Action Combination Processing to the Eurocodes - Basis of Software

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					Action Combination Processing to the Eurocodes


- Basis of Software to Assist the Engineer


           Yannig Robert, Arnold V Page, Rémi Thépaut, Christopher J Mettem.
                                 TRADA Technology, UK




1 Introduction
The aim of this research is to provide for the designer a practical and transparent software
solution for use with the structural Eurocode suite [1] [2] [3] [4] [5] [6]. This provides
choice between speed of design and optimisation. It is also intended to leave the option to
proceed to an accurate design with the result obtained from an anterior rapid design
without reprocessing all the actions.
Eurocode 0 indicates that the actual effects of actions need to be combined together, rather
than the values of the actions themselves as normal with permissible stress codes. This
approach provides more accurate results but can be time consuming since the number of
combinations to be performed increases quickly with the number of actions applied to the
structure. Nevertheless, when a linear elastic analysis is carried out, as it is often the case
in timber structural design, the scope of necessary checks can be reduced. Action
combinations may be pre-processed to limit or even sometimes remove the need to
combine effects of actions at a later stage. Also, the kmod factor can be introduced early to
reduce the number of cases to be investigated, by identifying the critical load duration
cases.
Because of timber’s moisture and time-dependent properties, conforming to the Eurocodes
can become more complex and error prone especially for timber designers who lack a
knowledge of limit states design, or for others whose knowledge of timber design is
limited.
It should be noted that the basis of the logic is founded in EN 1990. Hence, the action
combination processing method applies for steel or concrete structures as well as those in
timber. With experience, mixed material structures (timber with steel, for example), or
timber-concrete, timber steel composites are feasible.
The theoretical basis of the software will be discussed in this paper.




                                              1
2 Design methodology
The software under development is intended to permit the designer to check a structure
using the following sequence:


2.1 Preliminary tasks
       -   Quantify the actions on the structure: pattern; characteristic value(s); associated
           load duration.
       -   Group all of the actions with the same patterns together. Two actions are
           considered as having the same patterns as one another when they are applied at
           the same position, with the same distribution and in the same orientation.
           However, they can have different load durations, be of a different nature, and
           have favourable or unfavourable effects without being regarded as a separate
           group.
       -   Use the action pre-processor to pre-process each group into an equivalent action
           of the same pattern as the initial action with a design value for each duration, a
           reduced design value for each duration, a critical load duration case and, for
           each duration, an indication of the leading variable action of the group




           Group 1                                                        Group 2




                  Figure 1 Example of a pre-processing logic with actions F1,
                  F2 having one pattern and F3, F4, F5 another pattern
After this preliminary stage, the designer has the choice between a rapid but conservative
method and a precise method.


2.2 Rapid method
The rapid method is illustrated in Figure 2. Below are the steps which the designer needs to
take:
       -   For each load duration which proves to be critical for at least one group of
           actions, calculate the effects of the corresponding ULS design values of all the
           actions groups.


                                              2
       -     For each SLS combination which has to be
             checked, calculate the effects using the SLS
             design values of all the actions groups.
       -     Check ULS and SLS to the relevant material
             code.




                                                   Figure 2 Rapid processing of above example
2.3 Precise method
The precise method is illustrated in Figure 3. The designer takes the following steps:
       -     For each load duration which proves to be critical for at least one group of
             actions, take each group in turn and combine the ULS design values of its
             equivalent action with the reduced design values of the other groups for that
             load duration.
       -     For each SLS combination which has to be checked, take each group in turn
             and combine the design values of its equivalent action with the reduced design
             values of the other groups.
       -     Check that ULS and SLS limits are not exceeded, by applying the relevant
             materials code.




 Group 1                                                                     Group 2
dominates.                                                                  dominates.




Figure 3 Accurate processing of Figure 1 example for one load duration or SLS combination




                                             3
3 Basis of the action pre-processor

3.1 Restrictions and hypothesis
In order to make possible the design of the action pre-processor, the following assumptions
were made:
         -     The structure is designed and checked using EN 1990, EN 1991, and the
               appropriate material codes.
         -     The structural model used to calculate the action effects assumes a linear
               deformational behaviour of the structure.


