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D10 – Glued Laminated Girder

FRILO Software GmbH

www.frilo.com

[email protected]

As of 28/07/2016

D10

FRILO Software GmbH

Glued Laminated Girder D10

Note: This document describes the Eurocode-specific application. Documents referring to former standards are available in our document archive at www.frilo.eu Service >> Documentation >>Manuals >>Archive.

Contents

Application options 5 Basis of calculation 6 Input 7 Basic parameters 7 System 8 System lengths 8 Truss geometry 9 Supports 10 Loads 11 Standard loads 11 Snow and wind loads 11 Additional loads 13 Design 14 Design options 14 Support torsion 14 Limitation of the deflection 15 Transverse tensile reinforcements and ridge verification 15

Drawing view/relocation of reinforcements 17 Fire protection 18 Design and calculation 19 Internal design forces 19 Stress verifications 19 Stability (tilting) 23 Recommendations concerning transverse tension 24 Output 25 Application-specific icons 25

http://www.frilo.eu/

Glued Laminated Girder

Software for structural calculation and design

D10

FRILO Software GmbH

Application options

The D10 application is suitable for the design of

- trusses with straight or curved top and bottom edges

- double-pitch roof trusses with straight or curved bottom edge including the variants: - no saddle, - sway saddle, - fixed saddle, - high dry joint and - arched beam.

The plies can optionally run in parallel to the truss top edge if the geometric conditions allow this.

The software application offers various additional options that range from the calculation and fully automatic relocation of transverse tensile reinforcements with fully threaded rods and glued-in threaded rods to the verification of the fire resistance period.

In addition to typical standard loads such as dead loads, snow and live loads over the total length, other load types (concentrated and trapezoidal loads) with permanent and variable portions can be included in the calculation and the corresponding action type can be taken into consideration. Moreover, the user can define alternative snow loads by specifying a freely selectable factor.

The structural systems that can be handled in this software application comprise single-span beams with one or two cantilevers.

Standards

EN 1995-1-1:2008 / 2014

DIN EN 1995-1-1:2010 / 2013

ÖNORM EN 1995-1-1:2009 / 2010 /2015

BS EN 1995:2012

NTC EN 1995:2008

DIN 1052:1996 (Berechnungsverfahren Abs. 8.2.3)

DIN 1052:2004 (Berechnungsverfahren Abs. 10.4.)

DIN 1052:2008 (Berechnungsverfahren Abs. 10.4. )



Basis of calculation

All internal forces, superpositions and verifications are calculated with consideration to the special requirements of the selected design standard and its National Annexes.

Verifications are available to check bending load resistance with consideration of cut grains, shear load resistance, stability (against tilting, with different effective lengths for the cold and hot design, if applicable) and serviceability (deflection).

In the area of the ridge and the curvatures, additional verifications to check increased strain on the longitudinal edge, transverse tension and interaction of transverse tension and shear force can be performed.

The design of transverse tensile reinforcements follows the rules of the selected standard. If it does not specify any rules for transverse tensile reinforcements, the calculation is based on the National Annex for Germany, which is considered as a generally acknowledged rule of engineering in this case.

The verifications in the area of the cantilevers are limited to bending and shear stress resistance. We like to point out, however, that due to the complex geometries, which can be defined in the supporting area, stress states similar to that of in the ridge area might occur under particular conditions. The required verifications cannot be handled in this software application.

The beam is divided in subsections according to the changes in its geometry. Internal forces and deformations are determined in a strut and tie calculation.

Axial forces are not taken into account in the verifications.

The design procedures prescribed by the standards provide for applications restrictions concerning the top chord inclination and the cross grain-cutting angle. In general, the calculation methods used here are permissible for more or less symmetric conditions, roof inclination …δ <= 20° and cross grain cutting angle α <= 10°. However, the software application also allows the calculation of geometries not treated in the standards, in order to provide designers with a tool for the evaluation of their construction also when deviating from the standards.

For trusses non-compliant with standard geometries, verifications that are more accurate might be required and axial forces must be taken into account under particular conditions.

A verification of the stability against displacement is not performed.

Verifications for notches and transverse tensile reinforcements in the supporting area are not available.

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FRILO Software GmbH

Input

General notes concerning the input fields

The software application allows the calculation in accordance with various standards and National Annexes. Some of these standards differ considerably in regard to the load application, the combination rules, the determination of the decisive internal forces and the verification process.

