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StatconAnalyzer Technical documentation

StatconSolver

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Statcon Technical documentation

C:\Utv\Workspaces\3501-Statcon\documents\StatconSolverDocuments\StatCon Analyzer Technical document.docx Sid 2 av 42 Utskrivet 2018-01-16 14:18:00

Content 1 General ................................................................................................................... 5

1. 1.1 Analyze ............................................................................................................. 5

1.1.1 Definitions in Statcon ........................................................................................ 5

1.1.2 Internal element forces ..................................................................................... 5

1.1.3 Node properties ................................................................................................ 8

1.1.4 Element properties............................................................................................ 8

1.1.5 Section properties ............................................................................................. 8

1.1.6 Fixings .............................................................................................................. 9

1.1.7 Element Loads .................................................................................................. 9

1.1.8 Node loads ....................................................................................................... 9

2. 1.2 Design codes and standards ............................................................................ 9

1.2.1 Basics ............................................................................................................... 9

1.2.2 Loads ............................................................................................................... 9

1.2.3 Steel ............................................................................................................... 10

1.2.4 Wood .............................................................................................................. 10

1.2.5 Applications .................................................................................................... 10

2 Materials ............................................................................................................... 10

3. 2.1 Wood .............................................................................................................. 10

2.1.1 Softwood ........................................................................................................ 10

2.1.2 Hardwood ....................................................................................................... 10

4. 2.2 Glulam ............................................................................................................ 10

2.2.1 BauBuche GL70 ............................................................................................. 10

5. 2.3 LVL ................................................................................................................. 10

2.3.1 Kerto ............................................................................................................... 10

2.3.2 BauBuche ....................................................................................................... 10

6. 2.4 Steel ............................................................................................................... 10

7. 2.5 Manufactured elements .................................................................................. 11

2.5.1 I-Beams .......................................................................................................... 11

8. 2.6 Special............................................................................................................ 11

2.6.1 ComWood [Obselete] ..................................................................................... 11

9. 2.7 CL – Cross laminated wood ............................................................................ 12

2.7.1 KL according to Martinsons Standard ............................................................. 12

2.7.2 Modelling ........................................................................................................ 14

3 Sections ................................................................................................................ 15

10. 3.1 Standard ......................................................................................................... 15

11. 3.2 Rolled steel ..................................................................................................... 15



12. 3.3 I-Beams .......................................................................................................... 15

3.3.1 Masonite ......................................................................................................... 15

3.3.2 Ranti ............................................................................................................... 15

3.3.3 Hunton ............................................................................................................ 15

3.3.4 Dudek ............................................................................................................. 15

13. 3.4 Special............................................................................................................ 16

3.4.1 Mono tapered elements .................................................................................. 16

3.4.2 Duo tapered elements .................................................................................... 16

3.4.3 ComWood ...................................................................................................... 16

4 Loads and load combinations ............................................................................... 16

14. 4.1 General ........................................................................................................... 16

4.1.1 Code Combination .......................................................................................... 16

4.1.2 Example ......................................................................................................... 17

15. 4.2 Templates ....................................................................................................... 17

4.2.1 Load case Template ....................................................................................... 17

4.2.2 Action Template .............................................................................................. 17

16. 4.3 Loads applied onto the model ......................................................................... 17

17. 4.4 Crane loads according to EN 1991-3 .............................................................. 18

4.4.1 Partial coefficients according to table A.1 ....................................................... 18

4.4.2 Ψ values for crane loads according to table A.2.3 ........................................... 18

5 Element Design .................................................................................................... 18

18. 5.1 General ........................................................................................................... 18

5.1.1 Results ........................................................................................................... 18

5.1.2 Safety classes in SS-EN ................................................................................. 19

5.1.3 Reliability classes in NS-EN ............................................................................ 19

19. 5.2 Wood and wood based materials .................................................................... 20

5.2.1 General ........................................................................................................... 20

5.2.2 Load durations ................................................................................................ 20

5.2.3 Service class .................................................................................................. 20

5.2.4 Material properties .......................................................................................... 20

5.2.5 Tension (parallel to grain) ............................................................................... 21

5.2.6 Compression (parallel to grain) ....................................................................... 21

5.2.7 Bending .......................................................................................................... 21

5.2.8 Bending combined with tension ...................................................................... 21

5.2.9 Bending combined with compression .............................................................. 21

5.2.10 Lateral Torsonial Buckling............................................................................... 22

5.2.11 Shear .............................................................................................................. 22

5.2.12 Bearing ........................................................................................................... 24

