TOPIC: TRUE SHAPES (LAMINAE)
As it has been discussed that true shapes of solid object could be found by construction(drawings) especially when given the front elevation and the plan in particular, so also can the true shapes of plane figures like triangular laminae (inclined or not) be found.
The method(s) adopted for finding true lengths of lines and true angle of inclination can also be used.
Let us consider some examples with procedure and explanation.
FINDING THE TRUE SHAPE OF A GIVEN INCLINED TRIANGLE
(NOTE: THE PROCEDURE IS GIVEN IN THE RELATED DIAGRAM, CHECK THE PAGES FOR DRAWING)
FINDING THE TRUE SHAPE OF A TRIANGLE WHEN GIVEN THE PLAN AND THE ELEVATION AND THAT ONE EDGE LIES ON THE HORIZONTAL PLANE
1. Draw the given front elevation and plan of the triangle(edge AB rests on the H.P.).
2. Extend A1B1 to any convenient length (B1D). Draw a perpendicular to B1D at D (DE).
3. Extend a line parallel to B1D from C1 and mark the “vertical height” on it from DE to give point F.
4. With centre D and radius DF, draw an arc to touch DE at G.
5. Draw a line perpendicular to B1D from G to touch HJ at K.
A1B1K is the required true shape of the triangle.
FINDING THE TRUE SHAPE OF ANY TRIANGLE AND ITS ANGLE TO THE HORIZONTAL PLANE WHEN GIVEN THE FRONT ELEVATION AND THE PLAN OF THE TRIANGLE
Procedure 1. Draw the front elevation and plan. 2. Draw horizontal line from A1(A1D1) and project the plan of this line, AD. 3. Extend line AD and draw lines parallel tp it from B and C. Draw X1Y1 perpendicular to AD extended at any convenient place. 4. Project an auxiliary elevation A2B2C2 from the plan (project at right angles to X1Y1) making the distance of A2 from the X1Y1 = the perpendicular distance of A1 from XY, etc. 5. Draw a ground line X2Y2 parallel to line A2B2C2 at any convenient place and project an auxiliary plan, making the distance of A3 from X2Y2 = the distance of A from X1Y1, etc.
The triangle A3B3C3 is the required shape.
The true shape of the triangle can also be found by finding the true length of each side in turn.
This was mentioned at the introduction to this lesson.