design industrial buildings

Helsinki University of Technology 14.04.04 1(27) Department of Civil and Environmental Engineering Laboratory of Steel Structures, Seminar in Structural Engineering

Presentation of Risto Siirilä

Industrial Buildings Frames, Bracings and Diaphragms



1 Contents 1 Contents.........................................................................................................................2 2 Introduction ....................................................................................................................3 3 Industrial hall buildings....................................................................................................3

3.1 Load conditions .......................................................................................................3 3.2 Roof systems...........................................................................................................4 3.3 Wall systems ...........................................................................................................5 3.4 Framing schemes....................................................................................................5

3.4.1 Economic considerations ..................................................................................6 3.5 Bracing systems ......................................................................................................6

3.5.1 Wall bracing......................................................................................................6 3.5.2 Roof bracings ...................................................................................................7

3.6 Crane girder design .................................................................................................8 3.7 Column design ........................................................................................................8

3.7.1 Simlifying assumptions .....................................................................................9 4 Stressed Skin Diaphragm Design ...................................................................................9

4.1 Design Principles.....................................................................................................9 4.1.1 Introduction.......................................................................................................9 4.1.2 Principles........................................................................................................10 4.1.3 Benefits, conditions and restrictions ................................................................11 4.1.4 Types of diaphragms ......................................................................................11

4.2 Strength and flexibility of shear diaphragms...........................................................12 4.2.1 Diaphragm strength – four sides fastened .......................................................12 4.2.2 Diaphragm strength – two sides fastened........................................................14 4.2.3 Diaphragm flexibility........................................................................................15 4.2.4 Sheeting spanning parallel to length of building...............................................17

4.3 Design expressions – sheeting spanning perpendicular to length of building ..........17 4.3.1 General note...................................................................................................17 4.3.2 Diaphragm strength ........................................................................................18 4.3.3 Diaphragm flexibility........................................................................................19

4.4 Design expressions – sheeting spanning parallel to length of building ....................20 4.5 Diaphragms and stiff frames ..................................................................................20

4.5.1 Rectangular frames ........................................................................................20 4.5.2 Reduction factors – all frames loaded .............................................................21 4.5.3 Reduction factors – one frame loaded.............................................................22 4.5.4 Pitched roof frames.........................................................................................22

4.6 Other applications of sressed skin design ..............................................................22 4.6.1 Complex diaphragm........................................................................................22 4.6.2 Openings in diaphragms.................................................................................23 4.6.3 Diaphragm bracing .........................................................................................23 4.6.4 Folder plate roofs............................................................................................23

4.7 Simplified design methods .....................................................................................24 4.7.1 Conditions ......................................................................................................24

5 Conclusion ...................................................................................................................25 5.1 References............................................................................................................25 5.2 Notation.................................................................................................................25 5.3 Table of figures......................................................................................................27

Appendixes: Tables and worked examples



2 Introduction An industrial building is any structure that is used to store raw materials or furnished goods from a manufacturing process or house the process itself like:

− Food processing − Chemical processing − Paper and pulp industry

− Metals industry − Powerplants − Engineering industry

− Electronics industry or − High bay storages Industrial buildings can range from the simplest warehouse to highly sophisticated structures. Desing considerations vary depending upon the type of industry in question e.g.

− Heavy loads − Dynamic loads (vibration) − Noise

− Moistureb and − Aggressive chemicals This presentation concentrates in the statical systems of (simple) hall buildings without cranes or with crane runway systems. I have based this presentation totally, even accurately, on the book mentioned as reference.

3 Industrial hall buildings

3.1 Load conditions Requirements of building codes including dead, wind, snow, (seismic) and crane loadings need to be followed. There are some design considerations which in many cases have not been given attention enough: − Uplift due to wind load in the roof system and frames

− Effect of snow piling − Special problems associated with load combinations of several cranes Every industrial building is unique since the requirements of each owner are specialized and personal. The designer must establish the exact use to which the structure will be subjected. Interior vehicular traffic is one source of problems in structures. Fork lift trucks can buckle the flanges of a column, shear off anchor bolts in column bases and damage walls. Piled materials may fall down against the wall etc. Except in cases where no land is available, every industrial structure is a candidate for future expansion. Lack of planning for such expansion can result in future problems. On the other hand while industry-world is rapidly changing it is not wise to invest excessively into future changes.



The major difference between industrial buildings with cranes (crane buildings) and other industrial buildings is the frequency of loading caused by the cranes. The class of crane, the type of crane and loadings affect the design. The fatique considerations associated with crane class (depending on estimated life span, rate of loading and number of load repetitions) is especially important with respect to design of crane girders and its’ connections to columns. For example the cranes of the following building types are recommended to be considered as the most severe class of crane: − Batch annealing buildings. Scrap yards

− Billet yards. Skull breakers. − Continuous casting buildings. Slab yard. − Foundries. Soaking pit buildings.

