Sectional Views of Solids: Sectional Plane Perpendicular to HP

---

1. Classification of Cutting Planes Perpendicular to HP

When a cutting plane is perpendicular to the Horizontal Plane (HP), it is seen as an edge view (straight line) in the Top View. There are two standard orientations:

1. Sub-Case A: Perpendicular to HP and Parallel to VP
2. Sub-Case B: Perpendicular to HP and Inclined to VP (at angle $\phi$)

---

2. Sub-Case A: Perpendicular to HP and Parallel to VP

In this orientation:

• Top View (on HP): The cutting plane appears as a single straight line parallel to the $XY$ line (Horizontal Trace, $HT$).
• Front View (on VP): The cut surface is projected directly onto the VP, forming the Sectional Front View.
• Golden Rule: Because the cutting plane is parallel to the Vertical Plane, the Sectional Front View directly displays the TRUE SHAPE OF THE SECTION!

                FRONT VIEW (Elevation)
                +-------------------+
                |///////////////////|  <-- True Shape of Section directly in FV
                |///////////////////|      (Hatched at 45 deg)
            ----+-------------------+---- XY
                
                TOP VIEW (Plan)
            ----+-------------------+----
            Cutting Plane S ───────────── S (Parallel to XY line)

---

3. Sub-Case B: Perpendicular to HP and Inclined to VP (by angle $\phi$)

In this orientation:

• Top View (on HP): The cutting plane appears as an inclined straight line making angle $\phi$ with $XY$ (Horizontal Trace, $HT$).
• Front View (on VP): Appears as the Sectional Front View, but its dimensions are foreshortened (compressed horizontally).
• True Shape of Section: NOT visible in either the Front View or the Top View! An Auxiliary View must be drawn parallel to the cutting plane.

                         FRONT VIEW (Sectional Elevation - Foreshortened)
                               /\
                              /  \
                             / 1' \
                            / /  \ \  (Hatched apparent section)
                        ---+--------+--- XY
                           |        |
                         TOP VIEW
                           |   / S (Cutting Plane at angle phi to XY)
                           |  /
                           | / (Points 1, 2 on edges)
                           |/
                           S

---

4. Step-by-Step Procedure to Construct True Shape of Section

Given: Solid with axis vertical, cutting plane perpendicular to HP and inclined at angle $\phi$ to VP.

Step 1: Draw Standard Projections

• Draw the normal Top View and Front View of the given solid in light construction lines ($3\text{H}/4\text{H}$).

Step 2: Draw the Cutting Plane in Top View

• Draw line $S\text{---}S$ at the specified angle $\phi$ to $XY$ at the given offset distance from the axis in the Top View.
• Add directional arrows pointing towards VP (in the line of sight for the Front View).
• Label the cutting points where $S\text{---}S$ slices the base edges and lateral edges as $1, 2, 3, \dots, n$.

Step 3: Construct the Sectional Front View

• From each cut point $1, 2, 3, \dots$ in the Top View, project vertically upward to intersect the corresponding edges in the Front View to locate points $1', 2', 3', \dots, n'$.
• Connect points $1', 2', 3', \dots, n'$ sequentially.
• Hatch the enclosed area with thin lines at $45^\circ$ (Type B lines).
• Darken the remaining portion of the solid.

Step 4: Construct the True Shape of the Section (Auxiliary View Method)

1. Draw a new auxiliary reference line $X_1Y_1$ parallel to the cutting plane line $S\text{---}S$ at any convenient distance.
2. From each cut point $1, 2, 3, \dots$ in the Top View, project lines strictly perpendicular to $X_1Y_1$.
3. Measure the vertical height of each point $1', 2', 3', \dots$ above the $XY$ line in the Front View.
4. Transfer these heights along the corresponding perpendicular projectors, measuring outward from the $X_1Y_1$ line:

5. Join points $1_T, 2_T, 3_T, \dots$ with solid lines and fill with $45^\circ$ hatching lines.
6. The resulting polygon is the TRUE SHAPE OF THE SECTION.

---

5. Summary of Key Exam Points

1. Edge View Location: When a plane is perpendicular to HP, its edge view (line view) is strictly in the Top View.
2. True Shape Condition:
   • If cutting plane is $\parallel$ to VP $\implies$ True shape is the Sectional Front View.
   • If cutting plane is inclined to VP $\implies$ True shape requires an auxiliary projection on $X_1Y_1 \parallel \text{cutting plane}$.
3. Coordinate Transfer Rule:
   • Heights for the true shape are measured from the $XY$ line in the Front View.
   • Spacing along $X_1Y_1$ comes directly from the cut points in the Top View.
4. Hatching Orientation in True Shape: Hatching lines are drawn at $45^\circ$ to the $X_1Y_1$ line.