Therefore, the input fields and options can differ from those described below depending on the selected standard.

In the Further settings menu, the user can find the option "Always recalculate". Activating this function launches the recalculation of the system, each time a defined value is edited. The user can also do this

manually by activating the Calculate button .

The table below the graphic window displays the utilization of the truss during the different verifications.

Tip: The button [>>] allows the user to display other result views below the graphical window. Information concerning the transport height with or w/o assembled ridge can be found in this section too.

Basic parameters

Selection of the standards and the materials (quality classes). Definition of the service class, consequence class and the specific weight.

Tip: Change the default standard in the Further settings menu.

Basic shape

Selection of the basic truss shape.

Straight TC/BC parallel chord truss or single-pitch roof truss

double tapered beam double-pitch roof truss with straight bottom edge

curved or pitched .. truss with curved bottom edge, with or without fixed saddle and arch beam



System

System lengths First, specify the horizontal dimensions of the truss. The system lengths L1 and L2 refer to the ridge point.

The truss spacing is assumed as affected width.

The spacing of the transverse supports sB indicates the free effective length of the truss for the stability verification. If you specify 0.00 for the spacing, no stability verification is performed.

The user can enter support dimensions independently from the horizontal lengths a1, a2, b1, b2. The verification of the bearing stress depends only on the support dimensions.

Tip: The "Symmetrical" option simplifies the definition of symmetrical systems.

Tip: Set the horizontal sections at the supports to 0.00 to define wedge supports with continuous grains in the supporting area.

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FRILO Software GmbH

Truss geometry In this section, the user can define the cross sections, the truss inclination, the type of saddle, the curvature, if any, and the thickness of the plies and their run.

The editing of a value launches a check and a recalculation of the geometry. The presentation of the system graph is updated, each time the user enters or edits a value.

The ply structure in the truss, which depends on the curvature (allowable ply thickness), is not checked by the software application.

The dimensions and the designations used in the software and the documentation are shown in the illustration below.

Curvature The curvature can be set via the length Lc or

alternatively the curvature radius Ru. Both values refer to the geometry at the bottom chord side. With double-pitch roof trusses, Lc specifies the length of the sway saddle.

The dimension hm indicates the vertical ridge height of double-pitch roof trusses. With general roof trusses, the cross sectional height is specified in direction of the curvature radius. Without saddle or with a sway saddle, it is the supporting cross sectional height.

Saddle The selection list offers the following options: - saddle (non-sway), - saddle (sway) and - no saddle.

With sway saddles, the static effect of the cross section in the area (Lc) above the outer curvature is not considered, whereas self-weight is included in the load assumptions. The geometry of the upper edge is described as a circular arc in parallel to the lower curvature, if one of the options "no saddle" or "sway saddle" was activated. The radius of this arc has the greatest possible distance to the centre of the truss.



Run of the plies The plies of the truss are assumed to run in parallel to the bottom chord as a default. Only if the defined geometry does NOT produce a kink in the truss top edge (arched beam), the option allowing a run of the plies in parallel to the top edge is enabled.

The ply inclination in the cantilevers and the support is assumed identical to that in the span adjacent to the support.

Notched support

This option is available in combination with trusses with straight top and bottom edge. The notch width is assumed in accordance with the specifications for a1, a2, b1 and b2. The reduced cross section is taken into account in the calculations and verifications.

Tips: Use the "Symmetrical" option to define symmetrical systems. It is a useful input aid and has no effects on the calculation.

In order to define an arched beam, select "General beam" and the option "no saddle" and set hm to 0.0. The cross section height is set to the smallest possible size.

Supports In this section, the user can define the lengths and widths of the supports. The support dimensions are limited by the length of the horizontal areas a1, a2, b1, b2 and the truss width.

The [...] buttons provide access to the well-known Frilo k90 dialog. The user can specify the kc,90 values for each support within the range permitted by the standard.

The "Horizontal fixed support" option allows the user to define the fixed support. Alternatively, the simulation of two very soft supports (spring 1 kN/m) is available to simulate a beam on two cantilever columns for instance.

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FRILO Software GmbH

Loads

Standard loads For the calculation of the internal forces, the truss is divided into sections. With conical (haunched) geometries, the cross-sectional differences within a section are automatically taken into account in the assessment of the self-weight. In the output, a mean value is given for the self-weight. This automatic process can be disabled via the option "Without dead load".