− Mixer buildings. Steelmaking buildings. − Mold conditioning buildings. Stripper buildings. − Scarfing yards. Horizontal forces (on the top of the rail) exist in crane loadings due to a number of factors including: − Runway misalignment, − Crane skew,

− Trolley accelerator, − Trolley braking and − Crane steering For one crane, each span must be designed for the most severe loading with the crane in the worst position relative to the calculation of a given parameter. When more than one crane is involved in making a lift, an engineering judgement on the specific application must be used. For most industrial constructions the owner will take much bigger role than in construction of e.g. apartments. The industrial building is the essence of his business. Thus the production and operation will dictate building design, and most industrial buildings are essentially pure structure. Sometimes unfortunately too little if any attention is paid to aesthetics. The design of industrial buildings may seem logically the province of structural engineer. In fact there are usually a lot of designers with other disciplines, too .

3.2 Roof systems The roof system is one of the most expensive parts of the entire structural system even though walls are more expensive per square meter. The roof often covers much larger area. The predominant roof system in industrial buildings involves the use of metal deck which is cold rolled from sheet steel in various gage thicknesses. The inclusion of cranes will generally not affect the basic roof covering system. Cranes will cause “movements” and any aspect in the roof system that might be affected by such a movement must be evaluated. This generally means close examination of details (flashing, joints, bearings, etc.)



3.3 Wall systems Depending on the height of the building, the total building area and the selected wall system the cost of a wall can vary by as much as a factor of three. Wall systems may include e.g.

− Field assembled metal panels, − Factory assembled metal panels,

− Precast concrete panels and − Masonry walls (part or full height). A particular wall system may be selected over others for one or more specific reasons including:

− Cost, − Appearance, − Ease of erection,

− Insulating properties, − Fire consideration, − Accoustical consideration, − Dust control,

− Ease of future expansion, − Interior surface characteristics, − Maintenance considerations and

− Environmental considerations. The special consideration which must be given to wall systems for crane buildings relates to movement and vibration. Columns are commonly tied to the wall system, to provide bracing to the column or to have the column support the wall. It is essential that proper detailing be used to tie the column to wall. When bay spacing becomes greater than e.g. 10 m additional intermediate columns (wind columns) are required to provide for economical girt design. Eave strut design must account for the lateral load forces at the top of wind columns. Wind columns may also act as part of the wall bracing system.

3.4 Framing schemes The selection of the best framing scheme is dependent on the interrelationships of numerous considerations and parameters. It may in fact not be possible to give a list of definive rules by which the best scheme can be chosen. Selection of the main framing system including optimum bay sizes and column spacings primarily depends on owners’ (processes’) requirements, the function of the building. Based on these requirements the relative costs of beams, columns, trusses, foundations, crane girders, etc., are important. The considerations of bay sizes must also iclude not only roof and frame factors but also the wall system. Braced frames require bracing in both walls and roof. Bracing frequently interferes with plant operations and future expansion. If either consideration is likely to be the case a rigid frame structure may be the answer. The bracing of roof systems can be accomplished through cross-bracing or using a roof diaphragm. In either cases the roof become as large horizontal beam spanning between the



end walls. A building with dimensions of 30m by 90m with potential future expansion will probably require rigid frames.

3.4.1 Economic considerations In general, as bay sizes increase the weight of the horizontal framing increases. This may mean more cost unless savings in foundations or erection exist. Depending on the type of structure and type of industry, there are number of economic and design considerations to be followed. It is impossible to give a complete list considerations. When steel joists are used in roof framing it is generally more economical to span the joists in the long direction of the bay. On the other hand short span joists are more economical than long span joists. For frames less than 15m in width rolled shapes (or plate girders) can generally provide economical roof framing members. For spans greater than 15m roof trusses are usually superior but in certain instances built up plate girders may prove to be more economical than trusses. This depend on location, steel availability and fabrication preference. No absolute statements can ever be made about the economics of one system versus another. Statements about what is economical relate of necessity, of current times, location, fabrication, experience, availability, material, pricing, and other similar factors. The most economical framing schemes in (heavy) crane buildings are normally dictated by the crane. Optimum bays are usually smaller for crane buildings than buildings without cranes and usually fall into the 8-10m range provided deep foundation systems are not rquired. Main bays of 15-20m with a mid wind column are more economical when deep foundations and heavy cranes exist.

3.5 Bracing systems There are many considerations involved in providing lateral stability to industrial structures. If a rigid frame is used, lateral stability parallel to the frame is automatically provided. However, for loads perpendicular to the main frames lateral bracing is not inherent and must be provided. Since indusrial structures are often both light and low in profile, wind (and seismic) forces are relatively low. Rigid frame action can easily and safely achieved by providing a properly designed rolled (or a welde plate) member at a column line. It may also be possible to achieve rigid frame action by extending the bottom chord of the roof joist into the column. The design forces (compression) for the bottom chords must be taken into consideration.

3.5.1 Wall bracing It is important to trace the longitudinal crane forces through the structure in order to insure proper wall and crane bracing. Since the crane longitudinal force line is usually eccentric to the plane of the bracing, the crane column will tend to twist unless provisions are made to prevent twisting. There are different bracing schemes used to resist the horirizontal crane force effects depending on the demands of the industrial process (fig 1 ).



