The 3-D graphic on the right shows an Irish hotel with a modern roof structure - Leaving Cert DCG - Question C-2 - 2012
Question C-2
The 3-D graphic on the right shows an Irish hotel with a modern roof structure.
Hyperbolic paraboloid surfaces are often used in structures such as this.
Fig. C-2 ... show full transcript
Worked Solution & Example Answer:The 3-D graphic on the right shows an Irish hotel with a modern roof structure - Leaving Cert DCG - Question C-2 - 2012
Step 1
Outline of surface ABCD in elevation
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To outline the surface ABCD in elevation, begin by sketching the curve from points A, B, C, and D as per the provided dimensions in the elevation drawing in Fig. C-2. Ensure that the curve reflects the hyperbolic nature by connecting points B and D to represent the sagging curvature appropriately.
Step 2
Elements in elevation (incl. division)
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Divide the elevation into appropriate sections. Use horizontal lines to indicate construction elements at critical points such as the peaks and troughs of the hyperboloid. This would typically involve drawing line segments that connect the midpoints of the edges to the center, maintaining symmetry.
Step 3
Outline of surface ABCD in plan
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In the plan view, the outline of surface ABCD should reflect a symmetrical diamond shape with straight edges connecting the corners A, B, C, and D. Use the measurements provided in the plan view to ensure accuracy, while ensuring the proper curvature is represented despite the flat representation.
Step 4
Elements in plan (incl. division or proj.)
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Display the elements in plan by plotting the necessary grid lines that reflect the divisions of the hyperbolic paraboloid. These lines should help with visualization of the surface forms projecting into the 3D view. Highlight any significant feature that corresponds to the elevation division.
Step 5
Curve in elevation
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Illustrate the curve in elevation using a dashed line to differentiate it from physical elements, demonstrating how the surface dips and raises in a hyperbolic structure from point to point, reflecting changes in height as per the given coordinates.
Step 6
Determine heights and widths for surface ABCD
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To determine the heights and widths, calculate the dimensions between each key point (A, B, C, D) in the drawing, using measurements provided in Fig. C-2 to ensure that the values correspond accurately to the drawn elements.
Step 7
Draw the outline of the hyperbolic paraboloid
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Draw the outline of the hyperbolic paraboloid by creating a smooth, continuous curve that interlinks all the edges of the surface determined in earlier steps, ensuring that the elevation and plan outlines align seamlessly.
Step 8
Draw the elements
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Draw the elements of the hyperbolic paraboloid by sketching vertical sections from each point (A, B, C, D) downward to the base outline. This should create the visual perspective of depth and provide assistance in understanding the surface transitions.
Step 9
Curve in end view
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For an end view, portray the main curve of the hyperbolic surface while indicating the transitions and the drop in height at the central apex. The curve should visually communicate the overarching form that the hyperbolic paraboloid takes.
Step 10
Presentation
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Ensure that the overall presentation of drawings is neat and legible, using appropriate scaling, labeling, and shading to emphasize the structural elements. Quality of line work, clarity of dimensions, and presentation layout play crucial roles in delivering a professional representation.
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