5.2.13 Bearing Check (NS-EN) .................................................................................. 26



5.2.14 Bearing check (SFS-EN) ................................................................................ 26

5.2.15 Bearing contact plate (Layup protection plate) ................................................ 27

5.2.16 Support material control .................................................................................. 28

5.2.17 Tapered elements ........................................................................................... 29

5.2.18 Vibrations according to EN ............................................................................. 30

5.2.19 Vibrations (NS-EN) according to NBI – “Komfortkriteriet” ................................ 32

5.2.20 Vibrations (SFS-EN) according to RIL............................................................. 32

5.2.21 Holes in solid wood, glulam and LVL .............................................................. 33

5.2.22 Deflections ...................................................................................................... 33

5.2.23 Fire design ...................................................................................................... 34

5.2.24 Column feet .................................................................................................... 35

20. 5.3 Steel ............................................................................................................... 37

5.3.1 General ........................................................................................................... 37

5.3.2 Classification of cross sections ....................................................................... 37

5.3.3 Warping Constant ........................................................................................... 37

5.3.4 Crititcal Buckling Force, Ncr ............................................................................ 37

5.3.5 Elastic critical moment for lateral torsional buckling ........................................ 37

5.3.6 Critical axial load for torsional and flexural torsional buckling modes .............. 38

5.3.7 Tension ........................................................................................................... 38

5.3.8 Compression .................................................................................................. 38

5.3.9 Bending .......................................................................................................... 39

5.3.10 Shear .............................................................................................................. 39

5.3.11 Bending and shear ......................................................................................... 39

5.3.12 Bending and axial compression ...................................................................... 39

5.3.13 Flexural buckling ............................................................................................. 39

5.3.14 Torsional-flexural buckling .............................................................................. 39

5.3.15 Lateral Torsional Buckling............................................................................... 39

5.3.16 Members in bend and Compression - Interaction formula ............................... 40

5.3.17 Deflections ..................................................................................................... 40

5.3.18 Fire design ..................................................................................................... 40

5.3.19 Column feet .................................................................................................... 40

6 References ........................................................................................................... 42



1 General

1.1 Analyze The analyze of the structure is performed by using an extern FEM module. The system is prepared for different solvers but the default solver is developed in Norway and is called Solve3d. The solve3d32.dll is installed alongside all other satellite assemblies used by the application. The analyze is a 1st order linear analyze, dealing with 3D problems such as bending about 2 axis.

1.1.1 Definitions in Statcon The global coordinate system is based on the right hand rule, where the global z axis is the vertical axis. The model is made by placing nodes in a 3D space (X,Y,Z) and connect elements to existing nodes. Each element end can be defined with 6 DOFs (Degree Of Freedom). Movement in all directions (X,Y,Z) and rotation about all axis (rX, rY, rZ). The connections can be set with springs but this feature is not used in Statcon (2011.3 SP1) A node must be connected to an element or assigned to a fixing point (support).

1.1.2 Internal element forces

Nx, axial force. Negative forces are compressed.



Vy, shear force in the direction of the local y axis of the element. Vz, shear force in the direction of the local z axis of the element.

My, moment bending about the local y axis of the element. Mz, moment bending about the local z axis of the element.



(Mx, torsonial moment about local x axis.) Example of an element rotated 45 degrees about local x axis ,loaded with vertical line loads and an axial load. The result forces are picked from a point within the element.

Example of an element with 2D bending only:



1.1.3 Node properties X – X location in the global coordinate system, mm. Y – Y location in the global coordinate system, mm. Z – Z location in the global coordinate system, mm.

1.1.4 Element properties Lcy – Theoretical buckling length about the local y axis. Lcz – Theoretical buckling length about the local z axis. This is a user input since it’s a 1st order analysis.

1.1.5 Section properties

A – Cross section area, mm² Iy – 2nd moment of area about y axis, mm4 Iz – 2nd moment of area about z axis, mm4 iry – Radius of gyration about y axis, mm. irz– Radius of gyration about z axis, mm.



cy – Shear centre offset to centeroid along local y axis, mm. cz – Shear centre offset to centeroid along local z axis, mm.

1.1.6 Fixings A fixing (aka support) can be assigned with 6 DOFs. Movement in all directions and rotation about all axis. The DOFs refer to the global coordinate system. Supports can be set as springs in all 6 directions.

1.1.7 Element Loads Line load applied onto an element

1.1.8 Node loads Point load assigned to a node.

1.2 Design codes and standards Statcon Structure uses EuroCode to design analyzed elements.

1.2.1 Basics EN 1990

1.2.2 Loads EN 1991-1-1 General, live loads EN 1991-1-3 Snow EN 1991-1-4 Wind EN 1991-3 Actions induced by cranes and machinery.