Figure 1 Portal type wallbraces

3.5.2 Roof bracings Consider the bracing design for steel frame shown in fig 2. Assume that the bents are constructed using simple framing. The stability of the system for lateral loads is thus dependent upon bracing placed in the walls and in the roof. For the laterally applied load shown this could be obtained using conventional cross-bracing in the roof and in the end walls. The bracing in the roof plane acts as a big truss. The end walls transmit the end reactions of the roof truss to the foundations.

Figure 2 Roofbracing of a steel frame

Roof bracing is very important in the design of crane buildings. The most economical is the stiff system of roof bracing. It does not matter what the framing scheme is, i.e. rigid frames of shapes, plates, trusses or braced frames. The roof bracing allows the lateral crane forces to be shared by adjacent bents. This reduces column moments. However the moments in rigid frames cannot be reduced to less than the wind induced moments.

Figures 3-4 illustrate the concept of using roof bracing to induce lateral crane load sharing in the columns. The addition of roof bracing will create load sharing. The two bents adjacent to the loaded bent can generally be assumed to displace equally with the loaded bent. Analytically the stiffness of the adjacent bents can be represented by a “pseudo member” in the analysis of a planar frame.



Figure 3 Displacement of frames and columns due to wind loading

Figure 4 Column displacements in a crane building with or without roofbracings

3.6 Crane girder design Wheel loads, their spacing and girder span determines the design of crane girders. They must be designed as members subjected to combined bending about two axes and e.g. for excessive local longitudinal bending stresses in the top flange of the girder due to the passage of the crane wheel. Also the rotation of the top flange if the crane rail is not directly centered over the web should be taken into account.

3.7 Column design In most structures a column is structurally indeterminate. Normally the column is restrained at the top by the chords of a trusss or by rigid frame action and restrained at the bottom by some degree of base fixity. The designer may require either a fixed base or a small footing with a pair of anchor bolts to permit base rotation. A proper design of crane columns can only be achieved when column moments are realistically determined. This may require a complete frame analysis in order to obtain reliable results. Certain simplifying assumptions must still be made.



3.7.1 Simlifying assumptions

Figure 5 Different types of crane columns with fixed base

Crane columns are constructed in different ways (fig 5). In each case the eccentric crane loads and lateral loads produce moments in the columns. The distribution of column moments is one principal consideration. There are two parameters which have a marked effect on columns moments: base fixity and load sharing to adjacent bent. Base fixity. A simple base (hinge) will result in large moments in the upper portion of the column and the structure will be more flexible than a fixed base solution.Theoretically full fixity cannot be achieved in any practical detail. However the crane induced loads are of short duration and an essentiallly fixed condition can normally be achieved through proper design. Reduced column moments can often be achieved using fixed base condition. In some cases it may be wise to take foundations, pilings and soil conditions into account in the analysis. There will be cases where subsoil conditions, existing construction restrictions, property line limitation, etc., will demand a hinged base intead of a fixed one. Load sharing to adjacent bents. If a stiff system of bracing is used then the lateral crane forces and shares can be distributed to adjacent bents thereby reducing column moments. Studies indicate that for usual horizontal bracing systems a lateral load applied to a single interior frame will be shared almost equally by at least five adjacent frames. It is, however, recommended that load sharing be limited to three frames (the loaded frame plus the frame to either side). The reason for this is that in practice a certain amount of movement may occur before the truss/bracing becomes fully effective. Note that lateral loads due to wind are not distributed because all frames are assumed loaded equally and simultaneously.

4 Stressed Skin Diaphragm Design

4.1 Design Principles

4.1.1 Introduction The most economical roof bracing system is achived by use of a roof (metal deck) diaphragm. The deck is provided as the roofing element and the effective diaphragm is obtained at almost no cost. A roof diaphragm used in conjunction with a wall cross-bracing or a wall diaphragm



system is probably the most economical bracing system. A light gage steel diaphragm is analogous to the web of a plate girder. That is, its main function is to resist shear distorsion. The perimeter members of the diaphragm thus serve as the flanges of the plate girder. Since design of the diaphragm is essentially that of a deep beam, it is essential to realize that for such a deep beam shear deformations are usually more significant than deformations due to principal stresses in the chord elements. It is a fact that the framework and cladding will always interact to profoundly affect the behaviour of a complete building. Consequently, frame stresses and deflections calculated on the basis of the bare frame are quite fictitious. And are usually quite different from the real values. By taking the cladding into account, the real behaviour of the building can be predicted and worthwhile savings in the cost of the frames can usually be made.

