The case is parameterized by CADRE and initial dimensional ... and the overall length of a building, are generated automatically in CADRE through context.
1
CASE BASED PRELIMINARY BUILDING DESIGN By Simon F. Bailey1 and Ian F. C. Smith2
ABSTRACT A team of civil engineers, architects and computer scientists is using CaseBased Design (CBD) as an approach for integrating preliminary architectural and structural design. This approach focuses on dimensional and topological adaptation of geometric models of existing buildings in order to find solutions for new design problems. An advantage of such an approach is that a case is used in which integration has already been achieved and the design process is therefore one of adapting the case to achieve new goals whilst maintaining the original building features. Conclusions of this work are that cases consisting of a geometrical building model both simplify design knowledge acquisition and provide a valuable initial integrated design solution which serves as a useful starting point to the design process.
INTRODUCTION
Computer Aided Design (CAD) is currently one of the most active fields of research and development in artificial intelligence. Many systems have been developed in order to study human problem solving as well as to test the potential for CAD in design practice. An examination of how these systems have evolved and the difficulties that were encountered during their development is given in the paragraphs that follow.
1 Research Engineer, ICOM (Steel Structures), Department of Civil Engineering, Swiss Federal Institute of Technology (EPFL), GCB-Ecublens, CH-1015 Lausanne. + 41 21 693 2425. 2 Adj. Dir., Artificial Intelligence Laboratory (LIA), Department of Computer Science, Swiss Federal Institute of Technology (EPFL), INR-Ecublens, CH-1015 Lausanne.
2
The Integrated Building Design Environment (IBDE) ( Fenves et al 1989 ) was one of the first integrated CAD systems to be implemented. Design knowledge from various building design domains is organized into independent rule bases in separate system modules. The design of foundations, the core and column layout, for example, are treated as separate design sub-tasks. A control module in a blackboard architecture (Hayes-Roth and HayesRoth 1980) determines the solution sequence for each sub-task. The IBDE suffers from the problems of conflict and possible looping between modules in a blackboard system ( Schmitt 1989 ), caused by decomposing the design process into sub-tasks which are in fact interdependent. Prototypes ( Gero et al 1988 ) are parametric models of design objects which are adapted to solve new design problems. The prototype approach demonstrates the advantage of starting the design process with concrete examples of solutions. Disadvantages are that parametric models must be formulated by generalizing both design and domain knowledge, and this is difficult to achieve for complex objects, such as buildings, which are characterized by many thousands of parameters. Mutation ( Zhao and Maher 1992 ) is proposed as a means of increasing the creativity of prototypical design. In this approach analogical reasoning is used to adapt prototypes to include parts of others, thus making solutions more innovative. The paradigm of Case-Based Reasoning (CBR) originates from psychological models of human memory structure ( Schank 1982 ). The underlying concept is that humans use not only heuristic rules to solve problems, but also refer to solutions of previous similar problems. For example, when faced with the task of designing a new warehouse, the case of an existing warehouse is adapted to suit new needs, rather than starting with a set of rules which say that roofs are supported by beams, beams are supported by columns, and columns must be founded, etc. Cases in some early CBR systems consist of the ’ingredients and steps to follow’, as in CHEF ( Hammond 1986 ) which produces new recipes from existing ones. This type of case is a plan of the design process, formulated at the knowledge acquisition stage, as with
3
prototypical design. Existing solutions must be evaluated by a human designer and a case formulated to suit the way it will be used during reasoning. This complicates knowledge acquisition. CYCLOPS ( Navinchandra 1988 ) is a landscape planning and design system in which a case is both a previous problem and its solution. Analogical reasoning is used to identify cases, not necessarily from the same domain, which match the current design problem. The identification of relevant matching cases from other domains necessitates a great deal of domain independent knowledge. Furthermore, cases must be formulated so that the useful information is represented explicitly. Due to the belief that a practical CBR system would need many hundreds of cases from which to reason, much research has been concentrated on indexing and retrieval of cases ( Kolodner 1989 ). Systems have been developed which find the best case, rather than reason with the case once selected. ARCHIE ( Domeshek and Kolodner 1992 ) indexes and organizes decomposed cases (annotated building plans) in memory and provides a case browser for the retrieval of stories, which are defined as ’selective presentations about a case which have a lesson to teach’. The user is left to interpret a story, as ARCHIE does not reason, being a problem sensitive teaching tool rather than a design system. CADSYN ( Zhang and Maher 1993 ) is a case based building design system which considers architectural space planning, structural design and services design. The system assumes that design problems can be decomposed to nearly independent sub-problems which can be solved independently and then recomposed to provide a complete solution. As with a blackboard system however, ignoring the interdependence of sub-problems can lead to conflict and looping upon recomposition of sub-solutions. The DDIS system ( Wang and Howard 1991 ) combines case based reasoning with design independent knowledge in a blackboard framework. The system represents design knowledge with cases consisting of the problem specification, final solution, intermediate propositions, design history, etc. Cases are retrieved by users who decide similarity to the new design problem. The system treats the design of steel columns, and is therefore yet to be tested on complex tasks.