The defined area loads ga (permanent loads), q (live loads) and s0 (snow loads) [kN/m²] are multiplied with the truss spacing. Please take account of the reference areas of the loads: Floor area (floor plan projection) and roof area

The snow loads and the live loads are considered as constant loads acting on the entire beam.

If live loads should apply spanwise, the option "Live load spanwise" should be enabled.

Snow and wind loads The user can define the snow load manually via the field "Snow load µ * sk". The value is set to zero, however, if the user specifies a value in the field "Snow load sk". This option is only available to ensure compatibility with former versions and should not be used any longer.

Recommendation: Use the button "Snow and wind" to comfortably define snow and wind loads with the help of zones in the same way as you might know it from other Frilo applications and take these values over to the fields "Snow loads sk" and "Imp. wind pressure". The available options and fields allow you to define snow overhangs and wind directions to be examined. In most cases, two load arrangements are generated for each wind direction because suction and pressure can apply alternatively in some roof areas. The selection field "Area" allows the user to define whether the truss is in the middle of the shop roof or close to the edge. For information, the wall and roof areas where wind from the defined directions applies are specified. The "Building length Ly" (in direction of the drawing plane, perpendicular to the truss axis) determines the lengths of the roof area as well as Lx (in direction of the truss axis). The length Lx is automatically calculated from the span length, the cantilever lengths and the distances to the facades on the left and the right. If the facade is located outside of the cantilevers, the shop is longer than the truss in x-direction. This information provides for the adjustment of the wind uplift areas at the cantilevers and edges and in corners. In addition, wind uplift acting on the cantilever is aligned to the location of the facade. In the calculation, always cp10 is used because the affected areas of typical roof trusses are considerably larger than 10 m².

Wind-induced internal pressure can be included with a positive or negative cpi value.

In order to handle the automatically generated snow and wind loads manually, the user can turn off automatic adjustments via the option "Wind as additional load". Wind load is then accessible via the Additional loads table.



Accidental snow load

In combination with some standards, the user can optionally take snow load as an accidental alternative load case into account. To do this, activate the option "Snow as accidental loads (A)" and enter a factor into the corresponding field. The accidental snow load is combined with all other loads in accordance with the combination rules except with normal snow loads. Tick the option "Only in combination with permanent loads" to make sure that the accidental snow load is only superimposed with the permanent loads.

Proposal for the use in the Northern Lowlands

In this case, snow must be taken into account as an accidental alternative load case. Under normal conditions, factor 2.3 should be used.

In particular cases, local construction authorities might impose other values.

You can also activate the option "Only in combination with permanent loads".

Interpretation of DIN 1055-5, consecutive number 30 of the German Building and Civil Engineering Standards Committee (NABau): "As an accidental load in the sense of DIN 1055-100, snow must only be combined with dead load." "Include additional loads" option

Activating this option includes all additional loads in the accidental snow load combination that are member of the same action group than the snow load in the Loading menu and the alternative group of which is equal to zero. Note: The activation of the option "Include additional loads" is imperative for the internal

handling of the loading with the new snow loads generated automatically.

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FRILO Software GmbH

Additional loads You can define additional loads via the corresponding menu item. Available are uniformly distributed loads, concentrated loads and trapezoidal loads. The loads are not distributed according to spans.

Load type Selection of the load type (uniformly distributed, concentrated or trapezoidal load) via the expandable list or the specification of the load number.

Depending on the load type, the cursor jumps to the relevant input columns.

Dist. VK distance to the beam front edge in [m]

Gle/Qle left load ordinate for permanent loads/variable loads

Gri/Qri right load ordinate for permanent loads/variable loads

Distance distance to the previously defined point VK from the front edge of the truss to be measured from the left (with concentrated and trapezoidal loads) in [m]

Load length projected length of a trapezoidal load in [m]

Factor multiplication factor of the load ordinates

Groups of actions Allows you to assign the variable load portion to an action group. For each load, an

individual load case is generated and combined with the other load cases. Simultaneous group Loads assigned to the same simultaneous group always apply simultaneously (value > 0).

Example: Appended load, fixed at two points. Alternative group Loads of the same alternative group exclude each other and do not apply in the same

combination. Example: Wind loads from different directions.

Loads of the same simultaneous group and the same alternative group apply simultaneously AND alternatively to loads of the same alternative group and different simultaneous groups.