4.1.2 Principles In a flat roofed building subjected to side load (fig 6) each of the roof panels acts as a diaphragm taking load back to the gable ends. In a pitched roof building (fig 7) under vertical or side load, there is a component of load down the roof slope so that the roof diaphragms

Figure 6 Diaphragm action in a flat roof building

Figure 7 Diaphragm action in a pitched roof building

tend to prevent the building from spreading or swaying. The flatter the roof pitch, the less effective the diaphragms are in resisting vertical load. The action of the sheeting is for the roof to behave like a deep plate girder. If the frames of fig 6 are pin-jointed, then the side loads are resisted entirely by stressd skin action. The structure must be adequately braced during erection. If the frames have rigid joints, then the side loads are shared between the frames and the diaphragms



4.1.3 Benefits, conditions and restrictions Some of the benefits, conditions and restrictions of stressed skin design are as follows Benefits a) Frame stresses and deflections are usually smaller b) Calculated and observed stresses and deflections agree c) Bracing in the plane of the roof is eliminated d) Frame details are standardized by omission of bracing e) The method is particularly effective where lateral loads act only on one or two frames f) The actual forces on the cladding and fastners can be calculated so that inadvertent

overstressing can be avoided. Conditions a) End gables must be braced or sheeted b) Edge members must be provided to panels and these members and their connecttions

must be designed to carry the flange forces c) Sheeting must be fastend to members with proper connections d) Seams between sheeets must be fgastened with proper connections e) Suitable structural connections must be provided to transmit diaphragm forces into the

main framework f) The average shear stress in the sheets should be less than 25% of the maximum

bending stress in the sheets g) Roof light openings should be less than 3% of the relevant roof area unless detailed

calculations are made, in which case 15% is allowed Restrictions a) Stressed skin design should normally be restricted to structures in which most of the

load is applied via the sheeting itself b) Consequently if sheeting is removed most of the load is also removed c) Sheeting should not be used for helping to resist other fixed loads, e.g. mechanical

plant sheeting is a structural component and must not be removed without proper consideration

d) The design documents should clearly draw attention to the fact that stressed skin methods is used

4.1.4 Types of diaphragms Typical plan views of flat roof of a building are shown in figures 8 and 9. Whenever possible, each panel of sheeting should be fastened to all four edge members to get greater strength and stiffness. This is not always possible (fig 8). Then shear connectors may be used over the rafters. Sheeting fastened only to the purlins is still permissible provided that the end panels of sheeting are fastened on their third side to the end gables. The purlin/rafter connections at the intermediate rafters must be strong enough to introduce the loads at these rafters into the diaphragm.



Figure 8 Sheeting spanning perpendicular to length of building

Figure 9 Sheeting spanning parallel to length of building

Figure 10 Typical diaphragm panel

4.2 Strength and flexibility of shear diaphragms

4.2.1 Diaphragm strength – four sides fastened For a typical panel attached on all four sides as shown in fig 10. The diaphragm strength Vult

in the direction of load V depends on the sheet tearing strength of:



1. A line of seam fastners or 2. A line of shear connector fastners. Those two failure modes being ductile, are

taken as the design criteria. Any other failure mode required to have greater strength than lesser of the above calculated values. Such other modes include:

3. Failure at the sheet/ purlin fastners 4. Shear buckling of the sheeting 5. Failure of the edge members under tension or compression 6. Gross distortion or collapse of the profile at the end of the sheeting. The design expressions for modes 4 and 5 incorporate a 25% reserve of safety and the mode 3 includes a 40% reserve. The reserves are necessary because failure modes 3-5 can occur suddenly and are therefor undesirable.

Figure 11 Ultimate shear strength due to tearing at the seam fastners (left) at the shear connector fastners (right)

Figure 12 Failure due to tearing at sheet/ purlin fastners (four sidea fastened)

In the sheeting itself, the combined effects of normal bending stress and shear stress (limited to 25% of the max bending stress) result in an increase in principal stress of only 6%, so it is not normally necessary to take diaphragm action into account when designing sheeting for its primary function in bending.



4.2.2 Diaphragm strength – two sides fastened For panels attached on two sides only (and to the end gables) the diaphragm strength in the direction of load V depends on the least strength of a) A line of seam fastners b) The line of shear connector fastners at the end gable or c) The end sheet/purlin in intermediate panels (fig 14). Any other mode of failure e.g. failure of the purlin/rafter connections due to bending (fig 15) or modes 4-6 in previous section should incorporate a 25% reserve of safety.

Figure 13 Failure due to tearing at sheet/purlin fasteners (two sides only fastened)

Figure 14 Flexibility of purlin/rafter connection (left) and definition of shear flexibility (right)

By systematically considering the strength of all the components of a diaphragm as indicated, the weakest link in the chain can be established and steps can be taken to improve the diaphragm strength.



4.2.3 Diaphragm flexibility The shear flexibility of a diaphragm is the shear deflection per unit shear load in a direction parallel to the corrucation (fig 10). The total shear flexibility is calculated by summing the following component flexibilities:

Figure 15 Distortion of profile, fastened in every trough (left) and in alternate troughs (right)

Figure 16 Intermediate purlins in a diaphragm. Total number of purlins 7 (left). Number of sheeting lengths is 3 in depth of diaphragm (right)

a. Flexibility due to sheet distortion (c1-1). This flexibility depends on

− The geometry of the trapezoidal profile,

− The sheeting thickness, − Sheeting fastened in every corrugation or alternate corrugations (fig 15),

− The number of intermediate purlins, − The number of sheet lengths in the depth of the diaphragm (fig 16) and

− The flexibility may be reduced if insulation is bonded to the top of profile in the case where sheeting is fastened in alternate corrugations.

b. Flexibility due to shear strain in the sheet (c1-2 ) see fig 17. This flexibility depends on

− The geometry of the profile, − The sheeting thickness and − If there are intermediate purlins a multiplying factor must be included.

