Lesson Notes By Weeks and Term v3 - Senior Secondary 3
Scalling Enlargement and Reduction
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Scalling Enlargement and Reduction
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Subject: Building Construction
Class: Senior Secondary 3
Term: 1st Term
Week: 1
Theme: Building Dawing
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AutoCAD is a powerful commercial software application for 2D and 3D computer-aided design and drafting, widely used in architecture, engineering, and construction (AEC) industries globally, including Nigeria. It allows users to create precise digital drawings more efficiently than manual drafting.
Relevance to Scaling: Drawing at 1:1 Scale: In AutoCAD, objects are typically drawn at their actual (true) dimensions (1:1 scale) in "model space." Layout/Paper Space for Scaling: Scaling is then applied when printing or plotting drawings from "layout space" (or "paper space"). Viewports are used in layout space to display parts of the model space drawing at specific scales (e.g., 1:50, 1:20).
Representative Fraction (RF) or Ratio Scale: Expressed as a ratio (e.g., 1:100, 1:200, 2:1). The first number represents the unit of measurement on the drawing. The second number represents the unit of measurement of the actual object. The units on both sides of the ratio must be the same (e.g., 1 mm on drawing = 100 mm on actual object, or 1 cm on drawing = 100 cm on actual object).
Reduction Scale: When the first number is smaller than the second (e.g., 1:10, 1:50, 1:100, 1:200, 1:500, 1:1000). Commonly used for plans, elevations, sections.
Enlargement Scale: When the first number is larger than the second (e.g., 2:1, 5:1, 10:1). Used for small, intricate details that need to be shown clearly.
Full Scale: When the numbers are equal (e.g., 1:1). The drawing is the same size as the actual object, often used for very small components or prototypes.
Graphical Scale (Bar Scale): A line drawn on the plan that is divided into actual units (metres, millimetres). This scale remains accurate even if the drawing is photocopied or resized, as it scales proportionally with the drawing itself. Enlargement is the process of drawing an object or a detail larger than its actual size. This is essential for showcasing small components that would be illegible or unclear at a reduced or full scale.
When to Use Enlargement Scales: Detail drawings of connections (e.g., roof truss joint, door frame joint). Illustrations of specific components (e.g., a unique window latch, a type of brick bond). Sections through small elements (e.g., a damp-proof course detail, a concrete beam reinforcement detail).
Common Enlargement Scales: 2:1, 5:1, 10:1, 20:
1. Method of Enlargement (Mathematical Calculation): To enlarge an object, multiply its actual dimensions by the enlargement factor (the first number in the ratio).
Worked Example 1: Enlarging a Building Detail Problem: A steel plate used in a column base connection has actual dimensions of 50 mm x 30 mm. Draw this detail at an enlargement scale of 2:
1. Solution: Identify the scale: The scale is 2:
1. This means every 1 unit on the actual object will be represented by 2 units on the drawing.
Calculate drawing dimensions: Actual length = 50 mm Drawing length = Actual length × Enlargement factor = 50 mm × 2 = 100 mm Actual width = 30 mm Drawing width = Actual width × Enlargement factor = 30 mm × 2 = 60 mm Draw the detail: The steel plate will be drawn as a rectangle measuring 100 mm by 60 mm.
Label the scale as 2:
1. Reduction is the process of drawing an object or a structure smaller than its actual size. This is the most common form of scaling used in building construction to represent large buildings, sites, and plans on standard drawing sheets.
When to Use Reduction Scales: Site plans (1:200, 1:500, 1:1000) Floor plans, elevations, sections (1:50, 1:100, 1:200)
Location plans (1:2500, 1:5000, 1:10000)
Common Reduction Scales: 1:50, 1:100, 1:
2
0
0. Method of Reduction (Mathematical Calculation): To reduce an object, divide its actual dimensions by the reduction factor (the second number in the ratio).
Worked Example 2: Reducing a Building Plan Problem: A classroom wall is 9 meters long. Draw this wall on a floor plan using a scale of 1:
1
0
0. Solution: Identify the scale: The scale is 1:
1
0
0. This means every 100 units on the actual object will be represented by 1 unit on the drawing. Convert actual dimension to a consistent unit: It's often easiest to work in millimetres (mm) for drawing. Actual length = 9 meters = 9 × 1000 mm = 9000 mm Calculate drawing dimension: Drawing length = Actual length / Reduction factor = 9000 mm / 100 = 90 mm Draw the wall: A line representing the wall will be drawn 90 mm long.
