The image on the right shows the Salmon Weir Bridge over the river Moy in Co - Leaving Cert DCG - Question A-3 - 2018
Question A-3
The image on the right shows the Salmon Weir Bridge over the river Moy in Co. Mayo.
The drawing below shows an incomplete elevation of the bridge.
(a) The curved s... show full transcript
Worked Solution & Example Answer:The image on the right shows the Salmon Weir Bridge over the river Moy in Co - Leaving Cert DCG - Question A-3 - 2018
Step 1
Draw horizontal lines dividing rectangle into a number of equal parts.
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Answer
Begin by drawing the rectangular boundary in which the parabola will be inscribed. Divide the rectangle horizontally into equal segments, ensuring that there is symmetry about the vertex V.
Step 2
Draw corresponding dividing lines radiating from V.
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Answer
Draw lines radiating from the vertex V to the points marked on the horizontal divisions. These lines will help locate the points on the parabola more accurately.
Step 3
Locate points on parabolic curve.
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Answer
Using the dividing lines as guidelines, plot the corresponding points that will lie on the parabolic curve. Ensure the points are placed symmetrically about the vertex.
Step 4
Draw parabolic curve (Any 'x' is acceptable).
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Answer
Connect the plotted points smoothly to form the parabolic curve, ensuring it touches all the points accurately and reflects the parabolic shape.
Step 5
Draw support cable joining P to F.
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From the point P, draw a straight line to the focal point F of the parabola. This represents one of the support cables.
Step 6
Construction to determine tangent at P.
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To find the tangent at point P, utilize the derivative of the parabola at point P, or geometrically construct a line that is perpendicular to the radius drawn from F to P.
Step 7
Draw required tangent at P.
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Draw the tangent line at point P, ensuring that it just touches the curve at P without crossing it.
Step 8
Draw second support cable at 25° to correct tangent as required.
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Answer
From point P, draw a second cable inclined at 25° to the tangent line just constructed. Ensure this cable is properly aligned with the tangent for structural accuracy.
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