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The graphic shows a footbridge near Liverpool which is based on a hyperbolic paraboloid - Leaving Cert DCG - Question C-2 - 2018
Question C-2
The graphic shows a footbridge near Liverpool which is based on a hyperbolic paraboloid. The projections of the bridge are given in Fig. C-2 below. The elements of ... show full transcript
Worked Solution & Example Answer:The graphic shows a footbridge near Liverpool which is based on a hyperbolic paraboloid - Leaving Cert DCG - Question C-2 - 2018
Step 1
Draw the given plan and elevation of the hyperbolic paraboloid ABCD, using the number of elements shown and include the projections of the walkway.
Answer
- Begin by sketching the hyperbolic paraboloid ABCD using scale measurements based on the provided figure.
- Outline the points A, B, C, and D in both plan and elevation views, ensuring correct alignment with respect to the given dimensions.
- Include the projections of the walkway extending from the loop structure, ensuring it aligns with the designated points on the paraboloid.
Step 2
Curve ABC is a parabola in elevation with vertex at B. Draw the elevation of this parabola.
Answer
- Identify the vertex point B on the elevation view of ABC.
- Establish the axis of symmetry for the parabola, cascading from B to points A and C.
- Utilize the standard parabola equation to plot additional points if needed, ensuring the curve is smooth and symmetrical.
Step 3
Project, from the elevation, the given plan of the curved outline loop and project an end view. Draw the walkway in the end view.
Answer
- From the elevation drawing, project the outline of the curved loop to obtain its plan view.
- Ensure to maintain the same curvature and dimensions as it appears in the elevation.
- For the end view, draw the outline while ensuring that intersections and dimensional accuracy are preserved.
- Finally, incorporate the walkway into the end view sketch.
Step 4
The line CE is a normal to the parabola at point C in elevation. Determine the focal point and directrix of this parabola in elevation.
Answer
- Draw the normal line CE at point C, ensuring it is perpendicular to the tangent at that point on the parabola.
- Use the properties of a parabola to locate the focal point; it lies along the normal CE at a certain distance.
- Construct the directrix as a line that is equidistant from the focal point and the curve, marking both elements accurately on the elevation.