2.04 Interpret plans, elevations and architectural drawings

Plan and elevation views

Plan and elevation views in technical drawings are projections of a three-dimensional object onto a plane. In this chapter, we explore how this projection is realised in practice.

In the diagram, we are looking down on an object that may be the roof of a building. An axis has been constructed in the direction in which the projection is to be made. The projection plane is set perpendicular to the chosen axis. The projection will be an image of the building seen from one side. Such an image is known as an elevation.

We imagine rays perpendicular to the projection plane that connect each significant point with its image. Thus, each point on the object, which is visible from the chosen direction, has its image in the elevation.

We can make elevations from other directions. Seen from another side, the elevation may be as in the following diagram.

Continuing this procedure, we make an elevation representing the view from the other end of the building.

To complete the elevation drawings, an architectural draughtsperson would include details including the relevant measurements and scale and information about the materials to be used in the construction of the building. 

This elevation shows construction details for a steel shed. The dimensions are given elsewhere in the plans.

 

Dimensioning 3D drawings

As the name suggestions, 3D drawings have three dimensions.  They have a length, width and height, although sometimes the words breadth and depth are used as well.  

In the 2D drawing of a rectangle below, we don't need to mark on all the measurements for all $4$4 sides because we can tell from the markings on the diagram that the side marked with an $a$a, will be of length $8$8cm.  

Similarly in 3D drawings there is no need to mark on every dimension, just enough dimensions to be able to determine all relevant dimensions.  

 

Worked example

Example 1

Determine the dimensions indicated by $A$A and $B$B on the diagram.

The total width is $8$8cm, and we can see widths of $2$2cm and $4$4cm This means that A must be $2$2cm.  

The total length is $15$15 cm, and we can see sub-lengths of $5$5 cm and $5$5 cm already.  This means that $B$B must also be $5$5 cm in length.  

The key to solving these problems is to identify all the lengths that are relevant - and drawing on the diagrams can be a big help.

 

Practice question

Question 1

 

Scale drawings

The art of Technical Drawing for engineers, architects and other disciplines is expected to comply with conventions set out in the Australian Standards, in particular, the Australian Standard AS 1100. In this way, the symbols and styles used are kept reasonably uniform within the country and internationally.

For our immediate purpose, we are concerned with scaling in drawings.

In a scale drawing, an object is represented in a way that reflects, in two dimensions and restricted size, the important features of the object. The essential principle in scaling is that angles are preserved and lengths are held in proportion. Thus, the size usually changes but the shape is maintained in the drawing.

Proportions are indicated by a scale notation $a:b$a:b, meaning a distance of $a$a units in the drawing represents $b$b units in the real object. For example, $1:100000$1:100000 means $1$1 centimetre on the drawing is equivalent to $100000$100000 centimetres (or $1$1 kilometre) in the thing being represented. A scale like this would be typical of a map.

For smaller objects, like a house, the scale might be more like $1:100$1:100 or $1:200$1:200. The precise scale is chosen by the person making the technical drawing to ensure that the representation of the object fits comfortably onto the sheet of paper being used.

Notice that units are not used in a scale. This is because the same unit, whatever it might be, applies to both sides of the proportion.

 

Exploration

A floor plan or building plan is a scaled down representation of a building, including walls, windows, doors, stairs, and other fixtures. This floor plan has a scale bar to determine the true distances between objects. The scale bar represents $2$2 m.

 

The distance between the sink and the dining room table is approximately $3$3 lengths of the scale bar. So the distance between them is $3\times2$3×2 m , or $6$6 m. We can also identify certain rooms by their fixtures. The room in the top left is the kitchen corner as it contains a pantry, oven, sink and stove top.

Rooms that contain a shower, toilet, bathtub and sink can be easily identified as the bathroom or ensuite. An example of such a bathroom is given in the top right of the following floor plan.

Some symbols may be less intuitive than others. Here are some of the most common symbols used in floor plans - there may be others used depending on the architect, but they are often easy to guess.

Fixture	Door	Window	Wall	Stairwell	Shower	Toilet	Sink	Towel rack	Stovetop	Oven
Symbol

Here is the same building plan, but instead of a scale bar the true lengths of objects are given in centimetres:

We can use these lengths to find the dimensions of different rooms, so, for example, the internal dimensions of the bathroom will be $695$695 cm$\times$×$410$410 cm. Using internal dimensions means that measurements do not include the width of the walls.

