Sectional and Auxiliary Views

Learning Objectives

  • Construct a sectional view from the actual intersection between a cutting plane and the object.
  • Distinguish material, holes, voids, geometry beyond the plane, and longitudinal section exceptions.
  • Select among full, half, offset, aligned, revolved, removed, and broken-out sections.
  • Explain why cutting-plane bends are normally omitted from an offset section result.
  • Construct primary and secondary auxiliary views using folding lines and perpendicular projectors.
  • Quantify foreshortening and verify that the target surface has reached true shape.
  • Audit sectional and auxiliary drawings for geometry, convention, reference, and dimensioning errors.

Principal orthographic views do not always communicate interior or inclined geometry efficiently. A sectional view reveals selected internal features by imagining that part of the object has been removed. An auxiliary view changes the projection plane so an inclined or oblique surface can be seen in true shape. Both methods remain orthographic: every result must follow a defined line of sight, projector direction, reference line, and distance-transfer procedure.

Project Standards Govern Conventions

Section-line patterns, cutting-plane symbols, hidden-line treatment, longitudinal exceptions, view placement, and auxiliary reference notation vary by discipline and organization. This lesson teaches transferable geometry and review logic; use the project drawing standard for issued work.

1. What a Section View Represents

Cutting Plane

An imaginary plane that identifies where the object is conceptually cut. Its line, identifying letters, and arrows communicate the path and viewing direction.

Section Lining

Thin, evenly spaced lines or an approved material pattern applied only to surfaces physically intersected by the cutting plane.

Four Geometric Categories in a Section

  • Cut material: receives section lining.
  • Void or opening: remains clear even when enclosed by cut material.
  • Geometry behind the plane: may remain visible as object outlines where needed.
  • Geometry removed in front of the plane: is not shown in the resulting view.

Chord Created by an Offset Plane

For a plane at radial offset e cutting a circular boundary of radius R.

c=2R2e2c = 2\sqrt{R^2-e^2}

Variables

SymbolDescriptionUnit
ccChord length intersected by the cutting planemm
RRCircular boundary radiusmm
eePerpendicular offset from the circle centremm

Offset Cut Through a Hollow Sleeve

For an outer radius of 40 mm and a plane offset 24 mm from the centre:

co=2402242=64 mmc_o=2\sqrt{40^2-24^2}=64\text{ mm}

For an 18 mm bore, e>18|e|>18, so the plane does not intersect the bore. The resulting section is a solid 64 mm-wide chord through the sleeve height rather than an annular opening.

Interactive Section Geometry Laboratory

Move the cutting plane continuously through a hollow sleeve. The top-view intersections, outer chord, bore chord, approximate cut area, ligament, and resulting hatching update from one geometric model. Then compare longitudinal and transverse treatment of ribs, webs, shafts, fasteners, and adjacent components.

Cutting planes, actual intersections, hatching, and drawing conventions

Section Geometry and Convention Laboratory

Move a cutting plane through real geometry, distinguish material from void, apply longitudinal exceptions, and audit sectional-view decisions.

Technical drawing viewport

Continuous annular cutting-plane geometry

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CONTINUOUS CUTTING-PLANE GEOMETRY · SECTION A–APLAN / CUT LOCATIONAAOFFSET 0 mmRESULTING SECTION / MATERIAL INTERSECTIONOUTER CHORD 80.0 mmCLEAR BORE 36.0 mmCHORD = 2√(R² − e²) · HATCHED WIDTH = OUTER CHORD − BORE CHORD
Continuous annular cutting-plane geometry. Swipe horizontally to inspect dimensions, annotations, linework, and details at readable drawing scale.

Interpretation limit

The area metric is a didactic extrusion model for the sleeve. It is not a mass-property calculation for an arbitrary solid.

2. Building a Correct Section

Section Construction Workflow

  1. Select a cutting plane that passes through the features needed for the drawing decision.
  2. Draw and identify the cutting-plane line according to the selected standard.
  3. Confirm the viewing direction from the arrows.
  4. Imagine removing material between the observer and the plane.
  5. Project the remaining outlines orthographically.
  6. Identify every surface physically intersected by the plane.
  7. Hatch cut material while leaving holes and voids clear.
  8. Apply longitudinal exceptions and adjacent-part contrast deliberately.
  9. Omit unnecessary hidden lines unless they communicate essential information.
  10. Add dimensions and notes to visible, unambiguous geometry.

Hatching Quality

  • Keep spacing and angle consistent within one component.
  • Vary angle or spacing between adjacent parts.
  • Do not hatch across a hole, slot, bore, or cavity.
  • Break hatching around text or dimensions when required for legibility.
  • Avoid making section lines graphically stronger than object outlines.
  • Use material-specific symbols only when required and clearly defined.

3. Longitudinal Exceptions

Thin structural or fastening features can be misleading when sectioned lengthwise. Hatching a longitudinal rib or web may imply that its broad face represents actual thickness. Many drawing standards therefore show these features in outline without section lining when the cutting plane runs along them. When cut across their thickness, the same features are normally hatched.

Features Commonly Reviewed as Exceptions

  • Ribs and webs
  • Spokes and arms
  • Shafts and pins
  • Bolts, nuts, washers, and similar fasteners
  • Keys and cotters
  • Thin reinforcing plates cut along their length

An Exception Is Not Missing Material

Leaving a longitudinal feature unhatched does not mean the feature is hollow or absent. Preserve its visible outline and apply the convention consistently so the reader understands the geometry.