3.2 Design value and reduced values of a group of actions
The design value of a group for a particular combination is defined as the combination of
the characteristic values of the actions part of this group in accordance with the relevant
EN 1990:2002 equation.
Pre-processing actions into design values directly before performing a structural analysis
leads to inaccurate results. As they are combined in separate groups, each design value has
a leading variable action embedded in it. Thus if there is more than one group, some
actions that are not actually “leading” are considered to be so. This normally results in a
conservative design, since the representative value of a variable action (ψ F) is always
numerically larger when the action is assumed to be leading. Thus, the “rapid method” can
be safely used when speed of design is of importance.
To overcome this conservatism, a new value, the “reduced value”, has been introduced into
the logic. This is obtained using the combination of EN 1990:2002 appropriate to the limit
state under consideration, but assuming that no particular variable action is leading. For
instance, in the case of four actions Gk, Qk,1, Qk,2, Qk,3 having the same geometrical pattern
as one another, the design and reduced values of the actions group for the ultimate limit
states fundamental combination are respectively:
Fdesign = γ G Gk ,1 + γ Q (Qk ,1 + ψ 0, 2 Qk , 2 +ψ 0,3 Qk ,3 )

Freduced = γ G Gk ,1 + γ Q ( 0,1Qk ,1 +ψ 0, 2 Qk , 2 +ψ 0,3 Qk ,3 )
                           ψ
Thus when the “design value” of a group is combined with the “reduced value” of other
groups, a result fully in accordance with EN 1990:2002 is obtained. Nevertheless, in non
trivial cases, the group of actions containing the leading variable action cannot be
determined immediately, particularly bearing in mind for timber the additional
complication of the kmod effect. Hence, it is necessary to assess in turn each of the groups
as potentially leading.
Hence Ed, the design value of the effects of three actions groups for a specific design check
can be obtained:
              E {Fdesign ,1 ; Freduced , 2 ; Freduced ,3 }
E d = Max E {Freduced ,1 ; Fdesign , 2 ; Freduced ,3 }
              E {Freduced ,1 ; Freduced , 2 ; Fdesign ,3 }


                                                             4
Where E{Actions groups} = The effect due to the actions groups calculated with an
appropriate structural model.
And Max (value1, value 2,…) defined as the value having the maximum absolute value.


3.3 Leading variable action
Within a group of actions and for each combination and load duration case, the action
generating the greatest design value is the leading variable action. Thus, the software tests
in turn each of the variable actions as leading.


3.4 Determination of the limiting load duration case
In the case of an ultimate limit states check, the time dependent properties of timber’s
strength implies that separate checks are necessary for each load duration case.
                                                        Rk
Indeed, in prEN 1995-1-1:2003 we have: Rd = k mod ⋅
                                                        γM
                         ue
         Rd the design val of a load carrying capacity
                       on
         k mod modificati factor for duration of load and moisture content
Where
         γ M partial factor for material properties
                         stic load carrying capacity
         Rk the characteri
Because, kmod is load duration and moisture content dependent, Rd, the design resistance,
alters for each load duration case. Consequently, checks need to be made for each case in
turn. Nevertheless, governing cases can more rapidly be anticipated by integrating the kmod
factor early in the process.
According to EN 1990:2002 and prEN 1995-1-1, the following condition should be met:
                Rk
E d ≤ k mod ⋅                    Where Ed is the design value of the relevant actions effect
                γM

      Ed  Rk        
Or        ≤         
     k mod  γ M
           
                     
                     
Rk and γM depend only upon the material, and in some cases the geometry of the structure,
hence this particular ratio is not time dependent. Thus, for each load duration case in turn,
the ratios of Ed and kmod may be compared, with the highest result indicating the limiting
case. Thus the action pre-processor logic uses this observation to predict the limiting load
duration case for each group of actions.




