It would be good to start these reflections with the following quotes (Wilson, Jan 2002):

[My freshman Physics instructor dogmatically warned the class "do not use an equation you cannot derive". The same instructor once stated that "if a person had five minutes to solve a problem, that their life depended upon, the individual should spend three minutes reading and clearly understanding the problem"..."With respect to modern structural engineering, one can restate these remarks as "do not use a structural analysis program unless you fully understand the theory and approximations used within the program"]

It has been quite a while since starting my career; through which, I have attempted, or more precisely, life has taken me across a number of challenges, in a pursuit for engineering excellence that I hope would be reached one day. One of these dares is trying to track, or maybe confirm, the actual development in structural engineering, in light of the astronomical advancement of #CAD / #FEA and debate of responsibly deploying them. A debate usually witnessed among young and “older” professionals.

Let us imagine a journey in time, no farther than the late 1970’s; maybe similar discussions on the analysis and design aids were, as well, very much on the table. Examples include the use of ready design charts like column interaction diagrams versus establishing case-specific ones, or crack width tables for water-retaining structures, #Pucher_Charts for plate elements, and helical stairs analysis charts, etc... The older chaps back then used to, most probably, criticize the heavy reliance on these things “without understanding the basics”, albeit many of them now pride themselves on the ability to use the “old fashioned” charts versus “blind” #FEA software packages, by suggesting that using them is more sensible.

We have been living the same debate, and we will continue to do so. Yes, we see every day those who analyze deep beams as elastic shell elements, or even by applying WL^2/8 to design them, and yes, some analyze seismic excited structure with little or no information about basic vibration theory. We come across many of those who claim to design according to certain codes and in reality, they simply change the design option in the software without reading the code itself or having a copy of it. But after all, there are great engineers who attribute lots of their experience and development to FEA-provoked ideas and techniques.

It is not disputed that #FEA method has participated in expanding our theoretical knowledge and efficiency. For instance, we have a more accurate appreciation of materials behavior by modeling the non-linear parameters virtually without having to do full-scale testing; we can resolve n degrees of indeterminacy in no time. We have a much better understanding of the external loads applied to our structures; we can simulate them without shaking tables. We've recently started to consider adopting performance-based design (#PBD) over strict reliance on codes. Some have already ditched the inertia reduction factors suggested by seismic codes and found several ways to calculate them accurately. Others discovered that the “weak storey” doesn’t apply for the floors below and above Outriggers in Outrigger-braced Supertall buildings (Choi, Hi Sun, Goman Ho, Leonard Joseph, and Neville Mathias, 2014). Moreover, the #FEA use is evolving; we started to reconsider the deployment of existing analysis techniques like response spectrum analysis and have NL #time_history as a standard approach instead. We could very soon have topology optimization as a fundamental tool in every project. All of this has been made possible by the power of computers and #FEA, these horses that we ride extremely well sometimes, and awfully bad most of the time. In short, we must acknowledge that we are learning so much by interacting with #FEA packages. Something like putting the hands on a #Ferrari wheel for the first time, you must be trained, sluggishly at the beginning, until mastering it. You will later admit that you have never been a driver up until sitting on that red leather seat!

But here is the big question: Are the majority of structural engineers getting really better? I guess not at all, the overwhelming situation is worrying. There is a whole generation of structural engineers who can't make a single step without ETABS, SAP, RAM, and SPACE GASS, etc.. This is why it will be inevitable one day to enforce formal certification for using software packages. I guess we will see -in the future- licensed FEA Engineers pledged to abide by a code of conduct and committed to CPD in FEA particularly, just like #Chartered / #PE engineers around the world.

On a separate note, I guess the public see things in a simpler way: designers now, and in the past, are just the same, how can we say that is not true if we stand next to the 9-decades-old #Empire_State? It is undoubtedly a great engineering task, designed and completed in mere 20 months (S Ghosh, K Robson, 2015) with no, whatsoever, any aid of the advanced #FEA packages we wear on our heads every day. Is that a valid claim? Obviously not, because if we design the very Empire State today, adopting the same lateral system, we would have accounted, to say the least, for the stiffness contribution of the cinder concrete encasement put around all of its steel frame elements (Taranath, 1998) without calculations. This encasement has increased the intended lateral stiffness by 4.8 times. Taranath says: “The structural steel frame with riveted joints, while encased in cinder concrete, was designed to carry 100% of gravity and 100% wind load imposed on the building. The encasement, although neglected in strength analysis, stiffened the frame particularly against wind load. Measured frequencies on the completed frame have estimated the actual stiffness at 4.8 times the stiffness of the bare frame” (Taranath, 1998, p. 10).