This is the elevation view of the building, meaning we are looking at it side-on rather than top-down:

If we want to find $A$A, the width of the building, we need to first figure out which wall is shown in the elevation view by matching its features with the correct wall of the floor plan.

The side of the building we want to measure has a single window and a single door, and according to the floor plan, there is only one wall that has both a window and a door - the northern wall. The width of the northern wall is not labelled on the floor plan, but we can tell that it has the same width as the southern walls added together:

Width	$=$=	$25+550+25+680+25$25+550+25+680+25	(adding the lengths labelled on the southern wall)
	$=$=	$1350$1350 cm	(simplifying the addition)

 

So the width of the southern wall and northern wall are both $1350$1350 cm. In other words, $A=13.5$A=13.5 m.

With a scale bar or a scale ratio we can always accurately determine the real-life dimensions of the building or territory from the scale drawing or map, so look for that information first.

 

 

Worked examples

Example 2

Convert the following situation to a proper scale ratio: $5$5 cm on the map is equivalent to $25$25 m in real life.

Think: We need to have our two quantities in the same unit of measurement. Let's convert everything to centimetres. Once we have equivalent quantities, we can write the scale factor.

Do: First, convert to centimetres

$25$25m	$=$=	$25\times100$25×100 cm	$1$1m $=$= $100$100cm.
	$=$=	$2500$2500 cm

Then, rewrite the ratio of $5$5cm to $25$25 m using the same units:

$5$5cm : $25$25m	$=$=	$5$5cm:$2500$2500cm	Using the conversion above.
	$=$=	$5:2500$5:2500	Cancel the units.
	$=$=	$1:500$1:500	Simplify the ratio.

Example 3

The following is a scale diagram of a room using the scale $1:50$1:50.

(a) Find the actual length and width of the room life in metres.

Think: The scale factor of the diagram is $50$50, so the real lengths will be $50$50 times larger. Let's find the lengths and then convert to metres.

Do:

Actual length	$=$=	$19\times50$19×50 cm
	$=$=	$950$950 cm	Divide by $100$100 to convert to metres.
	$=$=	$9.5$9.5 m
Actual width	$=$=	$11.5\times50$11.5×50 cm
	$=$=	$575$575 cm	Divide by $100$100 to convert to metres.
	$=$=	$5.75$5.75 m

(b) Find the actual area of the room in square metres.

Think: We have just calculated the actual length and width of the room in metres, so we can use these to find the area of the room.

Do:

Area	$=$=	$L\times W$L×W
	$=$=	$9.5\times5.75$9.5×5.75 m2
	$=$=	$54.625$54.625 m2

Caution: Notice we have used the converted lengths to find the area. However, we could have used the lengths in the diagram to find the area and then scale the area. To scale the area after the calculation be careful to multiply by the $\left(\text{Scale factor}\right)^2$(Scale factor)2, since both length and width must be scaled. 

(c) What percentage of the room is taken up by the blue rug?

Think: We can calculate the percentage area the blue rug takes up in the scale diagram. The fraction covered by the rug will not change if we scale the picture up or down. 

Do: Find the fraction of the area of the rug over the area of the room and multiply by $100%$100% to express as a percentage.

Percentage rug of room	$=$=	$\frac{\text{area rug}}{\text{area room}}\times100%$area rugarea room​×100%
	$=$=	$\frac{4\times2.5}{19\times11.5}\times100%$4×2.519×11.5​×100%
	$=$=	$\frac{10}{218.5}\times100%$10218.5​×100%
	$\approx$≈	$4.58%$4.58%

(d) If a window that is actually $2$2 m wide was shown on the diagram, how many centimetres wide would the window be in the diagram?

Think: This time we have the actual length and want the length in the drawing, this will be $50$50 times smaller.

Do:

Drawn length	$=$=	$\text{Actual length}\div\text{Scale factor}$Actual length÷Scale factor
	$=$=	$2\div50$2÷50 m
	$=$=	$0.04$0.04 m	Multiply by $100$100 to convert to metres.
	$=$=	$4$4 cm

 

Practice questions

Question 2

Question 3