                                                 5
4 Comparison of the three methods
The following compares three methods: Conventional post-processing, the rapid method
using the software logic, and the precise method using the software logic.


4.1 Test case
To assess the various potential solutions to verify a structure, consider an imaginary
structure, which is submitted to a variable number of actions. These actions can be grouped
by patterns in n groups, each containing m variable actions and one permanent action.
Below is an example for three groups of actions each containing three variable actions.




Figure 4 Test case comprising three groups of actions
The effect of an action Qi,j is written qi,j. (Each action has various effects in different
regions of the structure, but for simplicity, qi,j is the effect relevant to the context).
It is also assumed that k ultimate limit states checks are required. When comparing the
methods below, the fundamental combination is considered in just one load duration case.
Nevertheless in the case of a real life design, all appropriate load duration cases would
need to be assessed. Also serviceability limit states checks would probably be required. It
is emphasised that the logic explained, and the software outlined, is to assist rather than
replace, the experience and judgement of the engineer.


4.2 Assessment of post-processing without the logic
The post-processing of actions entails calculating the effect of each action in turn and then
processing characteristic values of effects into design values. This method leads to the
optimum result. However the number of structural appraisals required is equal to the
number of actions; furthermore in permutation. Each time the designer deems a check to be
necessary, he or she needs to combine the characteristic effects of the actions together in
all their permutation and then check the structure to the relevant code. For all but the most
trivial structures and loading schemes this is a formidable task.




                                             6
4.3 Assessment of the rapid method using the software logic
With the exception of the early pre-processing, the rapid method is similar to the design
procedure which would be used while checking a structure with a permissible stress code.
Thus, it can be expected to be quite practical. Nevertheless, the method generates
somewhat conservative results.
Considering the test case, it can been shown that for an ultimate limit states check with the
fundamental combination:


                                                                      Frapid = value obtained with this method
                                                                      Fd = value obtained by post - processing
Frapid                 n
         ≤                                                 Where n = number of action groups as in 4.1
 Fd        n − χ × (1 − ψ 0 ) × (n − 1)
                                                                      χ=
                                                                                   ∑q      i, j

                                                                           ∑q      i, j   + ∑ gi
                                                                      ψ 0 as defined in EN1990 : 2002
These values are plotted in Figure 5 with a ψ0 assumed to be 0.7. This shows that the
simplified but rapid method is more conservative for very light structures, and for
structures which are submitted to many different actions with varying patterns. In the case
of timber structures, χ is typically between 0.5 and 0.8, so that values obtained with the
simplified method are likely to be at the most 30% conservative.


           1.4
  Frapid 1.35
    Fd     1.3                                                                                     1.35-1.4
          1.25                                                                                     1.3-1.35
           1.2                                                                                     1.25-1.3
                                                                                                   1.2-1.25
          1.15
                                                                                                   1.15-1.2
            1.1
                                                                                                   1.1-1.15
           1.05                                                                                    1.05-1.1
                 1                                                                                 1-1.05
                                                                                    6
                     0.1
                           0.2




                                                                                     n
                                 0.3
                                       0.4
                                             0.5
                                                   0.6




                                                                               1
                                                         0.7

                                                               0.8

                                                                     0.9




                                 χ
                                                                           1




Figure 5 Rapid method compared with precise values
Since it is a time-efficient solution, designers are likely to regard it as of value, especially
at the preliminary design stage. Particularly with bespoke or architect designed structures,
many trade-offs and radical alterations occur before the final proposed solution is
presented to the client and approving authorities. The entire structural form, element types
and connection arrangements may be subject to alterations, and the engineer is expected
swiftly to be able to indicate the likely implications. [7]