4. Choosing the Section Method

Seven Section Methods

  • Full section: the entire projected view is sectioned by one plane.
  • Half section: one half shows the interior and the other half shows the exterior of a symmetric object.
  • Offset section: a stepped plane includes non-collinear features and presents them in one continuous section.
  • Aligned section: a radial feature is rotated into the cutting plane by convention.
  • Revolved section: a local cross-section is rotated into the parent longitudinal view.
  • Removed section: a cross-section is placed away from the parent view and referenced clearly.
  • Broken-out section: an irregular local break exposes only a nearby interior region.

Seven-Method Section Builder

Use one reference component to compare all seven section methods. Select the features the section must communicate, inspect the cutting path and result, and solve realistic method-selection cases.

Section selection, cutting paths, conventional rotation, and communication intent

Seven-Method Section View Builder

Compare full, half, offset, aligned, revolved, removed, and broken-out sections using one reference component, then choose the method that best solves each drawing problem.

Technical drawing viewport

Full section comparison drawing

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PARENT VIEW / CUTTING METHODAARESULTING SECTION / CONVENTIONAL PRESENTATION
Full section comparison drawing. Swipe horizontally to inspect dimensions, annotations, linework, and details at readable drawing scale.

Offset and Aligned Sections Are Conventional Results

An offset section is not drawn with visible steps in the result. The selected features are treated as if they lie in one cutting plane. An aligned section rotates a radial feature into the plane before projection. These conventions improve communication but must not imply a literal geometric relationship that does not exist.

Section View Audit

5. Why Inclined Faces Need Auxiliary Views

Auxiliary View

An orthographic view projected onto a plane other than a principal projection plane, normally used to reveal the true shape or true size of an inclined or oblique feature.

A plane surface reaches true shape only when the projection plane is parallel to that surface. In a principal view, an inclined face is foreshortened. The construction begins from a view where the target face appears as an edge. A new folding line is drawn parallel to that edge, and projectors are drawn perpendicular to the folding line.

Foreshortened Area

Simplified area relationship when a planar face is inclined by angle θ to the projection plane.

Aapparent=AtruecosθA_{apparent}=A_{true}|\cos\theta|

Apparent Area of an Inclined Rectangular Face

A 120 mm × 70 mm face has true area 8,400 mm28{,}400\text{ mm}^2. At an inclination of 37°:

Aapparent=8,400cos376,708 mm2A_{apparent}=8{,}400\cos37^\circ\approx6{,}708\text{ mm}^2

The smaller principal-view area is not a change in the object; it is projection foreshortening.

6. Primary Auxiliary Construction

Primary Auxiliary Workflow

  1. Identify the principal view where the target surface appears as an edge.
  2. Draw folding line X1Y1X_1-Y_1 parallel to that edge.
  3. Draw projectors perpendicular to X1Y1X_1-Y_1 from every controlling vertex and feature centre.
  4. Transfer distances from the related principal view along those projectors.
  5. Connect corresponding points in sequence.
  6. Add holes, slots, centre marks, and dimensions only after the true-shape boundary is established.
  7. Verify that known right angles, parallel edges, and circles recover their true geometry.

Folding-Line Distance

Moving the folding line closer to or farther from the parent view changes drawing placement only. It must not change the size or shape of the auxiliary result. If geometry changes when the folding line moves, distances are being transferred incorrectly.

7. Secondary and Partial Auxiliary Views

A surface oblique to all principal planes may not appear as an edge in any principal view. A primary auxiliary is first constructed to create an edge view. A second folding line parallel to that edge then establishes a secondary auxiliary plane parallel to the target surface. When only one feature requires clarification, a partial auxiliary view can reduce clutter.

Primary and Secondary Auxiliary Studio

Adjust face inclination, folding-line placement, projector accuracy, secondary obliquity, and partial-view extent. The studio quantifies apparent area and deliberately introduces projector error so the visual consequences can be diagnosed.

Folding lines, perpendicular projectors, distance transfer, and true-shape recovery

Auxiliary View Construction Studio

Construct primary and secondary auxiliary views, quantify foreshortening, introduce controlled projector errors, and audit projection logic.

Technical drawing viewport

Primary auxiliary view construction

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PRIMARY AUXILIARY TRUE-SHAPE CONSTRUCTIONFRONT VIEW · TARGET FACE APPEARS AS AN EDGEEDGE VIEW OF INCLINED FACEABREFERENCE X–YFOLDING LINE X₁–Y₁ PARALLEL TO TARGET EDGETRUE SHAPE 120 × 70 · Ø30CONSTRUCTION INVARIANTX₁–Y₁ ∥ edge view of face; projectors ⟂ X₁–Y₁; transfer depth distances from the related principal view. Folding-line distance changes placement, not true shape.
Primary auxiliary view construction. Swipe horizontally to inspect dimensions, annotations, linework, and details at readable drawing scale.

Do Not Stretch a Foreshortened Face

An auxiliary view is not a visually corrected or scaled copy of an inclined polygon. Each point must be projected normally and transferred from the correct source view.

Auxiliary View Audit

Key Takeaways
  • A section is controlled by actual plane-object intersections, not by visual approximation.
  • Hatch only cut material; keep holes and voids clear.
  • Longitudinal ribs, webs, shafts, and fasteners require deliberate convention review.
  • Full, half, offset, aligned, revolved, removed, and broken-out sections solve different communication problems.
  • True shape appears only on a projection plane parallel to the target surface.
  • Auxiliary projectors are perpendicular to the folding line, and distances transfer from a related view.
  • A secondary auxiliary may be required before an oblique face reaches true shape.