1.2.3 Steel EN 1993-1-1

1.2.4 Wood EN 1995-1-1

1.2.5 Applications

1.2.5.1 EN, Generic application No specific national application

1.2.5.2 SS-EN, Swedish application SS-EN versions of the above.

1.2.5.3 NS-EN, Norwegian application NS-EN versions of the above.

1.2.5.4 SFS-EN, Finnish application

2 Materials

2.1 Wood Rectangular and circular sections.

2.1.1 Softwood C14-C35

2.1.2 Hardwood D18-D70

2.2 Glulam GL38 – GL36. Code dependent. Produced and accepted according to EN 14080

2.2.1 BauBuche GL70 https://www.pollmeier.com/en/

2.3 LVL

2.3.1 Kerto Kerto S,Q http://www.metsawood.com/global/products/kerto/Pages/Kerto.aspx

2.3.2 BauBuche BB-S, BB-Q https://www.pollmeier.com/en/

2.4 Steel According to 1993-1-1



2.5 Manufactured elements

2.5.1 I-Beams

2.5.1.1 Masonite

2.5.1.2 Ranti

2.5.1.3 Hunton

2.5.1.4 Dudek

2.6 Special

2.6.1 ComWood [Obselete] A product manufactured by Martinsons Limträ. www.martinsons.se

*No longer an official product



2.7 CL – Cross laminated wood There are different CL applications on the market. Currently the CL implementation in Statcon is based on the production of KL wood at Martinsons

2.7.1 KL according to Martinsons Standard Elements of “KL” are treated the same way as beam elements. The KL material can be used in 4 different orientations.

2.7.1.1 Sizes KL is laminated into decided thicknesses by gluing different plies of wood in a certain way. The figure after the material index “KL” indicates the thickness of the lamination.

For slabs, Z is bound to the selected KL material. Y is the user input. Recommended value <=1200 mm For beams it’s the opposite, Y is bound to the selected KL material while the Z is user input. Recommended value <=1200mm

2.7.1.2 Weak slab The dominating grain direction is orientated perpendicular to the span.

2.7.1.3 Strong slab The dominating grain direction is orientated in the direction to the span.

2.7.1.4 Weak beam Bending is effecting dominating grain direction.



2.7.1.5 Strong beam Bending is effecting the dominating grain direction.



2.7.2 Modelling The static representation of KL is the same as for regular elements. The elements are point supported. Theoretically it means that a slab is supported across the entire width at each supported point.

Supports along the direction of the span are not implemented. Beams are modelled in the same way but with the cross section rotated.

Loads are applied along the theoretical centre line as for any element in Statcon. Load offsets are not supported in Statcon.



3 Sections

3.1 Standard Rectangular, Circular

3.2 Rolled steel IPE, HEA, HEB, HEM, UNP, UPE, KKR, VKR

3.3 I-Beams

3.3.1 Masonite R, H, HI, MP

3.3.2 Ranti IN,IB,IS

3.3.3 Hunton SJ(45,60,90) SW(45,60,90)

3.3.4 Dudek DIB47/DIB72



3.4 Special

3.4.1 Mono tapered elements Glulam only.

3.4.2 Duo tapered elements Glulam only

3.4.3 ComWood See 2.6.1

4 Loads and load combinations

4.1 General

4.1.1 Code Combination A code combination in Statcon terms is the equation stated in EuroCode telling how loads should be combined according to EN 1990 6.4 Statcon uses these code combinations to generate load case templates. A code combination holds information about limit state and partial coefficients. Load case templates are dynamically generated based on the applied action categories. Statcon combines all applied actions categories to make sure the worst load case is evaluated.



4.1.2 Example

4.2 Templates

4.2.1 Load case Template A load case template is based on a Code Combination. A load case template holds a list of action templates. The load case template also has information about the main (unfavourable) action category

4.2.2 Action Template An action template holds information about the action category according to EN 1991-1 6.3.1.1 The action template also holds the psi0, psi1 and psi2 load factor values for the current load case template.

4.3 Loads applied onto the model Based on the load case templates and its action templates, Statcon generates the actual load cases for the model to be analyzed.

If the load case template contains wind, and the user wants to check all four wind directions, one load case template will end up with four load cases to evaluate. The unfavourable action category is marked with an asterisk (*). The duration is presented within {}. The code combination is presented within <>.



4.4 Crane loads according to EN 1991-3

4.4.1 Partial coefficients according to table A.1 Variable crane load . 1.3 (STR) . 1.0 (EQU)

4.4.2 Ψ values for crane loads according to table A.2.3 1.0 0.9 (conservable set to 0.5)

4.4.2.1 SS-EN 1991-3 (EKS 9)

, 0.8

, 0.7

, (conservable set to 0.5)

, 0.5

, 0.5

, 0

5 Element Design Element design is performed after the model has successfully been analyzed. The design uses the internal forces, support reactions and deflections, calculated by the solver. Element design is implemented according to EuroCode.