Particularities in connection with concentrated loads

Concentrated loads in the proximity of supports are reduced in the shear resistance verification in accordance with the selected standard. The user can disable this reduction by activating the option "Concentrated loads w/o reduction" in the Design options menu. Please observe the explanations concerning the selected standard and its National Annexes and the information in the chapter Design when activating this option.

In the calculation, all loads apply at the member axis. Loading due to load transfer (e.g. transverse tension) is not included in the verifications.



Design

Design options Please observe also the information in the chapter Design and calculation!

Shear design

Where beams with supports at the lower edge and load action on the upper edge are concerned, the user may define the decisive shear force for the shear design at a distance a from the support depending on the selected standard. h in this connection is the height above the centre of the support.

Note: The shear design at the distance "a" produces the

effect that a concentrated load applying at a distance to the support edge smaller than "a" is not taken into account in the shear design.

If a reduction with a favourable effect is not justified, the user can disable the reduction by activating the option "Shear design in axis of support". For arithmetical reasons, the shear force is assessed immediately next to the axis of support.

Shear without reduced cross section

The loss in the cross section due to the drill holes for the reinforcements is not considered in the shear resistance verification. This option is useful if the shear force application area extends up to the support, but no reinforcement should be installed in the supporting area.

Ridge shear without reduced cross section

The loss in the cross section due to the drill holes for the reinforcements is not considered in the shear portion of the transverse tension analysis at the ridge (interaction between traverse tension and shear). Both options should be used with utmost care and only in special cases.

Reduction of concentrated loads in the proximity of the support

See Additional loads.

Lateral truss load with kmin, Nmax

The option "Max. lateral truss load with kmin, Nmax" enables an improved method, which calculates the lateral truss load in two ways: smallest tilting coefficient and largest compressive force.

Support torsion The unwanted torsion in the supporting area ("Md/80" torsion) can optionally be taken into account. The user can preset the size of the beam deformation for the calculation of the torsion.

e/h is the height level of the bracing in relation to the beam axis:

e/h = +- 0.0: the bracing is at the height of the beam axis and has no effect

e/h = + 0.5: the bracing at the height of the truss top edge

e/h = - 0.5: the bracing is at the height of the truss bottom edge (not very useful because lateral loads are calculated with a positive midspan moment for the stabilization of the upper chord).

The settings also apply to cantilevers. The calculated torsion loading is considered in the shear resistance verification on the support.

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FRILO Software GmbH

Limitation of the deflection The deflection limits are freely selectable. We recommend observing the values given by the standards unless other values are justified. The deflections are calculated with shear deformations by default. If shear deformations should not be included, the user must tick the option Without shear deformation. The available input fields vary according to the selected standard.

Time-dependent deformations

The creep portions of the deformations are calculated automatically. The combination coefficient ψ2 and the deformation coefficient kdef are taken into account.

Transverse tensile reinforcements and ridge verification If transverse tensile reinforcements should be required by the selected standard, the user can design the reinforcements with glued-in threaded rods or fully threaded screws.

The transverse tensile force (and/or the reinforcement ratio) "As per standard" can be increased with the help of the options "At least constructive reinforcement" and "Always full reinforcement".

Note: Even if a verification of the transverse tension resistance is sufficient, the NA Germany recommends the installation of transverse tensile reinforcement. To comply with the recommendation, activate the option "At least constructive reinforcement".

You can optionally preset the number of parallel rows, the type of threaded rods with their strength class and define whether the reinforcement should have a staggered arrangement in longitudinal direction from the second row on. The weakening of the cross section in the area of the transverse tension and/or the ridge is automatically taken into account in the stress resistance verifications. The result reveals the minimum and maximum length spacing permissible for the construction and the spacing required by the calculation. If the minimum spacing in transverse direction is not observed, a corresponding message is included in the output.

Particularities in connection with transverse tensile reinforcement The method prescribed by the selected standard is used. If a standard or NA does not describe any method that of the NA Germany is used.

The corresponding specifications can be made in the menu Transverse tensile reinforcement/fully threaded screws.



Particularities in connection with fully threaded screws

After specification of the outer diameter (root diameter) d of the thread, the inner diameter d1 (body diameter or core diameter for the calculation of the stress cross section) is automatically assessed in accordance with DIN 7998. The width difference df corresponds to the reduction of the cross section used in the bending design in the ridge area.

