properties suffer high variability and scale applies to different geometries and loading condition, and RC material, compeletly different from concrete, still depends on the geometrical configuration and the loading conditions. Get These in Control, then you obtain more consitent results.

Think of concrete source, gravale clinker, curing, schrinkage…….

Good question.. Please share me the best answer might you get.

I absolutely cannot share the reply of Mr. Hatahet. Following his arguments on concrete should rely even in case of bending…. The Task of researchers is to arrive to a reliable model. And we will manage it. Regards

The main reason is that the shear behavior of RC concrete is influenced by many parameters, which is impossible to consider all of them in a single model.Therefore most authors make assumptions and approximatation in their model, then the model can be applied to some cases but it can't be considered as a unified approach to predict the shear capacity of RC members.

Because we want a model that is at the same time physically meaningful, and simple to use, and accurate, and precise, and versatile.

To reduce complication due to influence of various parameters affecting shear behaviour of concrete, prepare grouping of parameters based on positive and negative effect on shear strength of concrete. Then neglect, those parameters whose contribution is very less.

As you are well aware, the shear's importance compared to flexural phenomenon for normal size of structural members such as beams and columns is lesser and shear is more important in deep beams which are not normally used in usual types of buildings. Despite of this the effect of shear stresses especially in supports and in the midpoint of the section is considerable and the stirrups and ties are calculated based on the existing shear stress. Accordingly in addition to the code of practices a lot of research have been performed on it that can be found in the literature. The other issue is the interaction between shear and flexural reinforcements that is recommended by the codes but normally in the design is neglected.

Briefly because shear in not the primary phenomenon in the design of the normal size structural members, it is less considered in the researches and standards compared to the other more important phenomena, i.e., the volumes of researches are proportional to the needs and importance of the subject.

All the best.

A shear model, which is presented in the following article, might be a step on the way to answering the question raised above.

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

I believe it is because shear is result of shear stress and bending moment. It makes it hard to analysis and draw a conclusion.

Dear Dr Tran

I think that making a physical sensed and clear understanding of the Shear, punching shear and torsion has been a worldwide research goal for a few decades. Thus excellent models including yours and many others. I do believe it is a matter of time until we get there and these issues are resolved. One day shear, punching shear, and torsion models will be as accurate as flexure.

I believe that compiling worldwide experimental databases and implementing their findings is one of the approaches to develop mechanical behavior models that make physical sense.

A mechanical shear model, consistent for both quasi-static and fatigue loads, is introduced in the following paper:

Article Shear model mSM-c for slender reinforced concrete members wi...

I hope you all enjoy reading it and would appreciate your feedback.

Best regards

Ngoc Linh Tran