Structural Design and Calculations

As you may have noticed elsewhere I try to avoid the use of the word “engineering”, this is because for me engineering takes place at the frontiers of science and technology. I don’t operate at the frontiers and most people don’t want their projects at the frontiers. Most people simply want “tried and tested” adapted to suit their specific needs. The activity of adapting is the process of design. Design is a creative solution finding exercise. Potential design-solutions are evaluated or assessed by calculation to determine if they meet the required objectives. The calculations are based on established technical science as it applies to the specific technologies under consideration.

For structures the technical science includes descriptive geometry (technical drawing), engineering mechanics (statics), and the mechanics of the strength and stability of materials. Mechanical design adds engineering mechanics (dynamics), along with vibration and fatigue.

We can consider machines to be structures which move, and non-machine structures to be mechanisms which are locked.

We can break most machines and structures down into the basic elements of beams and columns, or beam-columns. Columns experience axial loads typically compression. Whilst beams experience flexural loads, or bending loads. Beam-columns experience both flexural and axial loads. There are also torsional or twisting loads.

Structural design can be divided into the following tasks:

  1. Determine dimension and geometry (size and shape)
  2. Determine Design-Actions
  3. Determine Design-Action-Effects
  4. Design Member
  5. Design Connections
  6. Design Support Structure (eg. footings)

If the structure is simple, that is we can break it apart at each of its nodes or joints, and draw free body diagrams of each component and then resolve all the reactions on each component part, then the calculations are typically practical to do with pencil and paper, with the aid of a pocket calculator. If really simple the calculations can be done on the back of a small envelope, if simpler still the calculations can be done without writing anything down.

Even if the calculations are simple it may still be preferable to produce the calculations using a computer. The benefits are:

  1. Speed
  2. Consistency
  3. Improved presentation

A common tool for completing such calculations by computer is an electronic/digital spreadsheet, such as MS Excel or LibreOffice Calc. Other options include: ATCalc, SMath, FreeMat, SciLab, Octave, MathCad, MatLab.

If the structure is simple then all the calculations can be completed in Excel. If the calculations remain the same from project to project, with only changes to the input parameters, then significant productivity gains can be achieved. Full productivity gains are seldom realised as each project introduces the need for additional calculation sheets.

Now if the structure is not simple, then it is task(3), the determination of design-action-effects, where the complexity arises. In such situation everything else can still be completed in a spreadsheet, but the determination of design-action-effects needs calculating elsewhere, and that introduces a bottleneck to the entire process. Though VBA can be used to merge the task back into VBA.

However, matrix structural analysis (MSA) is not a simple thing to write software for and merge with a spreadsheet, so the typical approach is to use commercially available structural analysis software, such as MicroStran, MultiFrame, Spacegass. Then manually transfer the result to a spreadsheet for further calculation. However, most structural analysis software has the facility for member design, and a few packages have facility for connection design. Thus tasks 3, 4, can typically be completed using the structural analysis software, whilst tasks 5,6 need work completing elsewhere.

However, even if we need to use MSA, or finite element analysis (FEA) or finite element method (FEM), we can rough out the design of our structure by simplifying it to isolated beam-column elements. The use of FEA/FEM is likely to be needed if have membranes, plates, or shell elements in the main structure. Such methods may also be used for assessment of connections and footings.

Roughing Out the Structure

Design typically starts with a drawing. Structural drawings are typically stick diagrams. A simple line represents a beam, column or some more specifically named item such as: rafter, strut, tie, purlin, girt, bracing.

A simple line is used because, at the start, only the span of the element is known, and the point and purpose of the structural calculations is to determine the other dimensions relating to the element. For example know the element is a floor beam, but how much vertical space is the floor framing going to occupy? To answer this question need to know the depth of the beam, for which will also need to know other properties, such as the spacing of the beams, and the strength and stiffness of the materials being used.