5.1 General

5.1.1 Results In Statcon results are presented as “usage” or CSI Combined Stress Index. For an element to pass the design CSI must be <=1.00. Statcon presents the CSI colour coded, starting from dark green to red (>1). In application settings there is an option to display C.S.I as percentage. The GUI in Statcon Structure presents the results on screen.



When wanted, Statcon can provide a more detailed view of the result in any given point in any given load case as well as a reference to the design code.

5.1.2 Safety classes in SS-EN SS-EN 1990:2002 Appendix NB §10. There are three safety classes in SS-EN. Loads on an element in class 1 and 2 are allowed to be reduced while loads set on to an element in class 3 remains.

. = 0.83

. = 0.91

. = 1.00, no reduction.

5.1.3 Reliability classes in NS-EN According to NS-EN 1990:2002/NA:2008 NA.A1.3.1(901) there are four classes. As stated, variable loads on structures in class 1 may be reduced with the reduction factor kFi= 0.9.



This reduction is shown on screen and incorporated in all results as well as in resulting support reactions. Applied loads in class1:

Applied loads in other classes:

5.2 Wood and wood based materials Wood elements are designed according to EN 1995-1-1 implementing the appropriate national properties.

5.2.1 General Wood based materials must follow EuroCode standards for production. Characteristic properties for wood(C) and hard-wood(D) are taken from EN 338 or national documents. GluLam (GL) is taken from EN 1194 or national documents. Elements with predefined characteristic capacities, manufactured elements (I-Beams), must have approved documentation (ETA).

5.2.2 Load durations Loads applied onto wooden structures must be assigned to a duration class. The duration class tells how long period of time a particular load is action onto a structure. There are 5 duration classes according to EN 1995-1-1 2.3.1.2 (P) Permanent loads. (L) Long term loads. (M) Medium term loads. (S) Short term loads. (I) Instant loads.

5.2.3 Service class Wood elements are assigned to one of three service classes according to EN 1995-1-1 2.3.1.3. A service class is referring the moisture content in the surrounding environment.

5.2.4 Material properties The allowed design stress is calculated according to EN 1995-1-1 2.4.1



=×

(2.14)

; Characteristic material property value.

; Table 3.1, depending on the current service class, load duration and material. ; Material partial coefficient according to table 2.3

5.2.5 Tension (parallel to grain) According to EN 1995-1-1 6.1.2

, , ≤ , , || , , ≥

, , = ; ≥ 0

, , = , , ×

5.2.6 Compression (parallel to grain) According to EN 1995-1-1 6.1.4

, , ≤ , , || , , ≥

, , = ; ≤ 0

, , = , , ×

5.2.7 Bending According to EN 1995-1-1 6.1.6

, ,, ,

+ , ,, ,

≤ 1 | | ,

+ ,

≤ 1

, ,, ,

+, ,, ,

≤ 1 | | ,

+ ,

≤ 1

, , = ×

= ; designing bend stress about the local y axis

, , = ×

= ; designing bend stress about the local z axis.

= 0,7 for rectangular sections, otherwise 1.0

5.2.8 Bending combined with tension According to EN 1995-1-1 6.2.3 Bending according to 5.2.7 Tension according to 5.2.5 Interaction according to EN 1995-1-1 6.2.3 (6.17, 6.18)

5.2.9 Bending combined with compression

5.2.9.1 Small risk of buckling, rel.Y <= 0.3 and rel.Z <=0.3 Bending according to 5.2.7 Tension according to 5.2.5 Interaction according to EN 1995-1-1 6.2.4 (6.19, 6.20)



5.2.9.2 Risk of buckling, rel.Y > 0.3 OR rel.Z >0.3 Bending according to 5.2.7 Compression according to 5.2.6 Interaction according to EN 1995-1-1 6.3.2 (6.23, 6.24)

5.2.10 Lateral Torsonial Buckling According to EN 1995-1-1 6.3.3 A check for Lateral buckling effect is performed if ʎrel,m, (acc to EN 1995-1-1 6.3.3 (6.30)) ≥ 0.75. Effective length by length ratio (lef/l) is conservatively taken as 1.0 acc to EN 1995-1-1 6.3.3 (Table 6.1) Since EC5 is lacking interaction formulas when dealing with lateral Torsonial buckling Statcon uses an interaction formula published in the German application document DIN EN 1995-1-1. This is a complement to EN 1995-1-1 (6.35) taking all directions into account.

kc,y and kc,z acc to EN 1995-1-1 6.3.2 (6.25,6.26) kCrit acc to EN 1995-1-1 6.3.3 (6.34)

5.2.10.1 Critical bending stress

For rectangular sections of hard wood (D), GluLam (GL) or LVL, bending about its strong axis [Y], , is in Statcon calculated as,

, =,

E × G (1 − 0.63 ) , according to (Porteous & Kermani, 2009)

For rectangular soft wood sections (C), bending about its strong axis [Y], , is in Statcon calculated as,

, =.

