Unit: Scientific and Mathematical Applications for Construction, BTEC Level 1/Level 2 First Diploma in Construction and the Built Environment
Assignment - The Use of Mathematics in Construction
Learning aim: Use mathematical techniques to solve construction problems
Scenario You are working as a trainee quantity surveyor for a local construction company who have been commissioned to design and build a house.
The land is in the form of a trapezium as shown in Figure 1. The footprint of the house to be constructed is 10 m x 8 m. The house will be constructed with a pitched roof, the details of which are shown in Figure 2.
You will deal with all the matters relating to the project where application of mathematical knowledge is required. This would include calculations of areas and volumes, plotting graphs and using algebraic and graphical methods to solve problems.
Before construction work starts, you will carry out calculations to ensure that the materials used are of appropriate strength.
Task 1 For tasks a to e, in addition to calculations, you will need to provide written notes to justify the methods and techniques you used to solve these construction problems.
a) The site is to be cleared before construction work starts. The contractor requires the area calculations before a price is quoted. Calculate the area of land shown in Figure 1.
b) If the topsoil removed is 200 mm thick all over the site, what is the volume of this topsoil?
c) The plot of land is to be fenced using 50 mm diameter hollow posts and safety fencing. The pipes will be painted to protect against the weathering agents. The posts are to be placed on concrete pad foundations of 300 mm x 300 mm x 500 mm.
i. Calculate the surface area required to paint a post of 2.5 in length.
ii. Calculate quantity of concrete required for foundation of one post.
d) Earthworks are to be carried out before construction work could start. You have received quotations from two plant companies A and B. Company A uses a plant that will require 12 hours to complete the job while company B's plant could do it in 7 hours. Applying your knowledge of mathematics, calculate the time required to complete earthworks if your manager decides to employ both companies.
e) Using details in Figure 1 and 2, calculate:
i. area of the roof required for tiling
ii. the pitch of the roof (the angle the slope makes).
f) You have asked the materials' suppliers to test the materials and provide the data so that you could check their suitability. One of the suppliers has provided you with the following data:
|
Stress(N/m2)
|
110
|
101
|
80
|
75
|
55
|
43
|
31
|
|
Strain ε x 10-4
|
5.5
|
5.13
|
4.59
|
3.75 3.6
|
2.61
|
1.58
|
Plot a graph of this data by aking Strain along the X-axis and Stress along the Y-axis. Work out the gradient of this graph (E) and check whether the data and result obey Hooke's law σ = Eε
g) Another supplier has sent you the following test results. Using the given graph, estimate the compressive strength when water ratio is 0.35, 0.45 and 0.8.
Evidence you must produce for this task
You will submit a portfolio containing graphs, diagrams, written descriptions and calculations supported with sketches and illustrations.
You will also provide written notes to justify the methods applied in solving the construction problems.
Apply algebraic and graphical methods to solve two different practical construction problems.
Apply mensuration and trigonometry to solve two different practical construction problems.
Solve a practical construction problem using trigonometric, mensuration and algebraic methods.
Justify the application of algebraic and graphical methods, mensuration and trigonometry to solve a practical construction a problem.