Typically we deal with simple point loads, and uniformly distributed loads (UDL’s). The UDL’s may be distributed over areas or along a line. If distributed over an area then tend to call the load a pressure, and is measured in kN/m², whilst a line load is measured in kN/m. Pressures are typically represented by the symbols p and q, whilst line loads represented by the symbol w, lower case omega (ω), or q. Whilst point loads represented by P, W, or F. Point loads and UDL’s cannot be added together, but the bending moments can be.

For a simply supported beam the following formula are common:

  1. M=wL²/8 (UDL full span)
  2. M=PL/4 (Central Point Load)
  3. M=P.a.b/L (Point Load distance ‘a’ from left, and distance ‘b’ from right)

The formulae give the maximum bending moment which for cases 1 ad 2, occur at the mid span. For case 3, the maximum moment is at the location of the point load. The moments for cases 1 and 2 can be added to give the maximum moment if the two loads occur together. If case 1 and 3 occur together they can still be added together to get a conservative answer, but if wish a more refined answer then need to calculate the moment at different locations along the span, and add these together to find the moment at each point due to the different loads. Formula for this are:

  1. M=(wx/2) (L-x) {UDL full span}
  2. M[ab]=Pbx/L; M[bc]=Fa(L-x)/L {Point Load}

Where x is the distance along the beam measured from the left hand side, and M[ab] is the moment at a position to the left of the point load, and M[bc] is the moment to the right of the point load.

With these few formula we can rough out the member sizes of the beam elements in a more complex structural assembly, before diving into the use of MSA, FEA/FEM. Though we may also need to give consideration to other beams:

  1. Simple Supports (pin/pin)
  2. Cantilever (fixed/free)
  3. Propped Cantilever (fixed/pin)
  4. Fully Fixed, built-in, or Encastre (fixed/fixed)

The propped cantilever and encastre beams are indeterminate, we cannot determine the bending moment from the equations of statics as the fixed end moments (FEM) are redundant reactions, and as a result we have more unknowns than equations. To resolve this we need extra conditions, typically consideration of deflections. Deflections however are dependent on the structural section and materials being used, and the point of our calculations is to determine such properties.

Numerically therefore it becomes a trial and error exercise: pick a structural section carry out the analysis, pick a new section which is strong enough for the moment calculated, recalc the moments based on the new section properties, repeat until little change.

Algebraically however, we may get to simplify the equations and cancel the dependence on material properties. We can then provide tables of moment formula, especially FEM’s which can be used as a starting point for such techniques as moment distribution. Some additional formula are:

  1. M=wL²/2 {cantilever}
  2. M=wL²/8 (FEM); M=9wL²/128 (span) {propped cantilever}
  3. M=wL²/12 (FEM); M=wL²/24 (span) {encastre}

The three common structural assemblies, and plane frames, we are likely to encounter are:

  1. Triangular frame (2 elements; 3 joints)
  2. Rectangular frame (3 elements; 4 joints)
  3. Gable frame (4 elements; 5 joints)

In any of these frames the joints or nodes can be considered either fixed and moment resisting or pinned and not moment resisting. If the joint is moment resisting then there is a fixed end moment (FEM) for the element at that joint.

With the exception of the triangular frame, if all joints are pinned then the structure is unstable.

Considering the ground as an element spanning between the supports, then the rectangular frame is a 4 bar mechanism. If an horizontal load is applied to it, then it will fold flat against the ground. This can be prevented by triangulating the structure. This triangulation can be achieved by providing a diagonal brace, between the footing support on one side and the eaves joint on the other side. Alternatively a diagonal brace or knee brace can be applied across the eaves joint. Since the horizontal load can be applied from either side two braces are typically required. An alternative is to add one or more extra columns and provide cross-bracing to these. This is the typical situation found with the stick frame construction of houses.

For the gable frame, a beam can be placed between the column heads, triangulating the framework of the roof, however the whole thing is like the fully pinned rectangular frame: its a four bar mechanism, it can still fold up. However with the cross-bar in place the whole structure can be braced up in similar manner to the rectangular frame.