, E According to EN 1995-1-1 (6.32)

For other sections, bending about its strong axis [Y], , is in Statcon calculated as:

, =

, According to EN 1995-1-1 (6.31)

= Torsonial Constant, often written as or

5.2.11 Shear According to EN 1995-1-1 6.1.7

≤ ,



, =××

= current axis.

= Second Moment of Area about n axis. = Shear force in the direction of the n axis. = 2nd moment of area about n axis.

For rectangular sections the general formula can be simplified;

, =1.5 ×

×

, =1.5 ×

×

, = , × = According to EN 1995-1-1 6.1.7(2)

, National applications might state different values.

5.2.11.1 Shear reduction According to EN 1995-1-1 6.1.7(3) In Statcon, when allowed, applied loads close to the theoretical position of a support, may be ignored. Ignored loads will however still effect the support reaction.



No reduction applied Reduction applied

Shear reduction also covers line loads applied on the reduction area.

5.2.12 Bearing According to EN 1995-1-1 6.1.5 The bearing control is performed to validate the capacity of the lower fibre in a supported element.

5.2.12.1 kc90 “kc90” is taken from 1995-1-1 6.1.5(3,4) Looking at (3), elements continuously supported, i e a bottom rail with incoming studs, kc90 depends on the size of the bottom rail and the location of the studs in relation with the end of the bottom rail (a) and the spacing of the studs (L1).

Looking at (4), elements supported by point supports, i.e beam elements, it states that for concentrated loads, placed closer to the support than 2H, kc90 should be set to 1.0.

Statcon think of “concentrated loads” as point loads and looks for point loads in this area. When a point load is placed within 2H kc90 will be set to 1.0.

To force kc90 to 1.0, insert a small point load (1N) within 2H. This will have a small impact on the overall design of the element but kc90 will be set to 1.0.



The exception is when, according to A2:2014, the element is loaded by a series of point loads acting at close centres (e.g. joists or rafters at centres < 610 mm). If so the load may be regarded as a distributed load. Note: This will apply to imported point loads and point load +. Single point loads, even if manually placed in a series, will be treated as isolated loads. Statcon will treat more than 3 loading elements as a series of point loads.

5.2.12.2 With unspecified support:

. = ,

× , , × ,

, = . ( ℎ ).

= , ℎ ℎ ℎ . , = , EN 1995 -1-1 6.1.5(4)

Reported results

The needed effective length is assumed acting along the local x-axis of the element.

5.2.12.3 With specified support When the support is given a size, the contact between the element and support (bearing) can be checked.

= + = × (*)

, = ,

= ,

, , × ,

= ( ℎ ) ℎ

= ℎ ℎ, EN 1995-1-1 6.1.5(1)



(*) When the support is a post, Y is the min value between the size of the post and the width of the beam.

Reported results:

= . − ; The needed actual size of the supporting surface.

5.2.13 Bearing Check (NS-EN)

As an alternative to EN 1995-1-1 6.1.5, bearing check could be designed according to “Treteknisk Rapport #86”.

5.2.14 Bearing check (SFS-EN) In SFS-EN the validation is the same as in EN but with a different formula setup. Instead of calculating the stress based on the effective area the effect of the increased bearing length is implemented as a load factor,

= = +

= + , according to EN 1995-1-1 6.1.5(1)

EN:

, = , = ,

×≤ ×

. = × × × SFS-EN (RIL):

, = , = ,

×≤ × ×

=

. = × × × ×

. = × × × ×

. = × × × = .

∴ . = .



5.2.15 Bearing contact plate (Layup protection plate) Design method when checking the capacity of layup protection plates.

, = . ( ℎ ). = ℎ ℎ ( ) = .

= , ; ℎ .

= .

= , . Steel plate design check according to 5.3.11 Bearing check acc to 5.2.12 with “Leff” calculated using the steel plate size as “B”.

5.2.15.1 Bearing reinforcement (using SFS WT or WR connectors)

The idea is to distribute the support reaction in to the timber using the axial capacity (SFS-intec, 2013) of the connectors. The connectors are driven into the timber according the rules of the chosen connector. Then the protection plate is applied. The connection plate loads the heads of the connectors. The capacity of the joint is the combined capacity of the timber and the reinforcement.

, = . ( ℎ ).

, = ℎ ℎ .

, = ℎ . = .

, =

, = . − . .

= .

.

The steel plate is validated for the maximal bending moment between connectors.



