Fig. B-1 shows the plan and elevation (excluding hidden detail) of the structure. (a) Draw the given plan and elevation of the structure. (b) Determine the dihedral angle between the planes A and B. (c) Determine the true shape of the vertical surface A. (d) The director of a future Mission Impossible movie wants to shoot a scene that involves climbing the outside of the building. A stuntman is to travel down from point S along surfaces A, B and C to the ground. Determine the projections of the line on each plane that the stuntman must move along so that he travels the shortest possible distance on each successive surface as shown on the right.

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Fig. B-1 shows the plan and elevation (excluding hidden detail) of the structure - Leaving Cert DCG - Question B-1 - 2013

Question B-1

Fig. B-1 shows the plan and elevation (excluding hidden detail) of the structure. (a) Draw the given plan and elevation of the structure. (b) Determine the dihedra... show full transcript

Worked Solution & Example Answer:Fig. B-1 shows the plan and elevation (excluding hidden detail) of the structure - Leaving Cert DCG - Question B-1 - 2013

Step 1

Draw the given plan and elevation of the structure.

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Answer

To draw the plan and elevation of the Fountain Place structure:

The plan view should be oriented so that surface A is on the left side, with surface B in the center, and surface C to the right.
The elevation shows the height of each surface, with surface A being the tallest, followed by surface B and then surface C.
Clearly label all sides and dimensions as given, ensuring the angles between planes A and B are properly depicted.

Step 2

Determine the dihedral angle between the planes A and B.

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Answer

To find the dihedral angle between planes A and B:

Identify the normal vectors for both plane A and plane B, based on their surface orientations.
Use the formula: $heta = ext{arccos} rac{ extbf{n}_A ullet extbf{n}_B}{| extbf{n}_A| | extbf{n}_B|}$ where $extbf{n}_A$ and $extbf{n}_B$ are the normal vectors.
Calculate the angle $heta$ which represents the dihedral angle between the two planes.

Step 3

Determine the true shape of surface A.

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Answer

To determine the true shape of surface A:

Project the outline of surface A onto a horizontal plane to see its true dimensions.
Use the rabatment method to unfold the shape, allowing for accurate measurement and depiction.
Ensure that elevations and angles are consistent with the plan view, retaining all scale and projection standards.

Step 4

Determine the projections of movement path (d).

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Answer

To find the projections of the stuntman's movement path:

Start from point S which is on surface A.
Trace the path down to the intersection of surfaces A and B, marking the location of this line.
From this intersection, determine the inclination of the path down to surface B and indicate its completion on both elevation and plan views.
Continue from surface B to surface C, repeating the projection process for the shortest distance down to the ground.

Fig. B-1 shows the plan and elevation (excluding hidden detail) of the structure - Leaving Cert DCG - Question B-1 - 2013

Worked Solution & Example Answer:Fig. B-1 shows the plan and elevation (excluding hidden detail) of the structure - Leaving Cert DCG - Question B-1 - 2013

Draw the given plan and elevation of the structure.

Determine the dihedral angle between the planes A and B.

Determine the true shape of surface A.

Determine the projections of movement path (d).

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