When first looking at a structural proposal, the qualitative aspect of structural design is too look for triangulated frame works and mechanisms. If the structure is not adequately triangulated, then look at the connections to see if they are of a form which can be considered moment resisting.

If we have two supports, irrespective of the structural framework spanning between, we can consider the whole thing as a single span beam. We can therefore simply calculate M1=wL²/8 and M2=wL²/12, for the span, and without calculating loads we can use w=1 kN/m as a starting point. If the proposed section is smaller than M2 requires then either we need to refine the value of ‘w’, or the structural section is inadequate. If the joint is not capable of resisting M2, then the section is also inadequate. If we don’t have rigid connections then expect M1 to be controlling the size of the section.

Now for the sloping rafters of a gable frame or the triangular frame, wind load is applied normal to the slope, this is equivalent to applying a vertical load and a horizontal load. The moment due to the vertical load could be M1=wL²/8 , whilst that for the horizontal could be M2=wf²/8 where ‘f’ is the rise of the roof. For a nearly flat roof M2 will be small compared to M1 and therefore can be ignored for roughing out calculations.

Another design equation to know is M=F.d where ‘F’ is the force and ‘d’ is distance to axis of rotation or the distance between a coupled force. A coupled force would be the forces in the top and bottom chords of a truss, or flanges of a plate girder. So once I have a value for M, I can either calculate the depth (d=M/F) of the truss or the force (F=M/d) in the chord. Once I have the force in the chord I can look up the compressive buckling capacity of a suitable section. Or having chosen a section I can adjust the depth of the truss to match the capacity of the section.

Other quick checks for a gable frame concerns the removal of columns. In cold-formed steel sheds it is common to remove one or both columns from a frame to provide wider roller doors along the side of the shed. If a column is removed then the FEM to the rafter is also removed. If the FEM is assumed to exist then it becomes an applied torsional or twisting moment to the carry-beam, it is unlikely the structural section will have adequate torsional capacity. {NB: Whilst torsion and bending moments are both moments they have different affects on the structural section. Bending moment produces normal stresses which are maximum at the outer fibres, whilst a torsional moment produces shear stresses which are maximum at the outer fibres.}

So if columns are removed the FEM’s are removed. The roof can be assumed to be spanning from one column to the other, rather than assuming rafters span from the top of columns to the ridge. The roof is therefore a single span beam. Attached to the columns it is considered to be an encastre beam, the knee moment is M1=wL²/12 and the ridge moment M2= wL²/24. If one column is removed, then the roof is propped on a carry-beam at one end and fixed at the other and can thus be considered a propped cantilever. The ridge moment mostly unknown, but approaching M=9wL²/128, whilst the remaining knee moment is M0=wL²/8. If both columns are removed then the beam is propped on carry-beams at both ends, both ends are pinned and the roof is now a simply supported beam with a ridge moment M0=wL²/8.

The an encastre beam and simply supported beam can be considered idealistic extremes. No real connection is fully fixed and no real connection is fully pinned. The moment diagram for each case is a parabola with height M0. For an encastre beam the parabola drops below the x-axis by an amount M1, leaving M2 at mid point. A real beam can be considered as having a parabola lying between the two extremes. If the FEM is less than M1, then M2 increases, the parabola rises, it can rise until the mid span moment is M0.

It can be seen that:
M2=M1/2
M1=(2/3).M0
M2=(1/3).M0

So if we can achieve a fixed moment connection we can use a smaller structural section than if we have simple supports. However if we have a structural building system, we need the connection components to match the moment capacity of the main members being connected. Further more if we are going to permit removal of columns the connections and members need designing for M0 not M1 or M2. A ridge connection only designed for M2, will experience 3 times greater moment if both columns are removed. Whilst a knee connection designed for M2, will experience moment 1.5 times greater if one column is removed.

Our portal frame shed is not a stick framed house in which can simply remove stud walls and install lintels to support the roof. The rigid portal frame behaves differently to the pinned and braced stick frame construction of timber/steel frame housing.