, = . ( ℎ ).

= ℎ ℎ ( ) = ( ).

= , ; ℎ ( )

= , .

Steel plate design check according to 5.3.11 Bearing check acc. to 5.2.12 with “Leff” based on the load distribution of the connectors. Connector capacity and concept: SFS ETA 12/0062, WR-T SFS ETA 12/0063, WT-T

5.2.16 Support material control When assigned with data or involved in a load transfer chain the supporting material can be checked for compression. The compression check when the support is horizontal, is performed according to EN 1995-1-1 6.1.5 . Assuming the support is continuous, an additional 30+30 mm to included in the compressed fibres.

. = 30 + + 30.

If the support is compressed close to the edge;

. = 30 + There are two different “support situations” described in EN 1995-1-1 6.1.5. 1. The support rests on a continuous surface (typically a bottom rail)



2.The support rests on point wise elements (typically a top rail or a beam)

The support situation decides, alongside the material, kc90. When the support is set to be a post, the compression check is performed according to EN 1995-1-1 6.1.4, When the support is set with an angle the material control is performed on the compressing component of the vertical (and horizontal) reaction.

When a steel plate is used “Leff” is calculated using the size of the steel plate.

5.2.17 Tapered elements In Statcon, tapered elements are generated as an approximation of the tapered edge. This is necessary since not all solvers supports elements with inconstant section properties.

The section Heff (Z) used in the analyze is calculated as



= 1 +

2× tan ( )

5.2.17.1 Mono tapered elements According to EN 1995-1-1 6.4.2

5.2.17.2 Duo tapered elements According to EN 1995-1-1 6.4.3 Statcon implements load reduction at APEX according to equ. (6.55)

5.2.18 Vibrations according to EN In addition to the common design features, Statcon provides a function to check the vibrations of domestic floors according to EN 1995-1-1 7.3.3

- fundamental frequency - unit impulse velocity response. - instant deflection under 1 kN load

Statcon uses the approach in EN 1995-1-1, where the combined section of the floor decking and the joist act together as a unit. The joist is loaded with a 1 kN instant load, mid span, only. The Joists pacing has in this case no impact on the applied load. The joist spacing is simply telling Statcon the size of the combined section. The paradox is that in theory (and according to the method in EN 1995-1-1), a larger joist spacing is more efficient then a denser spacing since the larger spacing provides a stiffer section due to a wider flange.



5.2.18.1 Input (standard user)

Floor panel size perp. to joist layout.

Joist spacing, the distance between the joists. Thickness, the thickness of the decking. E-modulus, material properties of the decking. Number of joists, the number of similar elements within the floor cassette. Load reduction, function to reduce the applied point load.

5.2.18.2 Interaction between Joist and Decking The default value is “true”, there is interaction between Joist and Decking. If this interaction is impossible to achieve, the interaction can be turned off. If turned off, the vibration control will be run on the Joist only. Interaction No interaction

5.2.18.3 Load reduction There is a function for reducing the point load applied onto the joist. For this to apply there must be five or more joists within the cassette. It’s up to the user to decide if this method is valid since it’s not mentioned in any aspect EN 1995-1-1. The method used is described in (Swedish Wood, 2011).

=⁄

× ; 0 ≤ ≤ 1

= , ×; bending stiffness of the floor decking.

=−4.7 ² + 2.9 + 0.4, 0 < < 0.3

0.8 + 0.2 , 0.3 ≤ ≤ 1.0



5.2.19 Vibrations (NS-EN) according to NBI – “Komfortkriteriet” As an alternative to the suggested method in EN 1995, the Norwegian design code offers a different validation method, described in NBI document 522.351:

This method uses some of the parameters also used in the EN method but there are some differences.

5.2.19.1 BTAB - NBI The floor can be validated based on the theory of BTAB. This theory dates back to the early 70’s:

Supporting documents can be found downloaded from: http://www.elecosoft.se/refDok/produkter/10/BTAB_Documentation.zip

5.2.20 Vibrations (SFS-EN) according to RIL In Finland there is a different method suggested for validating vibrations. This method can be found browsing the “Puuinfo” website http://www.puuinfo.fi/

Basically, this method is more theoretical than the EN one. Noggins, up to three lines, are taken into account as well as the support condition. Also the stiffness of the connectors tying the noggins and cross battens to the main structure is taken into account. The requirements for deflection and frequency are rather strict compared to EN restrictions. In Statcon there is no option for upper decking (concrete and so on) only the structural floor board can be chosen. Particle, OSB and Plywood boards are implemented. User defined parameters are possible.