                                                                      7
4.4 Assessment of the precise method using the software logic
As is to be expected, the precise method leads to the exact result, but involves evaluating
more combinations. Each group of actions needs to be assessed as potentially leading in
turn, so that as many structural analyses are required as there are groups of actions.
Second order linear-elastic analysis is defined as “an elastic structural analysis using linear
stress/strain laws applied to the geometry of the deformed structure” [1]. In the case of
timber construction such analysis may be necessary to analyse slender spatial structures
such as gridshells. These types of structures bring into being the aesthetic exhilaration,
architectural quality, and potentially the sustainability benefit of timber [8].
Generally frame or space analysis programs which perform second order linear analysis
adopt a two step procedure. Firstly, the deformation of the structure is calculated, then
stresses are re-computed integrating the estimated deformations. It is also verified at this
stage that the structure is neither locally nor globally unstable. The action pre-processor
logic is thus an efficient approach to performing more precise second order linear analyses,
using commercially available, general-purpose structural software.


4.5 Comparison of methods
Table 1 below summarises and evaluates the number of tasks necessary to obtain design
values to verify to ULS a case such as that described above, using each of different
methods. It is clear that post-processing leads to the greatest number. Unless these are
entirely performed by purpose-written and independently checked and assured software,
such checking may be prohibitively elaborate.
           Stage                   Post-processing       Rapid method       Precise method
Pre-processing                           No                  Yes                 Yes
Structural analysis                   n(m+1)                  1                    n
                                   Process design
                                    values from                            Select the more
Post-processing                                              No
                                   characteristics                       severe result k times
                                   values k times.

Table 1 Summary and evaluation of tasks which each method entails.1
The comparison outlined in table 1 considers a single load duration. With more than one
load duration involved, pre-processing is likely to provide an even greater advantage.




1
    n = number of actions groups
    m= number of variable actions per group
    k= number of ULS checks which are required


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5 Conclusion
This research indicates that the pre-processing of actions is an efficient way of designing
with the structural Eurocodes. The logical approach provides the engineer with a choice
between precision and speed of design. It enables the upgrade of a rapid design into a
precise one, at “project stage 2”.
The logic and ensuing software under development requires testing with real life designs.
Timber construction has many forms, ranging from the single family timber dwelling to
long span structures such as sports halls and bridges. Thus different engineers designing
various structures are likely to come up with several solutions to prove the safety and
serviceability of these structures.
The authors would welcome comments on the paper and offer to test the prototype
software. Please address any responses to Yannig Robert from whom copies of the
software can be obtained.


6 Acknowledgement
The authors gratefully acknowledge the advice and assistance given by Buro Happold
Engineers especially by Jamie Siggers and Jonathan Roynon, Glued Laminated Timber
Association (UK), Gifford Consulting Engineers, Institution of Civil Engineers, Local
Authority Building Control (LANTAC), NHBC Engineers, and the Steel Construction
Institute.


7 References
[1] CEN, EN 1990:2002 Eurocode – Basis of structural design, 2002, Brussels, CEN
[2] CEN, EN 1991-1.1:2002 Eurocode 1: Actions on structures. General actions –
Densities, self-weight, imposed loads for buildings, 2002, Brussels, CEN
[3] CEN, EN 1991-1.3:2003 Eurocode 1: Actions on structures. General actions – Snow
loads, 2003, Brussels, CEN
[4] CEN, DD ENV 1991-2.4:1997 Eurocode 1: Basis of design and actions on structures.
Actions on structure - Wind actions, 1997, Brussels, CEN
[5] CEN, DD ENV 1991-2.6:2000 Eurocode 1: Basis of design and actions on structures.
Actions on structure – Actions during execution, 2000, Brussels, CEN
[6] CEN, prEN 1995-1-1:2003 Eurocode 5 – Design of timber structures Part 1-1:
General - common rules and rules for buildings, 2003, Brussels, CEN
[7] Natterer J and Sandoz J.L.”Conceptual design”, in Blass H J et al (eds) Timber
engineering STEP 2, (The Netherlands, Centrum hout, 1995), pp E2/1-E2/8
[8] Harris R et al, “The use of timber gridshells for long span structures”, Proceedings of
the 8th world conference on timber engineering WCTE 2004, Vol 1 (June 2004), pp. 99-104




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