Figure 17 Shear strain in the faces of a corrugation



Figure 18 Test to determine slip in a fastener

c. Flexibility due to slip in the sheet/purlin fastners (c2-1 ). The slip can only be determined by test (fig 18). the slip values of most common types of fastners have been determined. This flexibility depends on − The slip value,

− The spacing of fastners and − A multiplying factor must be included if the sheetig is fastened to intermediate purlins. d. Flexibility due to slip in the seam fastners (c2-2 ) see fig 19. Slip in fasteners may be determined by test as shown in fig 18. This flexibility depens on the type of fastener (aluminium blind rivets are not strong enough) and the relative values of seam slip and slip at the adjacent sheet/purlin fasteners.

Figure 19 Shear slip between sheets (left). Seam fasteners in sheeting and decking (right)

e. Flexibility due to slip in the sheet/shear connector fastners (c2-3 ). Shear connectors often consist of short lengths of purlin which are bolted or welded to the tops of rafters. The flexibility depends on the slip value of the fasteners and the number per rafter. f. Flexibility due to the purlin/rafter connections (c2-3 ) in case of the sheet fastened to the purlins (fig 14) and to the end rafters only. Tests have been carried out on different connections and the flexibilities and strengths tabulated (table 10).



g. Flexibility due to axial strain in the longitudinal edge members (c3 ). This component refers to bending rather than shear. Nevertheless, it can be expressed in shear flexibility terms by calculating the difference in bending deflection over a panel legth (in multi-panel diaphragms) and dividing by the shear in the panel. This equivalent shear flexibility varies somewhat along the length of the building but is is quite adequate to take an average value. If there are a number of internediate purlins, a multiplying factor must be included.

4.2.4 Sheeting spanning parallel to length of building The design expressions which have been derived give the shear strength and shear flexibility in the direction parallel to the corrugation.

Figure 20 Shear strength and flexibility of panel in direction at right angles

Referring to figure 20 it can be proved that Shear strength V = Vo a/b and Shear flexibility c = co (b/a)2

The modified value of shear strength is used directly but the modified value of shear flexibility is applied only to the shear components a)-f) in previous chapter. It is not applied to component g) since this component is independent of the direction of the span of the sheeting.

4.3 Design expressions – sheeting spanning perpendicular to length of building

4.3.1 General note It is not in this space to derive and explain the design expressions used. Instead the design expressions are given here, and a guide to their use is given in the worked examples. The case considered is shown in fig 21.



Figure 21 Diaphragm roof – sheeting perpendicular to length of building

4.3.2 Diaphragm strength Usually the end panel is critical panel to be checked for shear, but conditions at the internal rafters should also be checked. a) Seam capacity Vult = ns Fs+ (β1/β3) ns Fs b) Shear connector fastener capacity (at end gables) Vult = nsc Fsc c) Shear connector fastner capacity at internal rafters (qa)ult = n’scFsc d) For sheeting attached to the purlins only and to the end gable rafters. Capacity of end

fastners in an internal panel (qa)ult = β2 n’p Fp. Capacity of purlin/rafter connections (qa)ult

= β2 n’p Fp. e) Design shear capacity: in an assembly of panels fig 21, V = qa(n -1)/2, so it can be

determined whether eqn a) or eqn b) is more critical for a panel fastened on four sides. For a panel fastened on two sides only, the most critical case from eqns b), d) or e) can be determined. The design shear capacity of the diaphragm V* is then the lesser of the values given by eqn a) and the most critical of the above values.

f) Sheet/purlin fastener capacity, in order to avoid the possibility of failure in the

sheet/purlin fasteners a 40% reserve of safety is allowed. It should be checked that (0.6bFp)/pα3 >= V*

g) Shear buckling of the sheeting: in order to avoid that, a 25% reserve of safety is

allowed in the expression for shear capacity. It should be checked that (14.4/b)Dx

1/4Dy3/4(np-1)2 >= V* . This expression involves the use of several additional

symbols, which are illustrated in fig 23 and listed below:

Dx = Et3 d / 12(1 - ν2 )u Dy = EI / d I = second moment of area of a single corrugation about its neutral axis u = perimeter length of a single corrugation



Figure 22 Shear buckling of profiled sheeting

h) Axial force in edge members: in order to avoid the possible failure a 25% reserve of safety is allowed. Referring to figure 21 the maximum load in an edge member may be

taken as qL2α3/8b. The calculation must also of course, take into account any bending due to vertical loads

i) End collapse of profile: in order to avoid this, the following limitations on shear force in a

panel should be observed: Every corrugation festened: 0.9 t1.5 bfy /d0.5 >= V* Alternate

corrugations fastened: 0.3 t1.5 bfy /d0.5 >= V*

4.3.3 Diaphragm flexibility With reference to the various flexibilities listed in section 4.2.3 , the design expressions are as follows:

a) Profile distortion c1-1 = ad2.5α1α4K / (Et2.5 b2)

b) Shear strain c1-2 = 2aα2(1 + ν)(1 + 2h/d)/ Etb

c) Sheet/ purlin fasteners c2-1 = 2asp pα3 / b2

d) Seam fasteners c2-2 = 2ss sp (nsh – 1) / (2ns sp + β1 np ss ) e) Shear connector fasteners c2-3 = 4(n + 1)ssc /n