Label the scale as 1:
1
0
0. Alternative approach (more intuitive for some):* If 1 cm on the drawing represents 100 cm (1 meter) on the ground, then 9 meters will be 9 cm on the drawing. 9 m / (100 m/1 drawing unit) = 0.09 m = 9 cm = 90 mm. This involves converting a 2D plan (e.g., a floor plan or elevation) into a representation that shows depth and volume, simulating how the building would look in real life. Common methods include isometric, axonometric, and perspective drawings. For Senior Secondary 3, perspective drawing is most commonly introduced. Perspective Drawing (One-Point and Two-Point): Perspective drawing aims to create an illusion of depth and distance on a flat surface, mimicking how the human eye perceives objects. It uses vanishing points on a horizon line.
Horizon Line (HL): Represents the eye level of the observer.
Vanishing Point (VP): A point on the horizon line where parallel lines receding into the distance appear to converge.
Picture Plane (PP): An imaginary transparent plane between the observer and the object, where the drawing is projected.
Station Point (SP): The position of the observer's eye.
One-Point Perspective: Used when one face of the object is parallel to the picture plane. All horizontal lines perpendicular to the picture plane converge to a single vanishing point on the horizon line. Vertical and horizontal lines parallel to the picture plane remain vertical and horizontal. Steps for a Simple One-Point Perspective of a Room: Draw the Horizon Line (HL) and a single Vanishing Point (VP) on it. Draw the front wall of the room as a rectangle. This rectangle is parallel to the picture plane and is drawn to scale. Draw lines from the corners of this front wall to the VP. These are called orthogonals and represent the receding edges of the room. Determine the depth of the room by drawing a horizontal line across the orthogonals. This line forms the back wall of the room. The distance from the front wall to this line determines the perceived depth. Add details (doors, windows) by projecting them to the VP from their positions on the front or side walls.
Two-Point Perspective: Used when no face of the object is parallel to the picture plane. Two vanishing points are used on the horizon line for horizontal lines receding in two different directions. Vertical lines remain vertical. Steps for a Simple Two-Point Perspective of a Rectangular Block/Room: Draw the Horizon Line (HL) and two Vanishing Points (VP1 and VP2) on it (usually one near each end of the line). Draw a vertical line (leading edge). This represents the nearest corner of the room or block. The height of this line is drawn to scale. Draw lines from the top and bottom of this vertical line to both VP1 and VP
2. These form the receding edges of the room. Determine the width and depth by drawing two more vertical lines (the far corners) between the orthogonals. Connect the tops and bottoms of these new vertical lines to the appropriate vanishing points to complete the top and bottom faces of the room/block. Erase construction lines and darken the outline of the visible surfaces.
Building Design and Planning in Local Communities: Building construction drawings, whether for a modest bungalow in a Nigerian village or a high-rise in a city like Lagos, are always drawn to scale. Architects and draughtsmen use reduction scales (e.g., 1:100, 1:50) to produce floor plans, elevations, and sections, which are then used by local builders and artisans. The ability to read and interpret these scaled drawings is crucial for accurate construction and adherence to design specifications, preventing costly errors and rework often seen in local projects. Material Estimation and Quantity Surveying: Quantity surveyors and building material suppliers in Nigeria rely heavily on scaled drawings to calculate the quantities of materials needed for a project (e.g., number of blocks, bags of cement, length of timber, area of roofing sheets). By understanding the scale, they can convert drawing dimensions back to actual site dimensions to prepare accurate Bills of Quantities, ensuring proper budgeting and procurement of resources for construction sites across the country.
Renovation and Extension Projects: Many older buildings in Nigeria undergo renovation or extension. Often, original plans are either unavailable or in a format that requires updating. Builders or owners might need to measure existing structures and produce new scaled drawings (either reduced for an overview or enlarged for specific details) to plan alterations, such as adding a new room, modifying a kitchen, or repairing a damaged façade. Understanding scaling allows them to accurately represent existing conditions and proposed changes.