4
INTEGRATION Buildings can be seen from many different points of view. For example, to a civil engineer a building consists of structural elements, whereas an architect may view it as a collection of rooms or as an envelope providing a filter between the surrounding environment and occupants (Fig. 1.). We refer to each of these interpretations as an abstraction. One of the most difficult tasks in design is resolving conflicts which occur when integrating solutions from multiple abstractions or decomposed sub-problems. The conflict between architects and engineers is traditionally one of the greatest problems in building design (Holgate 1986). In practice, designers rely heavily on their experience of conflict resolution in order to make tradeoffs. In design practice, as in CAD, integration is the key to good design. This is accepted by many researchers, but current CAD systems provide little support. As mentioned above, blackboard systems may loop between modules, unless the control module contains complete knowledge of all possible conflicts as well as effective strategies to resolve them. The weakness of blackboard systems is found precisely in the representation of knowledge for conflict resolution. An improved model of the design process is therefore needed.
FIG. 1. Multiple building abstractions : (a) Structure ; supporting loads. (b) Space ; a collection of rooms. (c) Envelope ; a filter between the surrounding environment and occupants.
CADRE In this project, we have implemented CBD in a system called CADRE, which focuses on the representation and adaptation of cases rather than their indexing and retrieval, as we believe that these are more important issues for case-based building design. The advantage of our approach is that a case is used in which integration has already been achieved, albeit for a different problem. Beginning with such a case means that the design
5
process is now one of adapting the case to achieve new goals whilst maintaining the original features of the building. These features include the tradeoffs which have been made in order to achieve the integration of solutions from each abstraction. Our approach is presented in the sections which follow. We begin with an outline description of the paradigm. A presentation of the technical details of each process follows and finally a description of how CADRE has been implemented is illustrated by a complete example of how the system has been used to adapt one of the computer science buildings at EPFL. Paradigm The cases used in CADRE are geometric models of both structural and architectural abstractions of a building. Users decide which building they would like to adapt by selecting an appropriate case. The case is parameterized by CADRE and initial dimensional constraints describing both structural and architectural abstractions and their relationship to each other are generated automatically. The user posts constraints which describe the new design problem. CADRE then attempts to solve the resulting system of constraints during the dimensional adaptation process. If a solution is not found, the user may ask CADRE to attempt topological adaptations of the building abstractions. A successful topological adaptation is followed by a reparameterization of the building, constraint posting by the user and finally a dimensional adaptation in order to fix dimensions for the new topology. This approach is illustrated in Fig. 2.
FIG. 2. Case Based Design in CADRE
Cases A case is a geometric model of both the structural system and the architectural layout of spaces. Much design knowledge is implicit in the cases, and therefore does not require explicit representation. Constraints used during dimensional adaptation are generated automatically by generic processes within the CADRE system. The information stored in a
6
case can therefore be limited to a minimum, and cases can be created from building plans without the addition of domain or design knowledge.
Formulation Of Dimensional Constraints During dimensional adaptation CADRE attempts to solve a system of constraints, which are derived at run-time from the geometrical model stored in the case. For any topology in any abstraction the geometry of a building can be expressed with constraints which, for example, describe the position of a column or the area of a room. The geometries of different abstractions are linked by using a common coordinate system. Constraints, such as span-depth ratios for beams or relationships between the spacing of structural frames and the overall length of a building, are generated automatically in CADRE through context sensitive evaluation of the existing case using generalized domain knowledge. Generic domain knowledge is used to determine supplementary constraints that define, for example, the maximum span for a given type of floor slab. These constraints are often expressed as inequalities, and it is therefore necessary to identify critical constraints, which are then treated as equalities during dimensional adaptation. The results of dimensional adaptation are checked with the remaining non-critical inequality constraints.