2 n’sc or f) Purlin/rafter connections (two sides only fastened)

c2-3 = 4(n +1)(spr + sp /β2 ) / n2 np

g) Axial strain c3 = n2 a3 α3 / (4.8 EAb2 )



The sum of the component shear flexibilities above gives the total shear flexibility c of the panel. The midspan deflection of the typical panel assembly, shown in figure 21 is given by

∆ = (n2/8)c(qa) . Notes.

− The sheeting constant K according to tables 1 and 2.

− The factors α and β are given in tables 3, 4 nad 5. There are several practical

possibilities giving rise to different combinations of values of K, α1 and α4 and these are summarised in table 5.

4.4 Design expressions – sheeting spanning parallel to length of building

As in the previous section, the design expressions can be produced analogously (see the reference book).

4.5 Diaphragms and stiff frames

4.5.1 Rectangular frames In the general case of loading on a rectangular frame (fig 23), the stressed skin action does not help in resisting no-sway moments. However, it may on the sway moments and forces. The amount of the effect depends on the relative flexibility of the frames and the sheeting.

Figure 23 Sway and no-sway forces on a rectangular portal frame

Figure 24 Definition of frame flexibility

The frame flexibility k is the eaves displacement of the bare frame per unit eaves load (fig 24) and it may be calculated by the usual elastic methods.



The relative flexibility of the panel to the frame is denoted by ψ , where ψ = c/k . If ψ is large

(i.e. stiff frames) then the sheeting does not have a large stiffening effect. If ψ is small the

stiffening effect is considerable and when it is ψ = 0 the frames are pin-jointed and sheeting takes all the load.

4.5.2 Reduction factors – all frames loaded Due to the forces P at frames 2, 3 and 4 (fig 25), the forces on the sheeting at those frames are R2, R3 and R2 and the forces on the frames as shown in fig 26.

Figure 25 Rectangular sheeted portal frame building

Figure 26 Forces and deflections a) on sheeting panels b) on frames

The deflections at the frames 2 and 3 are:

∆2 = c(R2 + R3 /2) = k(P – R2 ), ∆3 = c(R2 + R3 /2) + cR3 /2 = k(P – R3 ) From those equations we get

R2 = P(ψ + 2) / (ψ2 + 4ψ + 2), R3 = 2P / (ψ2 + 4ψ + 2) Hence, force on frame 2

= P – R2 = P(ψ2 + 3ψ) / (ψ2 + 4ψ + 2) = η2 P And force on frame 3

= P – R3 = P(ψ3 + 4ψ ) / (ψ2 + 4ψ + 2) = η3 P



It thus seen that η2 and η3 are reduction factors to be applied to the bare frame sway values of force, bending moment and deflection.

Values of the factors η are given in table 8. Thus:

Bending moment in clad frame = No-sway bending moment + η x sway bending moment

4.5.3 Reduction factors – one frame loaded The diaphragm action of a sheeted building is especially effective if only one frame is loaded. The effect of the sheeting is to distribute the load to a number of frames. The effect has been tabulated in table 9. Strictly, the factors given in table 9 are for the central frame only loaded, which is the worst case, but they may well be adequate for the other frames as well.

4.5.4 Pitched roof frames In the general case of loading on a pitched roof portal frame, the loading can be split up like in fig 27, the sheeting helps to reduce the sway and spread moments so that:

Bending moment in clad frame = No-sway bending moment + ηsw x sway

bending moment + ηsp x spread bending moment Where ηsw and ηsp are the reduction factors for the sway and spread cases respectively, see table 8.

Figure 27 Forces on a sheeted ptched roof portal frame (left) and the equivalent horizontal shear flexibility of panels (right)

4.6 Other applications of sressed skin design There are a number of applications which have been found to be important in practice.

4.6.1 Complex diaphragm The flat roof may consist of a number of diaphragms in different directions and at different levels. The walls supporting each diaphragms must be vertically braced. If one side cannot be braced, then the other three sides must be braced and the roof must be designed as a cantilever diaphragm.



4.6.2 Openings in diaphragms If a roof has for example roof lights or similar openings, particularly if they are in a continuous line, the roof diaphragm is weakened and made more flexible. If possible, openings should be avoided in the end panels where the shear is greatesrt. It is recommended that such openings up to 3% of the panel area may be permitted without special calculation. Openings up to 15% may be allowed if calculations are made properly.