Now at a junction the magnitude of the moments have to match. So if use MB1=wh²/2 for the column and MB2=wL²/12 for the roof, then they will not match. First because they have different formula, second because L and h are not equal, and third because the load w is unlikely to be the same for both members. There is thus a problem. Our beam formula do not present the complete picture, however they are still useful for roughing out the structural form and initial estimate of member sizes.

One approach to resolving the difference in moments is to use moment distribution. This approach starts with the FEM’s for the various beam spans and loads, so the column would have MB1=wh²/12 rather than the cantilever moment: irrespective or whether has fixed or pinned bases. the technique then redistributes the differences one joint at a time, until the differences at each joint are negligible. It is typically done numerically rather than algebraically. It is thus potentially easier to setup in a spreadsheet than using the likes of MathCAD.

Personally I have only used the technique on practice examples for continuous multi span beams. However the technique can be adapted for sway frames and multi storey buildings. However, the more members in a structure the more cumbersome it gets to work through and present. Hence matrix structural analysis (MSA) based of stiffness methods is typically the approach adopted for structural analysis by computer. That being said moment distribution is also dependent on member stiffness.

Spring stiffness is typically represented by k=F/Δ, where F is applied force and Δ is displacement or deflection. To get k for a beam we need to know the deflection formula, and rearrange into the form load divided by deflection. This will typically involve a factor E.Ixx/L where E is Young’s modulus or the elastic modulus of the material, and Ixx is the second moment of area about the x-axis for the structural section, and L is the span. The value of E for hot rolled steel and cold-formed steel is the same, so if deflection, or stiffness controls the design rather than stress, then have no choice but to use more material. So cold-formed steel only has weight saving benefit when its yield strength of fy=450MPa is the controlling factor compared against fy=300MPa.

That aside we can now see that we have to know both material properties (eg. E) and section properties (eg. Ixx) of the structural sections used so as to calculate the actual moment in the frame. Since we want to do the calculations to determine the size of section, where do we start? The answer is we start with our simple beam formula.

Now as with the indeterminate single span beam, solving algebraically may cancel out the material and section dependencies or it may not. Instead of using moment distribution an alternative approach is to use rigid frame formula, one common collection is the Kleinlogel formulae. Some of which are presented in the British Steel Designers manual. A review of these formula indicates that they are independent of ‘E’. Also rather than being dependent on Ixx they are dependent on the ration between Ixx of the column and the rafter. If the column and rafter are made from the same structural section which is common then the ratio is 1, and therefore don’t need to know the actual sections. Depending on circumstances a different ratio could be adopted for initial design, until at a stage you are able to calculate the actual ratio.

Other approaches for getting the actual moments in the frame or an estimate of the moments involve assuming points of inflexion and converting the frame from being indeterminate to being determinate, by inserting pins at the inflexion points and breaking the frame apart at these points.

Manufactured Structural Products (MSP’s)

Manufacturers of manufactured structural products (MSP’s) typically want product configurators so that sales people can specify the product at the point-of-sale (PoS) whilst discussing requirements with a customer.

Since they typically use MS Excel for cost estimating they want the structural calculations also included in MS Excel. So for example if change the height of the building, the structural calculations are carried out as appropriate and then the correct specification is returned for costing.

Most of the people asked to provide such spreadsheets, are long past moment distribution, never had and don’t have Kleinlogel formula, and certainly don’t have their own source code for plane frame analysis or 3D analysis.

Even if they have Kleinlogel formula, the increasing variety of structural forms which the manufacturers wish to supply, makes the using of Kleinlogel formula unproductive. First there has to be Kleinlogel formula available for the frame being considered. Second Kleinlogel calculations then have to be setup for each frame and required load case. It just becomes increasingly cumbersome and demanding of computer resources to set up. Making 2D/3D frame analysis software built around MSA more sensible, if seeking final solutions.

If not seeking final design-solutions, then the estimating approaches described above are more flexible. Keep it simple and aim to conservatively design beam and column elements. Also determine costs conservatively.