Constraint Posting And Relaxation. A new problem is defined in CADRE by the user posting additional constraints on the original case, for example by defining a new overall dimension for a building or a new number of offices. Multiple design criteria, for example, structural safety and serviceability, mean that a building may be over-constrained. The dimensional constraints which have been generated for each abstraction are then considered together with the posted constraints during dimensional adaptation. If the problem is over-constrained, the user is asked to relax certain constraints. Similarly, if the problem is under-constrained further constraints must be posted.
Dimensional Adaptation
7
Dimensional adaptation involves the solution of a set of linear and non-linear constraints on the parameters used to describe the building. The constraints to be considered are generated as described above. Adaptation at the dimensional level produces integrated solutions because constraints from all abstractions are considered simultaneously. The key to dimensional adaptation is dimensionality reduction, which we have implemented using the REDUCE system (Hua et al 1992). Dimensionality reduction is used to identify the key parameters which define the possible adaptations. This is different from prototypical design because the parameters we consider are identified at run-time. A factory and warehouse site is shown in Fig. 3. It is a gas and water pipe production and storage facility in St. Gallen in Switzerland. The task is to redesign the buildings to suit the same production but with a larger pipe storage area. This is an example of how dimensional adaptation in CBD is effective for generating routine solutions. As described above : • the original structure is evaluated using generalized domain knowledge and constraints governing the dimensions of the structural elements are generated • additional constraints are posted by the user to – define a new area for the warehouse, – fix its width in order to use the same type of overhead crane, and – fix the dimensions of the other buildings in order to use the same production line system. The base parameters and constraints describing the dimensions of the warehouse structure as well as the section properties of the crane rail beam, columns, roof beams and cladding are given below. They are a representative subset of the constraints considered during dimensional adaptation. The warehouse structure is shown in Fig. 4. The warehouse geometry is described by the following base parameters; the area A1, length L, half-width W1, frame spacing Sf, and purlin spacing Sp. They are governed by the following dimensional constraints : A1 = L * 2 * W1
(1)
Sf = L / 5
(2)
8
Sp = W1 / 17
(3)
W1 = 16.5 meters (posted by the user)
(4)
A1 > 1400 sq. meters (posted by the user)
(5)
The crane rail beam is represented by the following base parameters; Young’s modulus E, and the second moments of area Iy and Iz. Generalized domain knowledge is used to formulate the constraints for the crane rail beam, which is governed by limiting horizontal and vertical deflections, Dh and Dv, due to crane live loads, Qch and Qcv : Dv < Sf / 700
(6)
Dv = k1 * Qcv * Sf3 / (E * Iy )
(7)
Dh < Sf / 800
(8)
Dh = k2 * Qch * Sf3 / (E * Iz)
(9)
k1 and k2 are a function of the continuity and fixity of the crane rail beam at supports, and are determined from evaluation of the original case. Cladding is governed by strength criteria; the plastic moment of resistance must be greater than the applied moment due to snow load Qs and dead load G. The cladding base parameters are the material yield strength fy, and section plastic modulus Zy. The following constraint is expressed for a unit width of cladding : fy * Zy / γr > (γg * G + γq * Qs ) * Sp2 / 12
(10)
γq, γg and γr are the partial load and resistance factors. Inequality constraints that are critical are fixed as equalities and CADRE uses dimensionality reduction on base parameters to identify key parameters, reparameterize others, and determine which constraints can be ignored. This has the following effect on the base parameters and constraints listed above : • The frame spacing is identified by CADRE as the key parameter for dimensional adaptation of the warehouse area, and is solved as ; Sf = A1 / (2 * W1) / 5 = 8.5 meters ( from constraints (1), (2), (4) and (5) )
(11)
• CADRE determines that the purlin spacing Sp and distributed loads Qs and G are redundant parameters because they are independent of the warehouse length.
9
Therefore the cladding constraints are independent of adapted parameters and are ignored. The original section properties are maintained. • The crane rail beam deflection constraints are fixed as equalities, and they are reduced to; Iy = 700 * k1 * Qcv * Sf2 / E
( from constraints (6) and (7) )
(12)
Iz = 800 * k2 * Qch * Sf2 / E
( from constraints (8) and (9) )
(13)
• Qcv and Qch are determined to be independent of the adaptation; they are dependent on the type and size of gantry crane, which is fixed by constraint (4). The values of "k1 * Qcv" and "k2 * Qch" are evaluated from the original case and substituted into constraints (12) and (13). These constraints are then solved for the adapted value of Sf ; Iy = 700 * 557 * Sf2 / E = 0.000134 m4
(14)
Iz = 800 * 171 * Sf2 / E = 0.000047 m4
(15)
Since in this example there is enough knowledge to fix the adaptation, CADRE automatically resizes structural elements. These new dimensions are then checked with the constraints that were previously identified as not being critical. If there were remaining degrees of freedom the adaptation would be performed in collaboration with the user.