5.2.21 Holes in solid wood, glulam and LVL The design theory of holes is taken from the Swedish publication (Limträhandbok, Del 1-3) The theory is mainly based on the suggestions found in the German NA, DIN-EN 1995-1-1. Holes are complicated. To ensure sufficient security the methods described are conservative. Holes with no reinforcement will always be small in relation to the element. LVL elements cannot be reinforced in Statcon. The methods used only apply to Solid timber and Glulam elements where the grain direction runs along the element.

5.2.21.1 Reinforcement using Self-drilling screws. The methods described above suggest use of self-drilling screws as reinforcement surrounding holes. Statcon implements two different screws, SFS-WT-T and WR-T. WT-T can be counter sinked.

The deciding parameter of the reinforcement capacity is the effective anchorage length. Statcon suggest a very conservative approach to this. Since the most likely splice location can vary based on the direction of the bending moment it’s not sure which splice that is initialized first. To cover this, Statcon always look at the shortest possible anchorage length. A connector is allowed to be countersinked until the splice location is in the middle of the smooth shank. If a connector is countersinked to its max and the effective anchorage length is to short, a longer connector is necessary. To be valid, the effective anchorage length must be long enough according to the current code and connector diameter.

5.2.22 Deflections Wood based elements are normally designed according to EN 1995-1-1 2.2.3 based on the characteristic combination (6.14)



When applied Frequent and Quasi-Permanent states are designed acc. to 2.2.3(3) using material properties acc. to 2.3.2.2

5.2.23 Fire design Solid wood, Glulam and LVLs are designed according to 1995-1-2 Fire design of built up beams is not supported.

5.2.23.1 Loads Loads are applied according to 2.4.2(1)

5.2.23.2 Design Member design according to 4.2.2 – Reduced Section Method. Shear is disregarded as well as compression perpendicular to grain, according to 4.3.1

. = . × ,

. 2.3(1) (2.1)



kmod.fi = 1.0 according to 4.2.2(5). fk.20 = kfi × fk according to 2.3(3) (2.4) kfi according to Table 2.1 Reduced section according to 4.2.2 (1) (4.1)

ßn according to Table 3.1 t exposure time in minutes. k0 according to Table 4.1 d0 = 7 according to 4.2.2(1)

5.2.23.3 Stability Member restrains follow user input. Support conditions follow user input (as when not exposed to fire).

5.2.23.4 CLT elements Statcon calculates the remaining section based on the burn time. A smaller CLT material is automatically chosen to match the remaining material. The remaining CLT material is conservatively considered to be orientated in the weak direction. Each new layer exposed to fire, is considered as used, and deducted from the original material. CLT elements can only be exposed for fire on its flat sides.

5.2.24 Column feet For Solid wood, Glulam and LVL columns, a column foot connection can be designed.

- Column feet are designed according to EN 1995-1-1 8 , with support from: o Swedish Glulam handbook (Crocetti, 2016) o Structural Timber Design to EC5 (Porteous & Kermani, 2009)

- No torsional forces allowed. - Connector capacity and gusset stress capacity is checked. - Connector placing is validated according to code regulations. - Gusset adhesive capacity is not checked. - Splitting of the concrete is not checked.



5.2.24.1 Hinged support condition – No moment.

- Following the plastic-elastic theory described in the technical documentation of

Statcon Connections, forces are distributed across all active connectors.

5.2.24.2 Rigid support condition - Moment

- The compressed side of the column is validated for compression and is used to its

limit – no compression forces will be distributed to the connectors. - Tensile forces are considered to act on the opposite side of the column and be

distributed to the connectors. - Bolt cage is not designed. - No ‘weak axis moment’ allowed to be carried by a rigid column foot.



5.3 Steel Steel elements are designed according to EN 1993-1-1 implementing the appropriate national properties.

5.3.1 General Rolled steel sections material properties are used according to EN 10025. Elements with predefined characteristic capacities, manufactured elements (I-Beams), must have approved documentation (ETA).

5.3.2 Classification of cross sections According to EN 1993-1-1 Table 5.2

5.3.2.1 Class 4 Cross sections of class 4 is not fully supported in Statcon. Aeff is conservatively set as 0.5A and Weff is set as 0.5W. For a more precise result of class 4 sections, further design according to 1993-1-5 must be done outside Statcon. When a cross section is classed as a class 4 the user is alerted of the situation.

5.3.3 Warping Constant

In Statcon the Warping constant for a cross section is Iw and calculated for each section when missing in data sheet. For the most common section there are tabulated values. Calculations acc to (CISC, 2002).

5.3.4 Crititcal Buckling Force, Ncr

=×

5.3.5 Elastic critical moment for lateral torsional buckling When not given as an input value, the Elastic Critical Moment, Mcr, needs to be calculated.



