Structural Analysis: A StartUp Post

Writing blogs was never my passion. I am a structural engineer and I am not so good in writing. I found interest in writing blogs just lately. I was searching for some topics in structural engineering when I was led to a blog site of an engineer. Then I got the idea: why not make blogspot as tool for storing notes and ideas. Being in structural engineering field, I found blogspot as a right place to express engineering ideas by writing it out. In so doing, ideas are recorded for safe-keeping within an infinite period of time.

As a startup, I am reproducing an article I wrote long time ago pertaining to a project I was involved with during my stint as young aspiring structural engineer. The year was 2003 -- the period when I was still working in IHI (Ishikajima Harima, Inc), a Japanese design firm. The company is known for its expertise in cement plant engineering and design.

The article I wrote and submitted to our project manager for his validation was intended to argue with our 'design subcontractor' about a design analysis they carried out. It was my belief that what they did was wrong: they committed a structural blunder in engineering analysis. The story will be clearly told as you read my article. Here it goes: (This is for engineers)

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DISPLACEMENT COMPATIBILITY PROBLEM IN STAAD MODELING & ANALYSIS

This article is dedicated to AMRAM CEMENT project. Discussions herein are extracts from my notes I took while working with the project.

THE PRINCIPLE
Consider the two dimensional structure as shown:

When force P is applied at Node C, Node B will be displaced and takes a new position that is Node B'. The amount of DISPLACEMENT as indicated is dependent on two factors: the magnitude of force P and the stiffness of members converging at Node B.

By Hooke's Law, as discussed somewhere in this paper, we will find out that the greater the force P; the greater will be the displacement at Node B.

Inversely, by the same Law, the greater the stiffness of the structure, the smaller the displacement will be at some specific nodes in the structure.

While working in IHI Philippines, I observed when making a model in STAAD, sometimes a structure is sliced into two or more structural models. A common practice embraced by most engineers in STAAD Modeling, the idea of 'slicing the model' is attributed to the size and complexity of the structure. Staad software, even with its latest version, tends to crash during analysis and design operations especially if the model is relatively complex and large. This limitation leaves the 'Staad Operator' no other option but to 'slice' the model. In my own point of view, however, this practice holds some loopholes and lapses. These I will try to prove in the following discussions.

THE USUAL PRACTICE
Considering Figure 1, the structure may be sliced into two separate parts (assuming that it is large and complex). The separated structure may be represented into two model schemes as shown below: (Consider P a non-zero value)

In IHI's practice the models in each scheme are analyzed separately, each with specific sequence. The sequence in each scheme is determined by the inclusion and location of the 'dummy support'. In scheme 1, the sequence starts with Figure B; while in scheme 2, the sequence starts with Figure AA. The reason for the sequence is that the reactions R1 and R2 have to be determined first in order to proceed with the remaining parts.

This approach seems to be the most common philosophy applied by most engineers in STAAD 'modeling and analysis'. Apparently, without further investigation, this seems to be correct. However, I believe, this philosophy is a blatant blunder in structural analysis.

The basic philosophy behind this approach is simply a transfer of loading from one structure to another. Transfer of load is an ordinary and practical matter in structural analysis. But from my point of view, transfer of load is logical only to 'STRUCTURE-SUPPORT RELATIONSHIP'!. That is, the reactions due to the structure are transfered to the supports. However, for a single structure sliced into multiple models whose 'slicing' method conforms to the idea embodied in schemes 1 & 2 and analyzed separately, the process involved is not as simple as we think: there are critical structural principles involved. Consequently, the principle of load transfer is not applicable to nodes, specially if we treat nodes as supports, unless otherwise the displacement compatibility principle is not violated.

While working with AMRAN CEMENT project, I had the chance to share this view with Mr. Nishida and his army of engineers from CEC, the company that contracted the design of the project, in an effort to prove that the approach they employed in their analysis and design is a blunder. I tried to bring to their to their attention the principle of DISPLACEMENT COMPATIBILITY but apparently none of his armies, including himself, could appreciate the principle. Perhaps, none of them has those words in their vocabulary, hence justifying their approach. For this, I was enticed to believe that AMRAN CEMENT project was partly a product of analytical error due to ignorance; a fact that an engineer in-charge will certainly deny.

The sample problem that I discussed with Nishida and with his army of engineers is the same sample problem that I presented here. The following are the general statements of the structural problems that were encountered in AMRAN CEMENT project.

An engineer with a common sense must be keen enough to understand the following observations:

SCHEME 1 CONDITIONS
In Figure A:

• Node B has two degrees of freedom. Meaning, it can displace both horizontally and vertically due to load R1. This is incompatible with Node B in Figure B.
• All members absorbed stresses. This is contradictory to Scheme 2.
• Support reaction R1, a result from analysis of Figure B, has a NON-ZERO value.