Topological Adaptation In the event that a solution cannot be found by dimensional adaptation a topological adaptation may be tried. The aim is to adapt the original topology to a new one that will result in a new dimensional model and set of dimensional constraints that are then treated by dimensional adaptation processes. A rule based approach is used for the topological adaptation of the structure. Common sense domain independent rules are used to change the geometry. For example, if spans are to be increased then the number of frames must be reduced. Domain knowledge is used for deciding when the type of construction needs to be changed. For example, a flat slab floor system is suitable up to spans of 8m, but beyond that, a beam and slab system is
10
preferable. The function of structural elements is also considered during topological adaptation. Elements which contribute to the overall stability of the building (bracing, shear walls, etc.) are identified automatically and maintained during adaptation. Flemming’s algorithm for generating alternative arrangements of rectangles (Flemming 1985) is used for room layout adaptation. The need for topological adaptation is illustrated by the example shown in Fig. 5. The problem is to adapt the room and structural element layout so that columns can be concealed in walls. To begin with, there is a conflict in the dining room (Fig. 5 (a)). It is not obvious from the graphs of the two topologies (Fig. 5 (b)) that the central column is not coincident with a wall. This is due to difficulties in relating topologies from different abstractions to each other in order to detect conflicts. At the dimensional level (Fig. 5 (a)) the problem is obvious. For the overall dimensions shown in Fig. 5(a), dimensional constraints on minimum room dimensions and maximum span lengths (16 and 17) cannot be solved without topological adaptation.
room width, room length > 3.0 meters
(16)
column spacing < 5.5 meters
(17)
The task is then to direct this adaptation, without resorting to an arbitrary generate and test approach. CADRE uses information related to how the solution failed at the dimensional level. For example, we know that the conflict comes from the width of the rooms and the distance between columns in the x-direction. We therefore need to adapt topologies in order to change these parameters, that is, alter the number of column bays or rooms in the x-direction. Fig. 5 (c) illustrates possible adapted topologies. Fig. 5 (d) shows the corresponding geometries realized by dimensional adaptation using the new dimensional constraints.
11
LOUNGE
DINING
KITCHEN 8m
10 m
(a) Original case
Elements
Spaces LOUNGE
KITCHEN
DINING
(b) Original topologies
LOUNGE KITCHEN DINING
(c) Adapted topologies
(d) New geometries FIG. 5. Topological adaptation in CADRE : (a) Original case. (b) Original topologies. (c) Adapted topologies. (d) New geometries.
12
Implementation The CADRE system is implemented using Lisp and C. A user interface has been created within AutoCAD, which facilitates case creation and allows visualization of a case during the design process. Menus within AutoCAD are used to control CADRE (Fig. 6). Constraint posting by the user is also carried out graphically.
FIG. 6. The CADRE graphical user interface
Cases can be created through graphical input of structural elements and rooms which are then stored as objects, in order to build up geometric models of each abstraction. For example, a beam is represented as an object having a start point, end point, depth, width and a material type. The structural abstraction of a case is therefore a collection of many such elements. No further description of the structural elements in a building needs to be input. The layout and dimensions of spaces can be defined in a similar way. Services, such as power, water, heating and ventilation, can also be represented, but for the moment these are not included. Selected cases can be viewed before and after adaptation through the use of standard AutoCAD commands. Abstractions may be viewed simultaneously or independently, as in Fig 7.
FIG. 7. Viewing the structural abstraction of the INR building
AN EXAMPLE SESSION WITH CADRE
A complete example showing adaptation for one of the computer science buildings at EPFL (the INR building) is given below. This is one of six multipurpose buildings recently constructed at EPFL, and which are used by the Departments of Electrical Engineering and Computer Science. The future occupants of the INR building decided to change a room,
13
originally intended to be a laboratory, into a classroom. Unfortunately, a column is situated in this lab, which is unwanted in a classroom. The following example demonstrates how CADRE is used to adapt the INR building to avoid this conflict. Fig. 8(a) shows the conflict of the column in the classroom. A constraint is posted by the user to bind the x-coordinates of a wall and the conflicting column (menu "constraint-pos" in Fig. 6). CADRE attempts to solve the set of dimensional constraints. To model the four floors of the building in three dimensions requires more than 4000 parameters. Dimensionality reduction simplifies the problem to a set of eight constraints on eight key parameters, but finds that no solution exists, and notifies the user. The failure of the initial dimensional adaptation is due to conflicting constraints on the minimum area of the classroom and maximum spans for the floor slabs. This is a typical situation which could lead to looping in a blackboard system.