(NCCI) Statcon uses the formula above, found in NCCI: Elastic critical moment for lateral torsional buckling SN003a-EN-EU. C1 is depending on the load applied onto the element as well as the support conditions. C1 and C2 are evaluated based on the shape of the moment curve.

Statcon always consider the load to be applied at the least favourable position. zg will always be >0 (Normally 0.5*Z, Z being the height of the element)

5.3.6 Critical axial load for torsional and flexural torsional buckling modes In some cases, the “Critical axial load for Torsonial and flexural torsinoal buckling” must be calculated. Statcon calculate Ncr,T according to (NCCI) document SN001a

5.3.7 Tension According to EN 1993-1-1 6.2.3

5.3.8 Compression According to EN 1993-1-1 6.2.4



5.3.9 Bending According to EN 1993-1-1 6.2.5

5.3.10 Shear According to EN 1993-1-1 6.2.6 Shear area is calculated when missing in data sheet.

5.3.10.1 Shear Buckling The cross section is validated acc. to EN 1993-1-1 6.2.6(6), formula (6.22). If the section fails this validation the user is alerted. For details visit EN 1993-1-5.

5.3.11 Bending and shear According to EN 1993-1-1 6.2.8

5.3.12 Bending and axial compression According to EN 1993-1-1 6.2.9.1(6) (6.41)

5.3.13 Flexural buckling According to EN 1993-1-1 6.3 ʎ . according to 6.3.1.3 (1) according to 6.3.1.2 (6.49) If 6.3.1.2(4) applies buckling is ignored. Buckling curve according to Table 6.2 Imperfection factor according to Table 6.1

5.3.14 Torsional-flexural buckling According to EN 1993-1-1 6.3 ʎ . according to 6.3.1.4 (2) according to 6.3.1.2 (6.49) If 6.3.1.2(4) applies buckling is ignored. Buckling curve according to Table 6.2 Imperfection factor according to Table 6.1

5.3.15 Lateral Torsional Buckling According to EN 1993-1-1 6.3.2 Rolled sections are validated using 6.3.2.3 ʎ . according to 6.3.2.3 (1) (6.57). according to 6.3.2.3 (1) (6.57).



Note : , according to (6.58) is not implemented.

If 6.3.2.2(4) applies Lateral Torsional Buckling is ignored. Buckling curve according to Table 6.5 Imperfection factor according to Table 6.3

Note : All other sections than H and I will be set with buckling curve “d”.

5.3.16 Members in bend and Compression - Interaction formula According to EN 1993-1-1 6.3.3 Statcon offers a conservative approach to calculations of the interaction factors, kij, according to Method 1 in Annex A of EN 1993-1-1. When performing interaction check, NED, MyED, MzED are taken as the max value, respectively, occurring along the member in the investigated load case acc to EN 1993-1-1 6.3.3(4).

5.3.17 Deflections Three states can be evaluated acc to EN 1990-1-1 6.5.3 - Characteristic (6.14) - Frequent (6.15) - Quasi-Permanent (6.16) Normally the characteristic combination, 6.14, generates the largest deflections.

5.3.18 Fire design Steel members are currently not fully supported. The CSI is reported based on the FIRE load case and at normal temperature (t<=20 °C).

5.3.19 Column feet



- Hinged and rigid column feet are supported. - Column feet are designed according to EN 1993-1-8 6.2.8 with support from:

o NCCI: SN037a – EN-EU Design model for simple column bases – axially loaded I section columns, (NCCI).

o NCCI: SN043a – EN-EU Design of fixed column base joints, (NCCI). o SBI Column feet PF1 and PF2, (Construction, Publication 183, 2nd edition

2011)

- As selection of HE-A and HE-B column sections are supported. o HE-A [100-400] o HE-B [100-400]

- Base plate dimensions are predefined. - Two bolt layouts, PF1 and PF2

- No torsional forces allowed. - No ‘weak axis moment’ allowed to be carried by a rigid base plate.

- Splitting of the concrete is not covered.



6 References Carling, O. (1992). Dimensionering av träkonstruktioner (Timber structure design).

Svensk Byggtjänst.

CEN. (2004). EN 1995-1-1 Design of timber structures Part 1-1 General. Common rules and rules for buildings. CEN.

CISC. (2002). TORSIONAL SECTION PROPERTIES OF STEEL SHAPES. Canadian

Institute of Steel Construction.

Crocetti, R. (2016). Limträhandbok, Del 1-3. Svenskt Trä.

NCCI. (u.d.). Hämtat från NCCI: http://www.steelbiz.org/

Porteous, J., & Kermani, A. (2009). Structural Timber Design to EuroCode 5. Blackwell Publ.

SFS-intec. (2013). ETA-12/0062 ETA-12/0063.

Swedish Wood. (2011). Design of timber structures. Svenskt Trä.