The total load factor F (for non-uniform force transfer on the thread) should be similar to that for glued-in threaded rods (DIN 1052:2008(2004) Eq.186 + NA-Ger Eq. NA.89 F = 2.00 = default). The value may only be reduced for justified reasons and in exceptional cases (CE, BaZ, EN5-NA, NABAU, …) Recommendation: F = 2.

Particularities of EN 1995-1-1

Resistance of steel: The default value is fyk=300 N/mm². The user can specify other values or make a specification for Ftens,k . The software application synchronizes both values automatically.

Resistance of the thread: The user can set the pullout parameter fax,k and the associated characteristic bulk density ρa (of the test specimen used to determine fax,k) as per EN 14592 manually. If fax,k is set to zero, the value is calculated in accordance with EN 1995-1-1:2008 eq. 8.39. If ρa is set to 0, ρa = ρ k (truss) in the calculation, the factor used in eq. 8.40a (ρk/ρa) is equal to 1 in this case.

When calculating fully threaded screws (timber screws) in accordance with the National Annexes, the user can select the method for the assessment of the pullout resistance of the thread. The method has no effect on the steel resistance, but refers exclusively to the thread in the timber.

EN1995 standard (faxk): corresponds to the method prescribed by the Eurocode.

NA Germany: NCI NA.6.8.5(fk1k): corresponds to the method prescribed by the NA Germany. The input value faxk is ignored. This method is only allowed for screws with threads as per DIN 7998 and the software uses this method only for these screws. The software application identifies the screws by the ratio of the root diameter to the core diameter.

Note: The bearing capacity of the thread in the timber as per Eurocode (faxk-method) corresponds to the bearing capacity class 1 (TFK 1) in accordance with DIN 1052:2008. In accordance with DIN 1052:2008 the user may assign the bearing capacity class 2 (TFK 2) to threads as per DIN 7998. The fk1k method in accordance with the NA Germany produces higher bearing capacities that comply more or less with capacity class TFK 2 as per DIN 1052:2008. Consequently, the threads are limited to those stipulated by DIN 7998, for which a CE approval is not explicitly required in the NA Germany.

Suitable threaded rods as per DIN 7998 are Spax ABC threaded rods and SFS Intec Wb, for instance.

As these products are not only used in Germany, D10 offers the fk1k method also in combination with other NAs.

Before using this method in another country, the user should contact the reviewing engineer or the construction supervision authorities.

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FRILO Software GmbH

Drawing view/relocation of reinforcements If transverse tensile reinforcements are required and the user has selected a transverse tensile reinforcement and a permissible reinforcement measure was calculated (cal a > min a), this function allows the automatic relocation of the reinforcements (glued-in metric threaded rods and screwed-in threaded rods with timber thread). The construction drawing shows all details required for the manufacturing of these rods.

How to begin: First, activate the "construction drawing" button on the tool bar (below the menu bar). After this, activate the option Location of tensile reinforcements (FDC - Frilo.Data.Control) in the menu Design Transverse tensile reinforcement in the input window. Click to the Calculate button to display the dimensioned drawing. Various options are available to control the relocation.

Workflow

The outer and inner quarters of the traverse tension area are calculated from the geometry comprising the ridge, the secondary ridges (with high dry joint) and curvature areas. From the statically required distances, the location of the transverse tensile reinforcement is calculated with consideration to the constructive minimum and maximum distances, the number of rows and the arrangement in longitudinal direction (parallel or staggered)

After this, the location of the drill holes is determined and the dimensions are specified along the top and bottom edge of the beam. This facilitates measuring and drilling in the factory.

Dimensions suitable for the practical execution are obtained by activating the option "Round off spacing". The user can also overwrite the automatically calculated distances at the lower edge of the truss via the options "Distance inner quarters" and "Distance outer quarters". The value "0.0" (default) activates the automatic calculation.

The rounding off functions for the distances work well in standard areas. At transitions from straight edges to arcs or with exotic truss geometries, however, an optimized rounding off is not possible.

For reasons of fire protection, the length of the threaded rods is reduced by the thickness of a ply in comparison to the drill holes on each end. Therefore, the option "Deduction factor plies tplies" is available to shorten the threaded rods accordingly. A corresponding option is also available for the rounding off of the lengths.

Subsequently, the threaded rods are combined to items of the same length. Piece numbers, item numbers and dimensions are displayed in the drawing.

Finally, the list of joints and fastenings is generated and assigned to the corresponding items.