The difference between using C15015 or C15019 shouldn’t be all that significant to the overall cost of the structure. One estimate I heard was that cladding and immediate support structure accounts for 80% of the steel. If running around complaining that you cannot compete because of the size of the c-section for the main frame, then doing something wrong. Even a C15015 versus C25024 shouldn’t cause too much of an issue if sales people are selling quality and robustness rather than: mere code compliance and minimum price.

The other benefit of keeping the calculations simple is being able to map out a product range, and consideration of introducing new structural sections.

Mapping out Product Ranges and Product Limitations

When I started I wasn’t given a structure and told go analyse and find the member sizes. I was given standard calculations, told to revise and find the maximum height possible. The existing calculations weren’t ours, they were by persons no longer supplying to the client. So first question was do we even agree with the calculations and specifications. The answer to that question was not entirely: as there was something deficient in the structural assessment. That aside, the calculations provided the span, the section and the loading conditions. The reason for the revision was to revise from wind loading code AS1170.2:1983 to AS1170.2:1989. the change from permissible stress to limit state wasn’t adopted as not all the materials codes, and manufacturers data, had been converted at that point in time. The wind terrain category was basically used as the difference between one shed design and another.

After some quick scratch pad calculations off to the side of my main Quattro Pro spreadsheets, using simple beam formula, I wrote macros to generate data input files for our in-house plain frame program, as at that time we couldn’t afford commercial structural analysis software. The purpose of the macro was to calculate new wind loads as the height and proportions of the building changed. The basic wind pressure being dependent on the height of the building whilst the surface pressures are dependent on the proportions. So to increase the height of the building until reached the limits of the chosen c-section, I needed to recalculate the wind loads. Hence straight into automating my work by using a spreadsheet. As long as the frame was within the scope of what I had automated I could reply back to manufacturers within 30 minutes on the size of frame to use. Actually producing a calculation report with drawings could take a couple of days to a week. Or two to four weeks if columns ripped out all over the place and the structural form otherwise changed.

However I was seeking more than automating one-off calculations. I wanted to know the limitations of the available structural sections and the structural form. I also wanted to constrain the salespeople, because whilst I had thus far been able to prove just about everything they sold, it was a major headache and I was running out of refinements. Without constraint trouble was going to arise.

By Comparison

Method 1 (though not chronologically)

As my initial interest was checks on the plane frame analysis software, which did have a bug in it, and mapping out limitations, I got caught up in calculations. It was some time before the simple approach of just drawing templates of the known shed designs dawned on me. This I eventually wrote up as simplified design by comparison technical note #2

Another reason for the delay also concerned design charts in the British Steel Designers manual. These charts were based on h/L ratio’s for a specific roof pitch. Change the height span ratio of the shed then change the distribution of moment at the joints. I didn’t have confidence that using the standard shed design for anything smaller, as was common practice by the manufacturers and the city council’s, was a valid approach. I don’t believe it is valid if the connections are not designed to match the moment capacity of the c-sections: and the connections are not so designed.

However if have appropriately designed connections, then as long as the proposed shed fits inside the envelope of the known shed, the structural section used for the known frame, will be suitable for the proposed frame. If want more confidence, that the moments are decreasing then can also require that the h/L ratio is maintained. This can be done by drawing a diagonal line from the eaves on the right to the base on the left: as long as the height and span of the proposed shed intersect on this line the frame should be suitable.

Method 2 (method 1 chronologically)

This is not however where I started. Instead I started with a tables of c-section properties, which I set up as follows:

Typical table of c-section properties

One of the final subjects I studied at university was design for manufacture in plastics (polymers). A lot of these calculations were comparative from one material to another. That is calculate required Zxx or Ixx for use of steel, timber or polymer (eg. acrylic, nylon). Much of which isn’t done using actual formula but using simple ratios from known relationships. Such as:

  1. w ∝ p
  2. w ∝ s
  3. M ∝ w
  4. M ∝ L²
  5. ϕMs ≥ M
  6. ϕMs ∝ Z
  7. w ∝ M[z,cat]²
  8. w ∝ Mt²
  9. w ∝ Ms²
  10. Z ≈ D.B.T {for pair of flanges}
  11. W=w.L

Since this was relatively fresh in my mind at the time, this was the approach I started with. So I had a known gable frame shed design, C25024 being used in terrain category 2, spanning 12m with eaves height of 4.8m. How to expand that one design to the full range of c-sections as quickly as possible?

