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2. A parameter is a variable to which other variables are related, and these other variables can be obtained by means of parametric equations. FOR EXAMPLE: **The £I30 million International Terminal at Waterloo Station,International Terminal at Waterloo Station London, by the architecture firm Nicholas Grimshaw & Partners,Nicholas Grimshaw & Partners is a railway station on a complex site -The most impressive feature of the scheme from a CAD perspective is the massive curved train shed which gradually expands towards the station end. -The complexity and variation in the size and shape of the structural elements involved in the train shed were possible, the essential feature of which was the ability to represent parametric relationships. -The main parametric relationships involved in this project were concerned with the description of the structural form, in which the span and curvatures of individual arches were related. These relationships in turn determined the detail of the trusses.

3. *The international terminal at Waterloo, terminal at Waterlooterminal at Waterloo London, by the architecture firm London, by the architecture firm *View of the new train platforms from the concourse of the existing WaterlooWaterloo Train Station Train Station.

4. **Expressing the Structure Parametrically:- -The asymmetry of the trusses derives from the position of a single track tight onto The western edge of the site and the resulting need for the structure to rise more Steeply at this point to clear the trains. -The basic structure of the terminal is that of a flattened three-pin bowstring arch, because of the asymmetrical geometry of platforms, the center pin was moved to one side, allowing the arch to rise steeply on the west side to clear the structural envelope of the train, with a more gentle incline over the platforms on the east. *An isometric view of the Waterloo Station train shed, its arches varying in span from 107 to 159 feet (32.7 to 48.5 meters).

5. The arched roof of the train shed follows the curve of the railway, and increases in span down the length of the station to accommodate the increase in the width of the platforms. The roof is supported by a series of three-pin arches. Each arch and the related cladding are different as the roof changes width along the curved tracks. The variability of the arches is visible in both plan and isometric views. *Plan view of the train station showing varying roof truss sizes and expansion joints. By CAD modeling techniques, a single arch form could be modeled then duplicated 35 times down the length of the track,, with adjustments for the curvature of the track in plan.

6. - A single parametric model of an arch was modeled, such that it encod - A single parametric model of an arch was modeled, such that it encod encoded the underlying design rules for the whole family of arches. The complete roof model then became a series of instances of this parametric arch, each with a different value for the span parameter. encoded the underlying design rules for the whole family of arches. The complete roof model then became a series of instances of this parametric arch, each with a different value for the span parameter. -A complete three-pinned arch is composed of two bowstring trusses. - The longer trusses have tension rods on the inside, whereas the shorter trusses have tension rods on the outside. The cladding on the (western) short truss side is all glass, whereas the (eastern) long truss side is clad in stainless steel decking to reduce solar gains. *Construction line grid defining the truss geometry. The arch on the west needed a much steeper curve than the arch on the east to allow trains to arrive right underneath it.

7. **Applying CAD Techniques:- -The two primary elements involved in parametric expression for the Waterloo train shed are the minor and major trusses that form an arch. More specifically, their horizontal spanning distances B and C respectively, as shown at right. The size of the reduced truss is dictated by the parametric truss scaling factor (hx/H). The position of reduced trusses is determined by a parametric relationship which maintains the vertical cast pin dimension of 9.5 feet (2915 millimeters). *Minor and major trusses spanning lengths B and C respectively. The longer trusses have tension rods on the inside, whereas the shorter trusses have tension rods on the outside. *Parametric expression of the truss scaling factors.

8. -H and (hx) can then both be derived from a simple Pythagorean equation (the square on the hypotenuse is equal to be the sum of the squares on the other two sides). -H and (hx) can then both be derived from a simple Pythagorean equation (the square on the hypotenuse is equal to be the sum of the squares on the other two sides). *A cross section from the end of the Waterloo Station.

9. -A parametric CAD model (in which some dimensions are derived from others), on the other hand, can quickly and more easily be changed by choosing a particular dimension and changing its value. -A parametric CAD model (in which some dimensions are derived from others), on the other hand, can quickly and more easily be changed by choosing a particular dimension and changing its value. The truss scaling factor is based on the ratio of the pin hypotenuse (hx) to the other sides of the triangle. In other words: hx = [ (29152 + (B + C)2 ] 1/2 where B = minor truss span; C = major truss span -The parametric model can be extended from just the description of arches, through to the description of the connections between pairs of arches. -This model can then in turn be extended to the whole shed form, so that when any dimensional change is made, it is then propagated through the whole model. -Parametric expressions, therefore, allow users to change the values of key parameters, and to observe the propagation of changes on dependent expressions, and hence upon the dependent geometry. This is often referred to as strategic manipulation

10. *Computer rendering of the train shed interior. *CAD Principles for Architectural Design by Peter Szalapaj -when any dimensional change is made, it is then propagated through the whole model.

11. -Parametric expressions, therefore, allow users to change the values of key parameters, and to observe the propagation of changes on dependent expressions, and hence upon the dependent geometry. This is often referred to as strategic manipulation. -Parametric expressions, therefore, allow users to change the values of key parameters, and to observe the propagation of changes on dependent expressions, and hence upon the dependent geometry. This is often referred to as strategic manipulation. **A Technology for Architects? -Parametric design software has to date primarily been developed for mechanical engineers, civil engineers, and industrial designers. -Parametric expressions can represent a set of geometrical forms instead of just one. -The parametric expression of design relationships allows for the exploration of variation. -Parametric design is a relatively new form of expression in architectural design, with the potential to support design creativity. -It is also a further argument in support of the case for modeling vs. drafting approaches to CAD.