The option "Put out BOM" adds the bill of materials (similar to the steel list of a reinforcement drawing) to the output data.

Tip: In order to produce a CAD drawing from the construction drawing, activate the "construction drawing" button in the toolbar and select the menu item File >> Export >> DXF. When importing the DXF file into your CAD application, be aware that the units in your DXF file are cm and adjust the scaling factor adequately.



Fire protection Note: Fire protection is not supported in the old standard DIN 1052/A1.

In the menu Design Fire protection, the user can specify the required fire resistance period (tF) in minutes and select the exposed sides of the truss.

Based on this specifications, the software application selects the burning rates, which depend on the material and the selected standard.

Always verify shear resistance

The verification of the shear resistance under fire exposure is not required by all standards. There is no verification defined in EN 1995, for instance. If timber trusses are used, which often have the smallest cross sections in the areas with the highest shear loading, a verification should always be performed.

The option "Always verify shear resistance" ensures the required verifications also in combinations with standards and NAs that do not explicitly require this analysis. The verification is based on DIN 4102-4:1994 and DIN 4102-22:2004 in this case. According to these standards, the shear utilization under fire exposure is derived from the shear utilization at normal temperatures. It results from the expression:

NT NT NT mod,NTfi

f i f i f i

b h k0.5

b h kh ◊ ◊ ◊

h = ◊◊ ◊

Reference literature: Holz-Brandschutz-Handbuch, Ernst & Sohn publishing house

Always simplified

Most standards allow principally a more accurate and a simplified method. For some verifications, a particular method is stipulated.

Therefore, the application switches automatically to the suitable method in accordance with the selected standard, NA and the loading. The additional burning rates associated to each verification are automatically taken into account.

The "Always simplified" option makes sure that the simplified method is used in all verifications even if it is not allowed by the selected standard. In most cases, the simplified method in on the safe side.

The applied method and the residual cross sections are specified in the output.

Tilting

In the hot design, the same effective lengths are used as in the design at normal temperatures.

Other effective length for the hot design

Under particular conditions, stiffening components (such as bracing, panels, ...) have a lower fire resistance period than the truss. In this case, the user can specify another effective length for the hot design via this option

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FRILO Software GmbH

Design and calculation

From the defined geometry, a strut-and-tie model with variable cross sections is generated.

Internal design forces The decisive (maximum) internal forces for the design are assessed with consideration to the selected standard, the superposition and design options and with the help of kmod and M.

Note: For the design, the internal forces with the highest utilization are used. They may be smaller than the maximum internal forces.

Tips: Click to the "Calculate" button to display the individual utilizations at the bottom of the window. Via the button , the full output text is displayed on the screen for review.

Stress verifications All stress verifications are performed with the help of the previously determined internal design forces and in accordance with the selected standard. The cross section height of the supporting cross section is determined perpendicular to the member axis. In general, the verification points are at the locations where the greatest internal forces apply and the highest utilization is attained.

Resistance to bearing stress

The verifications for the left and right support are performed separately. The suspension effect in grain direction and the load distribution are taken into account.

Bending tension stress

The stresses are calculated with consideration to cut grains and non-linear distribution, if applicable. This also applies to the areas of the supports. With larger cantilever loading and redirection of forces in the border zone of the horizontal supporting areas as well as with notched supports, the utilization should be considerably smaller than one. In particular cases, additional verifications might be required.

Shear stresses

Shear stress is calculated on the cross section perpendicular to the member axis.

If the option "shear design in support axis" was not activated, the shear design in the area of the support is performed as follows: see the following page.



First, the decisive distance a for the shear design is calculated in accordance with the selected standard. In this calculation, a must not be greater than the distance of the intersecting point of a virtual line running at an angle of 45° from the upper edge of the support to the upper beam edge (red line). For beams with notched supports (birdsmouth joints), a is set to zero and the design is performed at the notch.

The concentrated load F1 outside of the supporting area is calculated either with or without deduction. If the user has ticked the corresponding option, the permissible factor specified by the selected standard is taken into account. In accordance with DIN 1053:2004 and 2008, deductions of concentrated loads are not allowed in combination with beam inclinations (δ) or cut grain angles (α) larger than 10°.

The calculation of the decisive shear force at the distance a produces the effect that a concentrated load (F2) applying at a distance to the support edge that is smaller than a is not taken into account in the shear design.