FIG. 8. Room layout and the structure in plan
The user decides to try a topological adaptation of the structure, selecting this option from the "CL-CMD" menu. CADRE uses the knowledge that dimensional adaptation failed because column spacing was too small and therefore adapts the structural topology to increase column spacing in one direction. The solution is to change the floor slab system from a flat slab to a one way slab and to reduce the number of building frames from six to four. New dimensional constraints are generated for this topology and subsequent dimensional adaptation finds a solution (Fig. 8(b)). The user then visually checks the effect of this new structure on the floor plans for other floors. Unfortunately, there is a conflict on the first floor (Fig. 8(c)). The user decides to try a topological adaptation of the first floor room layout. A topological adaptation of the first floor produces an alternative room layout and a corresponding set of dimensional constraints are generated. A further dimensional adaptation finds a solution and it is shown to the user (Fig. 8(d)).
14
DISCUSSION
A complete model of a building may involve many thousands of parameters and constraints, and it is therefore desirable to reduce these to a minimum. In the example of the INR building, each floor is composed of more than 30 rectangular spaces and there are 39 columns, 4 shear walls and a floor slab. More than 150 parameters are needed to represent the geometry of these objects in two dimensions. To model the four floors of the building in three dimensions requires more than 2000 parameters. If the positions of windows and doors and the dimensions of structural elements are included, this number more than doubles. In the example illustrated in Fig. 8, dimensionality reduction simplifies the problem to a set of eight constraints on eight key parameters. For complex, non-linear problems, this approach is more efficient than that of prototype based systems, which always have to consider all parameters and constraints in order to instantiate solutions from parametric models. However, the reduction process can take hours if the problem is large. The use of specialized constraint solving methods specific to those forms of non-linearity which occur in building design constraints (first and second order polynomials) can increase the speed of this process. A problem with case adaptation is that if it diverges too far from the original case, implicit features may be lost. For example, a change in orientation of the building may mean that windows no longer provide good natural lighting. CBD produces primarily routine solutions, and some that are innovative. However, creative design is not supported by this approach. The fact that new solutions are being derived from previous solutions in the same domain means that the process is not creative, and is the reason why many researchers are trying to use analogical reasoning to be able to consider solutions from other domains. For the moment, creativity should probably be left to humans. It is after all what they enjoy most in designing, whereas the routine tasks, such as sizing structural elements, are tedious. When designers are freed from such tasks, more time can de devoted to innovation and creativity.
15
CADRE integrates the adaptation of building abstractions at the dimensional level. However, treating multiple abstractions at the topological level is more complicated than at the dimensional level. This is because it is difficult to relate the topologies of different abstractions to each other. At the dimensional level all objects are represented by their dimensions and positions; thus a common reference is more readily available than at the topological level. This revives problems which are similar to those associated with blackboard systems since adapting one abstraction may lead to conflict with another. We are now working to improve integration of the topological adaptation processes by increasing the amount of information that one abstraction shares with another. Situations in which conflicts could arise as a result of topological adaptation can thus be avoided. For example, the architectural adaptation process must account for the position of shear walls so as to ensure natural lighting in rooms where it is needed (storerooms and bathrooms, for example, do not need large windows). Additional improvements are possible when topological adaptation is limited to a part of a building. For example, in the problem of the column in the room shown in Fig. 8, it is better to adapt the layout of rooms local to the column. In this way, adaptation is simplified and integration elsewhere in the building is maintained. Finally, current work is focusing on case combination as a method for increasing the power of topological adaptation. This work is expected to provide better support for innovative design.
CONCLUSIONS
• The use of geometric models of buildings as cases facilitates knowledge acquisition. Deriving dimensional constraints and symbolic representations of topology at run-time restricts the amount of information employed, and eases case creation. This is an advantage over other approaches which require that more information is included in the case, or that they be compiled to suit the design process.