Moreover, the same building today would have been designed for the accurate application of horizontal loads, followed by proper analysis and optimization. Not only this, it could have been provided with more efficient lateral systems without fearing the complex analysis and try-error cycles by hand.

To #FEA or not to be? I am sure you know the answer, but let us regulate it at least within our professional organizations, until there is something formal one day in the near future.

---

Works Cited

Choi, Hi Sun, Goman Ho, Leonard Joseph, and Neville Mathias. (2014). Outrigger Design for High-Rise Buildings: An Output of the Ctbuh Outrigger Working Group (2 ed.). New York: Routledge.

S Ghosh, K Robson. (2015). Analyzing the Empire State Building Project from the Perspective of Lean Delivery System—A Descriptive Case Study. International Journal of Construction Education and Research, 1-14.

Taranath, B. S. (1998). Steel, concrete, and composite design of tall buildings. New York: McGraw-Hill.

Wikipedia. (2018). Empire State Building. Retrieved June 1, 2018, from https://en.wikipedia.org/wiki/Empire_State_Building

Wilson, E. L. (Jan 2002). Three-Dimensional Static and Dynamic Analysis of Structures (3rd Edition ed.). Berkeley, California, USA: Computers and Structures, Inc.

Designing columns is possibly the most repetitive task structural engineers undertake in their daily routine. When we have a column subject to combined axial and bending, one might ask the following questions:

1. How slender is this column?
   Slenderness of any column is the single most important parameter we should determine at the beginning of the design task. As a rule of thumb, if the column is braced, then a height to width ratio (or slenderness) under 15 should make an axially loaded column fail at a loading nearing the squash load, i.e., the capacity of the section. Whereas in unbraced floors, the height to width ratio should not be any greater than 10; otherwise, failure will happen quickly on buckling way before the section capacity is suffering.
   Keep in mind 3 ratios: N*/BH, M1*/BH², and M2*/HB²; if the first one is above 15, then have a closer look, and if any of the other two is higher than 1.5, do the same! Also, make sure you are watching the moments applied at top and bottom; if they are resulting in single curvature deformation, then have a good check!
   Talking about braced or unbraced floor, or column, is also a very interesting topic! Providing a concrete core or shear wall does not tick the box, and we still need to make sure that the floor in question is sway or not. This can be easily checked by calculating if the following ratio (from ACI318-M): Q = (SP x D) / (V x L) Where SP is the sum of axial loads in the floor, D is the lateral sway from the same load scenario, V is the lateral load applied onto the floor, and L is the storey height. If Q is less than 5%, then the floor is column/floor deemed to be braced.
   When a floor is sway, which is not a good thing, we are entering a totally different league because the failure at buckling becomes really problematic, imagine that if you have a column of circa 3 meters in height, will have to be studied as 4.5 or 5 meters… too bad.
   In any case, braced or not, we need to calculate the Euler load of the column, that is:
   
   This is a Frankenstein version of the original Euler load which addressed steel columns, or more specific a material does not suffer cracking or load redistribution like concrete. So what our code writers did, they’ve invented a moment-curvature formula linking the inertia with concrete strain and moment capacity at the balanced condition (i.e. the highest moment capacity of column that coincides with some 30% of maximum axial load).
   Also when you look at this Nc equation, you will find that the higher is the sustained load on the column, the lesser is the capacity, something really interesting and eye-opening! When we talk concrete we need to count for cracking AND creeping.
   RKALC will help on this, and will determine each and every meaningful ratio:
   
2. Is there a problem in 3D? (Biaxial Moments)?
   In simple words, we need to study an interaction somewhere between the two for each axis, or under a performance point = (N,Mx,My) and this can be looked at in the Pink diagram of RKALC.
   Note the code formulae here is nothing but an equation of an ellipse, that becomes a circle at maximum, or a triangle at minimum. It is very interesting to see that the bi-axial capacity becomes less "triangle" when the column is subject to low axial loading, becomes high, or like a circle equation, when the axial load is high.
   