The design at a distance a in combination with uniformly distributed loads is due to the fact that shear force increases the shear resistance if loads apply on top of the supporting area. This conception is also the basis for the reduction of concentrated loads in the proximity of the support.

DIN 1052:2004 and 2008 limit the design at the distance a not to uniformly distributed loads. According to these standards, concentrated loads with a distance to the support smaller than a need not be taken into account. This is also proposed by EN 1995-1-1 (German version EN 1995-1-1:2004+A1+2008). However, some authors have a different opinion.

Finally, the smallest value among the cross-sectional heights h1, h2 and h3 is taken as the decisive shear cross-section height h in the supporting area to be verified. It is used to determine the length of the reduction area L = x h, which is the basis for the reduction of the loads in accordance with the selected standard. Fred = F / ( x h ).

The reduction of the cross section because of transverse tensile reinforcements in the supporting area (e. g. arched beams) is also taken into account in the shear design. In the verification of the torsional resistance and/or the resistance to torsion and shear, the cross section reduction is not considered for the torsional portion.

Torsion in the area of the support

Torsion in the area of the support, which is caused by truss imperfections (initial bow imperfection) and the deformation of the bracing under load, is derived from the conditions of the single-span beam under uniformly distributed load according to the expert literature.

Mtor,d = (p L/2) (2/3 fF)

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FRILO Software GmbH

The effect of the bracing is not considered in the design of the fork supports. In the shear design at the support, the bracing effect may be taken into account:

Mtor,d = (p L/2) (2/3 fF) – qd L/2 e

With:

P = uniformly distributed load

L = supporting width

fF = size of the horizontal deformation

= ( L/400 (imperfection) + L/500 (bracing deflection)

= 9/2000 L = 1/222 L)

qd = lateral truss load (stabilizing load) on the bracing, calculated with the help of Myd and the tilting coefficient (kmy,Kcrit) of the unstiffened beam (without bracing).

2/3 specifies the fullness of the deformation pattern, which corresponds to a parabola.

Setting in the values in the formula gives: MT = Myd/83.33. It is published in several standards in a well-known version MT = Myd/80. This expressions can also be used for approximation with loads that are not distributed uniformly.

With great and concentrated loads in the span centre (or at the cantilever tip), the approach based on the fullness of the parabola involves the underestimation of the torsional loading. In this case, the eccentricity fF should be increased adequately.

The D10 and H04 applications use this basic concept to calculate torsion also on trusses with cantilevers. When selecting the option "Parabola shape" the user can set the factor (83.33/80).

Span: Mtor,d = (p L/2) (2/3 fF) (83.33/80) - qd L/2 e

Cantilever: Mtor,d = (p Lk) (1/3 fk) (83.33/80) + qd Lk e

With fk = 2 Lk/222

The following sketch illustrates the Frilo approach.

Line 1: ideally straight member axes

Line 2, 2a: horizontal deformation by torsion in the cross section

Line 2a, 2b : variants of deformation by the maximum fork support moments



Note: According to DIN 1052:2008 8.4.3(2), torsion is to be considered for the fork supports and the shear resistance verification. EN 1995-1-1:2008 and NA Austria do not include any regulation on this matter, NA Germany of 2010 does, however.

Stress resistance verification in the area of the ridge and the curvature

The verifications of longitudinal tensile stress, transverse tensile stress and combined shear and transverse tensile stress are performed in addition to the other verifications at the ridge point and other points, if required. In these verifications, the considered beam height and decisive design moment are always assessed at the verification point.

D10

FRILO Software GmbH

Transverse tensile reinforcements

The input value for the verification of the transverse tensile reinforcements is the greatest transverse tensile loading found.

Lateral truss load (stabilizing load)

The lateral load for the calculation of the bracing is determined as follows:

To be able to calculate the lateral truss load, the tilting coefficient ( (kmy, kcrit) must be calculated on the unstiffened beam without bracing. For members and/or tilting fields with linearly variable cross section heights, the following applies: The verification may be based on the cross-sectional properties at the distance of the 0.65-fold member length from the member end with the smaller member cross section and the maximum value of the bending moment in the member. The software application first searches the cross section with the greatest cross section height in the central third of the supporting width for the determination of the tilting coefficient. The representative force acting on the chord is calculated with the help of max. Md. If applicable, a smaller cross section at max. Md is taken into account. Because max. Md occurs at the greatest cross section height on symmetrical saddle roof trusses, the representative chord force and the lateral load might be underestimated where slender saddle roof beams are concerned. Therefore, an additional method is available. Lateral truss load with kmin, Nmax