16 • Cases provide the design process with a starting point at which solutions in all abstractions are integrated. An advantage of our approach to CBD is that the tradeoffs made during design are implicit in cases, and conflict resolution knowledge need not be represented explicitly in the system. • Dimensional adaptation involving non-linear constraints is simplified by dimensionality reduction. • Topological adaptation increases innovation in case based design by changing the design solution space.
ACKNOWLEDGEMENTS
The development of CADRE has been funded by the Swiss National Research Foundation. The authors would also like to acknowledge Prof. G. Schmitt and S-G. Shih at the Laboratory for Computer Aided Architectural Design (CAAD) at the Swiss Federal Institute of Technology in Zurich, as well as Prof. B. Faltings and K. Hua at the Laboratory for Artificial Intelligence (LIA) in Lausanne. They have helped develop and implement most of the ideas described in this paper. Recent contributions of Bharat Dave and Laurent Bendel at CAAD and Kim Jent and Jean-Marc Ducret at ICOM are also gratefully acknowledged.
APPENDIX I. REFERENCES
Domeshek, E. A., and Kolodner, J. L. (1992). "A case-based design aid for architecture" Artificial Intelligence in Design ’92, Kluwer Academic Publishers pp. 497-516. Fenves, S. J., Flemming, U., Hendrickson, C., Maher, M. L., and Schmitt, G. (1989). "An Integrated Software Environment for Building Design and Construction."
CIFE
Symposium Proceedings March 1989. Flemming, U. (1985) "On the representation and generation of loosely packed arrangements of rectangles." Environment and Design, December 1985.
17
Gero, J., Maher, M. L. and Zhang, W. (1988). Chunking structural design knowledge as prototypes. The architectural computing unit, Department of architectural science, University of Sydney. Hammond, K. (1986) "CHEF : A model of case-based planning." Proceedings AAAI-86 pp. 267-271 Hayes-Roth, B. and Hayes-Roth, F. (1980) A cognitive model of planning. Morgan Kaufmann. Holgate, A. (1986). The art in structural design. Oxford University Press. Hua, K., Smith, I., Faltings, B., Shih, S., and Schmitt, G. (1992). "Adaptation of spatial design cases." Artificial Intelligence in Design ’92, Kluwer Academic Publishers pp. 559575 Kolodner, J. (1989). "Judging which is the best case for a case based Reasoner." Proceedings of the Darpa workshop on Case-Based Reasoning, pp. 77-81. Navinchandra, D. (1988). "Case Based Reasoning in CYCLOPS, a Design Problem Solver." Proceedings of the Darpa workshop on Case-Based Reasoning, pp. 286-301 Schank, R. (1982) Dynamic memory - a theory of reminding and learning in computers and people. Cambridge University Press Schmitt, G. (1989). "Architectural Pre-Processor for Engineering Expert Systems." Expert Systems in Civil Engineering, IABSE Colloquium, Bergamo, pp.291-302. Wang, J., and Howard, H. C. (1991) "A design-dependent approach to integrated structural design." Artificial Intelligence in Design ’91, Butterworth-Heinemann pp.151-170 Zhang, D. M. and Maher, M. L., (1993) "Using case-based reasoning for the synthesis of structural systems." Knowledge-based systems in civil engineering, IABSE Colloquium, Beijing pp.143-152. Zhao, F., and Maher, M. L. (1992). "Using network-based prototypes to support creative design by analogy and mutation" Artificial Intelligence in Design ’92, Kluwer Academic Publishers pp. 773-793
APPENDIX II. NOTATION
18
The following symbols are used in this paper: A1 =
warehouse area
Dh =
horizontal deflection of crane rail beam
Dv =
vertical deflection of crane rail beam
E
=
Youngs modulus
fy
=
yield strength of steel
G
=
self weight of cladding
γg =
dead load factor
γl
live load factor
=
γg =
resistance factor
Iy
=
second moment of area about the major axis
Iz
=
second moment of area of the upper flange about the minor axis
k1 =
elastic deflection coefficient
k2 =
elastic deflection coefficient
L
length of the warehouse
=
Qch =
horizontal live load due to the gantry crane
Qcv =
vertical live load due to the gantry crane
Qs =
distributed snow load
Sf =
spacing between building frames
Sp =
spacing between roof purlins
W1 =
half-width of the warehouse
Zy =
section plastic modulus
19
legend to Fig. 3 1 warehouse 2 small items storage 3 connecting structure 4 free storage 5 short term storage 6 truck access 7 factory
Keywords Artificial Intelligence, Case Based Design, Architecture, Buildings