3. How does it perform under fire?
   The Australian Standard gives good guidance on columns performing under fire; however, the method there is very crude and does not give full context on the assumptions. This is why we all use the Eurocode 1992-2, which is fully permitted under the Australian Standard.
   Basically, we apply the full dead load and a fraction of the live, and check if the column is subject to small, moderate, or high first order moment, then interpolate between nine tables C1 to C9 to determine the minimum width of the column.
   Our standard has taken tables C4-5-6 assuming moderate first order moment; this is why we do not use it unless the analysis shows moderate.
   RKALC is able to do the interpolation for you, using the EC2-2.
   
4. Does it need special confinement reinforcement?
   When the high-strength concrete is subject to high axial load or high bending, confinement becomes paramount; this is something you need to maintain near the junctions when the column is subject to double curvature moments, and within the centre height when single.
   RKALC is able to study this seamlessly:
   

STM is a very efficient and simple way to represent the stress flow within a concrete element or parts of it that are under the D region category, where Bernoulli assumptions are not applicable. Some say that the use of this method goes back to the early 20th century, yes, some 120 years ago when concrete was a new thing, and engineers used to rely on their intuition and expectation of load path.

STM was given several boosts between the sixties and early eighties when Schlaich et al. published guidance on the theory and given typical examples with load paths. Later, international codes started to implement and “regulate” it if you wish, to keep up with engineers, who always challenge the status quo.

In recent decades, computers have developed astronomically, to an extent that simulation of cracked concrete and non-linear analysis are becoming a standard. More interestingly, the load path is now easy to find via Topology Optimisation software packages, yet STM remains indispensable despite being a lower bound type.

Typically, you would start with a certain model or triangulated load path and assume truss as well as node depths, then draw geometry and analyze to check the stresses and reinforcement. This cycle keeps repeating until reaching reasonable convergence, i.e., stresses are slightly above code limits to claim the maximum truss depth for minimum REO percentage.

Clearly, it is tiring and needs to be automated somehow; hence, the RKALC’s STM calculator.

General rules to follow:

1. The concrete structure is basically divided into either B (Bernoulli) regions where the beam theory applies and stress distribution is linear within the section, or D (Disturbed) regions where it doesn’t.
2. Within the D regions, truss analogy can be applied by following the load path lines (principal stresses) and representing them as straight struts (compression members - concrete) and ties (tension members - reinforcement) intersect in nodes (concrete).
3. The angle between diagonal Struts and the horizontal line is feasible between 25º and 65º.
4. Equilibrium must be maintained while developing the STM model, and concrete must not fail before the steel reinforcement yields.
5. Tension is neglected in concrete, and forces in struts are uniaxial.
6. Anchorage and detailing are essential.
7. There is no exact STM model; however, there are poor and good models.
8. Struts can be categorized into prism, bottle, and fan.
9. Nodes (concrete) are categorized into 4 types: CCC, CCT, CTT, TTT (C stands for compression, and T stands for tension).
10. Stresses within struts, ties, support, and under load regions must be within allowable code limits.

Have you had a chance to explore our STM Calculator? (strut-and-tie method) Within its virtual walls, you'll discover a treasure trove of our most sought-after apps, each a shining star in its own right. These exclusive gems aren't just unique in the whole web – they're here to serve up engineering analyses and designs in a way that's nothing short of cutting-edge.

Meet the STM Wall app, a true time-saver when it comes to tackling iterative STM models. No more hours lost in geometry puzzles and stress calculations. With this app at your fingertips, you'll breeze through those tasks, giving you the freedom to focus on the finer points of your job and dive deep into detailed design processes. See Link

And that's not all – say hello to the RKALC Diamond app, your go-to guide for handling rotating columns with finesse. Imagine a column taking a 90-degree spin from basement to the ground floor. It's a sight to behold, and our RKALC Diamond app ensures that the transition is as smooth as sound. It helps you size up a column capital if needed, directing stress across a three-dimensional domain and channeling reinforcement through the column cores, creating a solid foundation for strength. See Link

Last but certainly not least, our Corbel app is your passport to perfect corbel creation, employing the Schlaich STM model. Just like its companion app, this tool lets you dive deep into the specifics of corbel design, sizing up nodes and selecting the ideal struts to ensure structural harmony. See Link

So, what are you waiting for? Embark on a journey through our suite of apps. It's more than just grim and boring calculations – it's about transforming your engineering experience to the KALC way where again, you put face to the KALC.