4.6.3 Diaphragm bracing

4.6.3.1 End gable bracing Load to the end gable (fig 28) is usually considered to be taken on the depth of two diaphragms. Vertical bracing must be provided in the side walls. The maximum shear per unit depth occurs at the ends and is equal to qL/4b kN/mm. If the decking is fastened on all four sides, the shear flow is equal in the x and y directions and the fasteners throughout should be checked to this shear.

Figure 28 Diaphragm bracing to end gables (left) and lateral bracing to beam (right)

4.6.3.2 Lateral bracing to beams A decking may be considered to give lateral support for beams or trusses (fig28). the maximum shear per unit depth is 0.015P/b, acting in the x and y directions, and the fastners should be checked to ensure that they can take this shear. If the same sheeting is required to provide bracing to both gables and the main beams, then the fastners should be adequate to take the sum of the shears.

4.6.3.3 Eaves bracing In pitched roof frames, the two lowest purlins are sometimes cross-braced together in order to provide resistance to any horizontal eaves forces (e.g. wind load) between the frames. This function can easily be performed by the sheeting acting as a diaphragm between one or two purlin spacings.

4.6.4 Folder plate roofs A development of stressed skin action in pitched roof buildings is to eliminate the intermediate frames completely and allow edge members at the eaves and apex to span the clear distance between the gables. Thus, the structure consists of only two elements (fig 29), fold line members which are normally cold formed from plate and profiled steel sheeting and profiled steel sheeting spanning between the fold line members.



Figure 29 Typical light gauge steel folded plate foof

4.7 Simplified design methods Various types of flat diaphragms are illustrated in fig 30. Some of the cases have been calculated using standard sheeting profiles and fixing conditions. The safe working load (unfactored loads) and the resulting in-plane deflection at the mid-length of the building have been tabulated in the tables 11 and 12.

Figure 30 Alternate fastener arrangements in a flat roof diaphragms

4.7.1 Conditions The actual conditions in the roof deck should not generally be more severe than following, upon which the tabulated values are based: 1. Roof deck: max height 85mm, min thickness 0,7mm, pitch of corrugation 150mm, 2. Sheet/purlin fastners: self drilling screws or fired pins in every corrugation

throughout, 3. Seam fastners: max spacing 300mm, 4. Sheet/shear connector fasteners at gable ends: max spacing 300mm, 5. Purlin/rafter connections: adequate strenght and stiffness (table 10), 6. Roof lights: should not exceed 3% of panel area, randomly arranged, 7. Used load factor 1,4



Table 11 gives the permissible distributed line load on the diaphragm for the case 2 (sheeting parallel – four sides fastened), and for case 3 (sheeting perpendicular – two sides + gable ends fastened). Table 12 gives the permissible distributed line load on the diaphragm per 1mm deflection. The max deflection is wperm/k mm.

5 Conclusion Into this presentation I have collected some information about the design of frames, bracings and diaphragm actions in simple industrial buildings. Taking into consideration certain simplifying assumptions the calculations and the design work is possible using simple sofware and in the simpliest cases even totally manually. Industrial buildings are, however, sometimes very different from simple hall buildings. The frames are complicated with different kind of spans and bays and with lots of loading alternatives. Some simplifying assumptions and more sophisticated software programmes are needed to excecute the design work.

5.1 Reference 1. Constructional Steel Design, An International Guide, Patrick J. Dowling et al,

Elsevier Applied Science, London and New York

5.2 Bibliography 1. European Standard Eurocode 3, Design of steel structures, versions of January

2004. 2. Eurocode 3: Design of steel structures, Part 1.3: General rules, Supplementary rules

for cold-formed thin gauge members and sheeting. 3. European Covention of Constructional Steelwork ECCS, Publication No.88 (1995),

European recommendations for application of metal sheeting acting as a diaphragm.

5.3 Notation A Length of diaphragm perpendicular to the corrugations (mm) A Cross-sectional area of longitudinal edge mamber (mm2) b Depth of diaphragm in a direction parallel to the corrugations (mm) c Overall shear flexibility of a diaphragm (mm/kN) d Pitch of corrugations E Modulus of elasticity of steel (205 kN/mm2) Fy Yield strength of steel sheeting (N/mm2) Fp Design strength of sheet/purlin fastener (kN), see note 1 Fpr Design strength of purlin/rafter connection (kN), see note 2 Fs Design strength of individual seam fastener (kN), see note 3 Fsc Design strength of sheet/shear connector fastener (kN), see note 1 h Height of profile (mm) k Frame flexibility (mm/kN) K1,K2 Sheeting costants, see note 4 l Width of corrugation crest (mm) L Span of diaphragm between braced frames (mm) m Number of panels within sheet length, see note 5 n Number of panels in the length of a diaphragm assembly, see note 5



nb Number of sheet lengths within depth of diaphragms assemly, see note 6 nf Number of sheet/purlin fasteners per sheet width nl Number of sheet lengths within length of diaphragm, see note 5 np Number of purlins (edge + intermediate), see note 7 ns Number of seam fasteners per side lap (excluding those which pass through both