The answer is by using ratio’s. If the height increases then the moment increases, in proportion to the square. If the span increases then the moment increases in proportion to the square.

So if L1=x.L0 where L0 is height or span of the known, and L1 is the height of span of the proposed. Then:

 M ∝ (x.L0)²
 M ∝ x² L0²

Thus if I know the ratio between my standard design and a proposed design I can find the increase in moment: ignoring that the wind pressures change. Then I need to relate this to the increase in capacity of the sections.

Z0=D0.B0.T0
Z1=D1.B1.D1
D1=x1.D0
B1=x2.B0
T1=x3.T0
Z1=x1.D0.x2.B0.x3.T0
Z1=x1.x2.x3.D0.B0.T0
Z1=x1.x2.x3.Z0
The required increase is x² and so:
x² = x1.x2.x3
x = √x1.√x2.√x3
x = √(D1/D0) √(B1/B0) √(T1/T0)
assuming breadth is unchanged then:
x = √(D1/D0) √(T1/T0)

So in the table presented above it becomes relatively simple in a spreadsheet to calculate the ratios for each section. As move along a row adjust for the change in capacity due to change in thickness, as move down a column of the table, adjust for change in capacity due to change in depth: for the row and column containing the known section. All other cells adjust for both depth and thickness, based on those for the known section. Once have the factors can adjust for any height or span. Can further introduce factors to allow for change in load, for example to drop the wind load from terrain category 2 to 3: which is a reduction in M[z,cat]. Such load reduction allows a span increase.

The result was that for terrain category 3, the maximum gable shed span was around 16.89m with eaves height of 6.75m, using C30030 with fy=450MPa. Thus to get greater spans either need more refined calculations or larger sections. But otherwise got my first rough and ready frame estimation tool.

Rough and Ready Frame Size Estimator

Still whilst this approach can map out the capabilities of a set of structural sections in less than a day, it still depends on the table providing dimensions which envelope the proposed shed. It also needs arithmetic to look at a more specific case: that is instead of using the tables we can calculate the load and span multipliers for the proposed shed, and relate directly to the known shed, and then calculate the increased capacity required and select a suitable c-section.

Method 3

What I wanted was a more visual and graphical approach, and moment distribution provided one approach for that. The frames can be considered as continuous span beams, spanning from the base connection on one side to the base connection on the other side. If the span changes then the moment in the frame will change. If we change neither the span nor the load, then the structural section adopted for a known design should remain suitable. The span of the frame is the perimeter (P) or the frame, and irrespective of its actually shape can be approximated by the rectangle below the pitched roof, or the rectangle fully enveloping the entire profile of the building. I chose the rectangle below the pitched roof, where H is the eaves height and L is the building width, and so P = 2H+L.

P=2H+L
H=(P-L)/2
H=-0.5L + k
where k = constant = P/2

From this get the basic concept that to increase the height by one metre need to reduce the span by two metres. I can thus draw the outline of the known shed on a chart, and then put a line through its right eaves node with a slope of -0.5, and quickly sketch the maximum height or span can expect to achieve.

Alternative Estimating Approach

For the example shown above I cut the diagonal line at 2.4m minimum height, rather than take all the way down to the x-axis. Additionally given that wind load changes with height I made some allowance, by adjusting the line. Since its some 20 odd years ago I originally created the chart, I’m not sure how I made allowance for the wind loading, though AS1170.2:1989 would have been what I was using at the time. Looking at AS1170.2:2011 there is no change to M[z,cat] in the height range considered. I may have just intuitively and arbitrarily adjusted the height by some percentage. Alternatively I may have made use of the other approaches to calculate an adjusted height and/or span.