First things first, as you read this post, please refer to Coupled Shear Wall calculator available at: See Link

The issue of coupled shear walls is one of the most debated topics among structural engineers. It's not surprising to see five people with twenty different opinions, each of valid points. Ove #Arup once said on this:

"The more you look, the more you see,
And that's why experts disagree.
For some look here, and some look there,
But no one can look everywhere.
For if they did, it seems to me
That they would hardly be experts, you see.
According to their point of view,
What they say may well be true,
But looking from another angle,
We tend to get into a tangle.
Which of the views is then correct?
That is not easy to suspect.”

Many of us might appreciate that the flexibility of the beams can affect the distribution of force within height. There's an old rule of thumb that states coupling beams experience maximum shear within the bottom quarter of the wall height (around 0.2 to 0.3 of H). According to a wise man by the name Juravski, a rigid beam takes shear represented by Vh/z. Here, V stands for the total shear applied to the wall, h represents the typical storey height, and z is the ratio of the wall length in plan (0.7L for single walls and approximately 0.85 for walls forming part of the core).

In cases where the geometry doesn't allow for squat-like or stiff beams with minimum depth and the span is relatively large, we refer to this as a flexible beam with an aspect ratio greater than, let's say, 4 (span to depth). In such scenarios, the maximum force travels from the bottom quarter to approximately 0.5 to 0.7 of H, resulting in a fairly uniform distribution of force across all beams. The magnitude, in this case, becomes a fraction of Juravski's formula, roughly ranging from 30% to 50%.

There's also a sweet spot, a range of medium stiffness with an aspect ratio between 2 and 4. Within this range, the shear suffered is approximately 75% of Juravski's formula, occurring at 30% to 50% of the height.

In any of the three cases mentioned above, the total sum of shears taken by the beams would be equal to the total reaction exerted by the wall pier connected to the group of beams.

It is unfavorable to have no coupling beams and solely rely on the slab as the coupling element. However, there may be situations where space constraints force such a configuration, and in those cases, the global behavior of the wall can be manipulated by transferring the force from one level to another.

Irrespective of beam depth or rigidity, some of us try to make sense of what we observe in ETABS. For instance, when adjusting beam stiffness to 40%, 70% etc., we are addressing a relevant matter. This involves artificially simulating post-ultimate loading event behavior by inducing cracking, a matter of judgement and thinking. Try all of these scenarios at our RKALC calculator.

Clause 10.3.1 of the Australian Standard AS3600-2018 includes a very interesting stipulation on columns in relation to the ratio of M1/M2. This applies to normal columns found throughout the building height, which are typically subject to double curvature behaviors.
According to the Standard, if the analysis moment is less than the minimum eccentricity moment about the respective direction or 5%DN*, the ratio above should be taken as negative. This means the column should be assumed to be subject to single curvature, making it more conservative due to the high moment magnifier (δb).
The logic behind this stipulation is that there may be inaccuracies or errors during installation or due to pattern loading. As a result, the column might experience single curvature loading or "snap through to single curvature mode," as stated in AS3600. Therefore, the analysis assuming double curvature moments would be overwritten by the opposite minimum eccentricity moment.
You might think that increasing the analysis moment above the minimum would result in less conservatism, which is bizarre! However, there is a slight problem with this logic. If there are out-of-position issues, the column would most likely remain subject to single curvature mode, regardless of the analysis moment. This is because an increase in axial load due to construction tolerances or severe pattern loading will induce single curvature.
For those who follow the letter of the Standard rather than its spirit, it is always advisable to have the ratio negative. However, if you can justify it by rationalising the moments from analysis to capture pattern loading or out-of-position scenarios, you may consider otherwise. Ultimately, the judgment is left to your discretion.
Visit our very popular and free Column Calculator in following link, we have added saving and opening files to the webapp to save time of re-entering parameters.