Photo AI
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.
Answer
To draw the plan and elevation of the structure:
-
Start with the elevation view:
- Represent the height of the building as 100m.
- Draw the outline based on the dimensions: the width of the base at 50m and the triangular profile.
-
Next, create the plan view:
- Based on the elevation, sketch the silhouette of the building from a top view. Ensure that the angles and edges correspond to those shown in the diagram.
Step 2
Determine the dihedral angle between the planes A and B.
Answer
To find the dihedral angle (φ) between planes A and B:
- Identify the lines of intersection of the two planes in the auxiliary view.
- Use the formula for the dihedral angle based on the normals of the two planes: an( rac{φ}{2}) = rac{||n_1 imes n_2||}{n_1 ullet n_2} where and are the normals to planes A and B, respectively.
- Calculate the required angle using the derived lengths for further calculations.
Step 3
Determine the true shape of the vertical surface A.
Answer
To determine the true shape of surface A:
- Start with the given dimensions and plan view of surface A.
- Use the method of rotation to represent surface A in such a way that all points lie in the same plane.
- Apply the relevant transformations to ensure that the shape is correctly represented when viewed directly.
Step 4
Determine the projections of movement path (S to A, A to B, B to C, and C to ground).
Answer
To compute the path the stuntman travels:
-
Location of line from S, per to line of intersection on T.S. of surface A:
- Identify point S and draw a vertical line to the intersection.
-
Location of above line in elevation:
- Project the vertical line onto the elevation.
-
Completion of path in elevation:
- Connect the points to create the pathway for the stuntman from surface A to B and then down to C.
- Ensure that all paths maintain the shortest possible route.