There are two methods to calculate the lateral truss load (min kmy(kcrit) and max Nd) with the help of max. Md. The representative range from 0.35L to 0.65L is evaluated and the point, where max Md applies, is additionally included for saddle roof trusses:

1. Unfavourable tilting coefficient (kmy, kcrit) at the greatest cross section height h = max ( h at 0,35L ; h at 0,65L ; h at ridge; h at max Md)

2. Highest compressive force Nd. Between 0.35L and 0.65L, the cross section height for the representative compressive force is determined as follows: h = min( (h0.35 + h0.65)/2 ; h at ridge; h at max Md)

Stability (tilting) The tilting stability of the truss is verified with the help of the preset max. distance sB of the top chord supports and the decisive design moment in each examined section. In each section, the defined distance of the transverse supports is assumed as the free effective length.



Recommendations concerning transverse tension The cause of many cases of damage in connection with laminated timber trusses is an insufficient transverse tensile strength. Therefore, a constructive reinforcement with threaded rods in the areas affected by transverse tension has become state of the art. Transverse tension occurs when the stress flow changes: at kinks, offsets or curvatures and also because of climatic loading (changing moisture content).

The verification of the transverse tensile strength in the ridge area is based on the methods prescribed by the standards.

These methods apply only to the following truss types and only if the system is more or less symmetrical:

- curved truss with constant height,

- curved saddle-roof truss,

- saddle-roof truss with straight bottom chord

Additional border conditions are as follows:

- inclined top and bottom edges δ <= 20°

- cross grain cutting angle α <= 10°

The exact limits of the individual parameters are specified in the standard or its National Annex.

For trusses with non-standard geometries, the transverse tension resistance is verified as follows:

If two secondary ridges instead of a single ridge result for a saddle-roof truss without fixed ridge and the distance of the secondary ridges to each other is smaller than the beam height, which produces overlapping of the transverse tension areas, the verification is performed at the equivalent ridge point between the two secondary ridges. The angles of the truss top edges outside of the ridge area are used.

If two secondary ridges instead of a single ridge result for a saddle-roof truss without fixed ridge and the distance of the secondary ridges to each other is larger than the beam height, which omits overlapping of the transverse tension areas, the verification is performed at the secondary ridges. The real differential angles at the top edge are used.

Where beams with asymmetrical ridge geometries are concerned that do not satisfy the above-mentioned conditions, the user should dispense with the transverse tensile reduction in the outer quarters of the transverse tension area via the value 2/3 in the design of the traverse tensile reinforcements.

We recommend assuming the transverse tension area of asymmetrical ridge geometries as shown in the illustration below. The following conditions apply:

a1 >= h/2

a3 >= h/2

a1 + a2 + a3 >= a4

a4 = arch length

D10

FRILO Software GmbH

Output Output of the system data, results and graphics on the screen or the printer. The output menu item in the main tree provides access to the following options:

Output control via the toolbar

The user can control the scope of the output via the options in the Text output and Graphical output menus

Word If installed on your computer, the text editor MS Word is launched and the output data are transferred. You can edit the data in Word as required.

Screen displays the values in a text window on the screen

PageView displays a preview of the printed page

Print starts the output on the printer

Output scope

The output always starts with the system and the loads. The results that the user has selected via the output options in the toolbar are added.

Application-specific icons

1 2 3 4 5 6 7 8 9 10 11

1. System graph

2. Moments limiting line M or Md (maximum values)

3. Shear force limiting line Q or Vd (maximum values)

4. Limiting line of the elastic deformations

5. Longitudinal stresses or d

decisive for the design (the design-relevant values at maximum utilization!)

6. Shear stresses or d decisive for the design (the design-relevant values decisive at maximum utilization!)

7. Maximum utilization related to the longitudinal stresses

8. Maximum utilization related to the shear stresses

9. Displays the supporting points used for the calculation of the truss geometry.

10. Displays the run of the member axes and the nodes of the generated strut-and-tie model

11. Displays the structural system as a construction drawing

Important note: If there are nonsensical offsets in the lines of the graphs 6 to 8, which result neither from the truss geometry nor the load pattern, the problem could be solved by changing kmod and/or M in the design. In the area of the ridge, these offsets could be due to increased longitudinal edge stresses in the ridge area exceeding the bending tension stresses. Please find some examples in the following.