In Figure B:

• Node B doesn't have any degree of freedom: it can neither displace horizontally nor vertically. This is incompatible with Node B in Figure A.
• Member BF is restrained at both ends; therefore it has ZERO stress. It is a contadiction to the original structural conditions in Figure 1.
• The load P is shared by two supports only, but in Figure 1 it is originally shared by three supports. There is, therefore, a considerable increase in stresses in Member CF as compared with Figure 1.
• Support reactions on Node F from Figure 1 and Figure B are not equal. These are supposed to be equal, regardless of the sequence being followed, because they both refer to the same thing and the same structure.

SCHEME 2 CONDITIONS
In Figure AA:

• Node B doesn't have any degree of freedom: it can neither displace horizontally nor vertically. This is incompatible with Node B in Figure BB.
• Member BE cannot absorb stress. Other members may absorb stresses.
• There are no applied loads, which imply that members didn't absorb stress rendering them useless. This is IRONIC since Staad, and even anybody, cannot design a member whose stress is ZERO. Subsequently, support reaction R2 has a ZERO value due to the absence of applied load in Figure AA.

In Figure BB:

• Node B has two degrees of freedom. This is incompatible with Node B in Figure AA.
• Member BF and the rest of the members have a NON-ZERO stress. This is a contradiction to Figure B.
• The load P is supported by a single support; but in Figure 1, it is originally shared by three supports. There is, therefore, a considerable increase in stresses in Member CE as compared with Figure 1.
• Support reactions on Node F from Figure 1 and Figure BB are not equal. These are supposed to be equal, regardless of the sequence being followed, because they refer to the same thing and the same structure.
• In addition, support reactions R1 and R2 both refer to the same node and same structure. Therefore, the must be equal in magnitude and direction! By inspection, however, schemes 1 and 2 showed the otherwise.

STRUCTURAL CONDITIONS
There are contradictions in structural conditions WITHIN schemes 1 and 2, respectively. There are even more contradictions in structural conditions BETWEEN schemes 1 and 2. These only manifest the inability of both schemes to reperesent the original structure. Insisting on 'Model-Slicing' to analyze and design the structure may result in either OVER-DESIGNED or UNDER-DESIGNED structural members, or may result in BOTH. Try to figure it out basing on schemes 1 and 2 how it is possible to happen.

Comparing each of the schemes to the original model yields irreconcilable differences in structural conditions, as itemized above. This further attests that "SLICING' approach employed by CEC and IHI structural engineers in Amran Cement Project is not feasible. The approach, a possible blunder in structural analysis that needs a further research, was a risky attempt to simplify the design process using Staad Software. Indeed, Staad is not a THINKING TOOL but a 'number-crunching' software incapable of logical thinking. Staad is a machine with a hundred percent effeciency; that is, in essence, if one's input is garbage, the output is a garbage, too.

POSSIBLE SOLUTIONS
There are no shortcut solutions to this problem but to resort to the creator of Staad, Research Engineers International (REI), by suggesting them to come up with a new feature for Staad. We may suggest to create a kind of virtual support that replicates the BEHAVIOR (ability fo displace) and PROPERTIES (combined stiffness and rigidity of converging members) of a node under a given applied load. The virtual support must be defined so as to ensure the displacement compatibility of nodes at separation line.

Having personally written some programs in structural analysis especially ones that involve matrix operations, I felt this is very much feasible for REI to come up with. REI website entertains opinions and comments from Staad users, I supposed.

Another logical solution is AVOIDANCE. In Amran Cement Project, the structures that were subject to slicing were conveyor supports. Due to its overall size (it's length in particular), the whole structure cannot be made as a single model. Staad, as mentioned earlier, has some computing limitations as to the size of the model being processed. As their last recourse, CEC and IHI resorted to structure slicing. This may be avoided by changing the nomenclature of the structure, sub-dividing it into component independent structures.

By sub-dividing the conveyor support into multiple independent and introducing roller supports on one end, the size of the model mey be reduced -- enough to be processed by Staad Engine without causing it to crash.

HOOKE'S LAW DEFINED
F = [AE/L] ΔL or
F = KΔL
Where:
K = Member Stiffness
=AE/L
A = Member Cross-Sectional Area
L = Length of Member
E = Modulus of Elasticity of Member
ΔL = Member Deformation
F = Member force due to external load that would deform a member by an amount, ?L.

The relation stated specifies that member capacity, F, is directly proportional to the stiffness of the member. And with the given stiffness, F would be proportional to the amount of deformation; that is, the greater the deformation, the greater is the force being absorbed by the member.

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