sheets and the supporting purlin) nsc Number of sheet/shear connector fasteners per end rafter n’sc Number of sheet/ shear connector fasteners per internal rafter nsh number of sheet widths per panel p Pitch of sheet/purlin fasteners (mm) q Distributed load on diaphragm (kN/mm) sp Slip per seam fastener per unit load (mm/kN), see note 2 spr Movement of purlin/rafter connectionbper unit load (mm/kN), see note 2 ss Slip per seam fastener per unit load (mm/kN), see note 3 ssc Slip per sheet/shear connector fastener per unit load (mm/kN), see note 1 t Net sheet thickness, excluding galvanising and coating (mm), see note 8 v Shear displacement of diaphragm (mm) V Applied shear force on diaphragm (kN) V* Design shear capacity of diaphragm (kN) Vcrit Shear force on diaphragm to cause overall buckling (kN) Vult Capacity associated with a given failure mode or ultimate load (kN)

α1 - α5 Factors to allow for intermediate purlins and number of sheet lengths, see note 9

β1 - β2 Factors to allow for the number of sheet/purlin fasteners per sheet width, see note 10

β3 Dist. between outermost fasteners across the sheet width – sheet width, see note 11

∆ Midspan deflection of a panel assembly (mm) ν Poisson’s ratio for steel (0,3) Notes 1. Typical values are given in Table 13a (examples) for fy = 280 N/mm2. For other

values the design strength should be multiplied by 280/yf

2. Test results of typical purlin/rafter connections are given in Table 10 3. Typical values of some seam fasteners are given in Table 13b for fy = 280 N/mm2 4. The constants are a measure of the flexibility of the sheeting due to distortion of its

profile when fastened in every corrugation and alternate corrugation respectively. Values are given Tables 1 and 2

5. The relationship of m, n and nI is illustrated in Table 6 6. The symbol is illustrated in Fig.16 and Table 5 7. The symbol is illustrated in Fig.16 8. Unless measured, the thickness of galvanising may be taken as 0,05mm (total for

both sides) 9. The effect of intermediate purlins is to reduce the shear flexibiloity of panels. Values

for α are given in Tables 3, 5, 6 and 7

10. The factors β1 and β2 allow for the distribution of forces in the sheet/purlin fasteners along the member. Values are given in Table 4. See section 4.2.2 comment d) and Fig.19

11. For sheeting (seam fasteners in the crests), β = n – 1/n . For decking (seam fasteners

in the troughs), β = 1.0.



5.4 Table of figures Figure 1 Portal type wallbraces.............................................................................................7 Figure 2 Roofbracing of a steel frame ...................................................................................7 Figure 3 Displacement of frames and columns due to wind loading.......................................8 Figure 4 Column displacements in a crane building with or without roofbracings ...................8 Figure 5 Different types of crane columns with fixed base .....................................................9 Figure 6 Diaphragm action in a flat roof building...................................................................10 Figure 7 Diaphragm action in a pitched roof building ...........................................................10 Figure 8 Sheeting spanning perpendicular to length of building ...........................................12 Figure 9 Sheeting spanning parallel to length of building.....................................................12 Figure 10 Typical diaphragm panel .....................................................................................12 Figure 11 Ultimate shear strength due to tearing at the seam fastners (left) at the shear

connector fastners (right) ..............................................................................................13 Figure 12 Failure due to tearing at sheet/ purlin fastners (four sidea fastened) ....................13 Figure 13 Failure due to tearing at sheet/purlin fasteners (two sides only fastened).............14 Figure 14 Flexibility of purlin/rafter connection (left) and definition of shear flexibility (right) .14 Figure 15 Distortion of profile, fastened in every trough (left) and in alternate troughs (right)15 Figure 16 Intermediate purlins in a diaphragm. Total number of purlins 7 (left). Number of

sheeting lengths is 3 in depth of diaphragm (right) ........................................................15 Figure 17 Shear strain in the faces of a corrugation ............................................................15 Figure 18 Test to determine slip in a fastener......................................................................16 Figure 19 Shear slip between sheets (left). Seam fasteners in sheeting and decking (right).16 Figure 20 Shear strength and flexibility of panel in direction at right angles ..........................17 Figure 21 Diaphragm roof – sheeting perpendicular to length of building..............................18 Figure 22 Shear buckling of profiled sheeting......................................................................19 Figure 23 Sway and no-sway forces on a rectangular portal frame......................................20 Figure 24 Definition of frame flexibility.................................................................................20 Figure 25 Rectangular sheeted portal frame building ..........................................................21 Figure 26 Forces and deflections a) on sheeting panels b) on frames ................................21 Figure 27 Forces on a sheeted ptched roof portal frame (left) and the equivalent horizontal

shear flexibility of panels (right).....................................................................................22 Figure 28 Diaphragm bracing to end gables (left) and lateral bracing to beam (right)...........23 Figure 29 Typical light gauge steel folded plate foof ............................................................24 Figure 30 Alternate fastener arrangements in a flat roof diaphragms...................................24

Appendix 1. Tables 2. Worked examples



Appendix 1

design industrial buildings

Documents

diaphragm strength

design principles

column design

wall systems

bracing systems

roof systems

stressed skin diaphragm

department of civil