Design Chart based on more Design Points

The above chart is based on more design points for a 7.6m span shed for terrain category 3. Once again I cut off the heights at a minimum of 2.4m. This time a C35030 is included in the assessment and it suggests can get to a maximum span of 23m at 2.4m eaves height. For a 6m height industrial building the maximum span is given as 16m.

Design Chart with estimation lines cut off by vertical and horizontal cut lines.

As well as limiting the minimum height of the building can also limit the minimum span of the building or the maximum height. From the chart it looks like I originally set the minimum span at 2m. Though another possibly is to set the maximum height at say 6m and then cut off the estimation lines. Anything which helps keep the guesstimate conservative.

Method 4

Now in terms of the rigid frame, the diagonal estimation line basically indicates heights and spans where there is significant interaction between rafter and column. If the shed gets too high, then the column effectively becomes a cantilevered post, with insignificant to zero moment at the knee, thus with fixed bases the moment at the base can be determined from MA=wh²/2.

Whilst if the width of the building gets to great, then the interaction of rafter and column reduces, and the roof effectively becomes a simply supported beam with zero end moments. The ridge moment can be determined from MC=wL²/8.

If we are looking for the rafter to interact, then they have to have the same moment at the knee, and typically expect to use the same structural section for the rafter and column. Therefore MA=MC.

MA=MC
wh²/2 = wL²/8
Assuming the loads are the same.
h²/2 = L²/8
h² = L²/4
h = √ (L²/4 )
h = L/2
h/L = 0.5

So if expecting interaction to occur the height of the building needs to be less than half the width. So for a given structural section can now calculate the maximum expected height and maximum span, and then draw these on a chart.

Two possibilities for the chart, simply plot h/L=0.5 passing through zero: not very helpful. The other option is to draw a line connecting the maximum span to the maximum height. The line becomes similar to the diagonal in the previous methods. Any proposed shed which has h and L which lies below the diagonal is assumed suitable for the structural section being considered.

Method 5

Use Kleinglogel formula in a spreadsheet. Manually change the heights and spans and find the limits of a given c-section, tabulate the results.

Method 6

Program the Kleinlogel formula, put in an iterative loop, vary height and span in increments, calculate the moments and tabulate.

Method 7

Having got Kleinlogel formula programmed. Vary the span in say 600mm increments and find the maximum span for a given height. Alternatively vary the height in 100mm for height.increments and determine the maximum height for a given span. Combine both loops and find the height and span envelope for a given section. Add an extra loop, and find height span envelopes for all the available sections for interest (C-sections, RHS, SHS, CHS, PFC, UB, UC’s).

Method 8

Use general purpose structural analysis software with a programming interface, such as Multiframe. This seemed like a good idea, but first trial encountered problems. As nodal coordinates changed, watching the screen updates, it appeared that loads were changing direction: this reduced confidence in the results. The process was also slow. So thus far I haven’t pursued this approach any further. Instead I stuck with generating data files (arc) for Microstran which Multiframe can also read: so I can do detailed checks of individual cases in the estimated ranges.

Overview

There are various methods to assess a range of structural products the graphical methods are the simplest and provide a lot of information in a simple visual presentation.

More refined result can be determined by programming iterative loops through the detailed calculations. This can be done for various structural forms and structural products. For example sheds, canopies, balustrades.

Future

In a future post I will cover creating a product configurator for manufactured structural products (MSP’s) in more detail. As well as compare the estimation approaches against the use of structural analysis software: especially the effects of removing columns on the moment frames.

The general concept is to try and keep things simple and provide background explanations for manufacturers of structural products.

-o0o-

WARNING: These are estimation approaches, they allow rejection of a proposal not acceptance. More detailed calculations are required to confirm acceptance of a proposal.


Revisions:

  • [18/05/2019] : Original [17:22]
  • [19/05/2019] : Rewrote and added more diagrams