Number Of Pages:
10     Double-spaced (2250 words)


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Type of Document:
Math/Physics/Economics/Statistics Problem


Academic Level:


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Solution Files(s):




It is construction mathematics,


You are working as a Senior Engineer for a large contractor who is completing a major new roadway in Oldham, Lancashire. You have asked to help various members of the site team with the processing and communicating of the mathematical problems listed below.

Task  1

a) An area of the site has been identified as needing a specific surface treatment due to the vegetation. The area is inaccessible due to the topography of the site but a series of whole circle bearings have been recorded from Station A (300.000m East,200.000n North) and Station B (500m East, 220m North) and are on the enclosed sheet 1 for your designation


Calculate the co-ordinates of each of the points and the area enclosed within the points.


b) A section of the site has a disused canal that requires filling. The canal is width and depth are provided on sheet 2. Soil investigation has identified that angle of repose of the soil is 32°. The project requires that no surplus is produced and that no imported material is used. Calculate the depth of fill that will be required to meet this requirement assuming 95% compaction is achieved.


c) The project has a number of double cantilevered beam. The structural engineer needs to know the location of the point of contra flexure (zero bending) calculate the location to 3 decimal places

Beam 1 BM = -30x2 +210x -210

                        Beam 2 BM = -20x2 +210x -420

d) The site has purchased a new 360˚ excavator at a cost of £125,000. This item of plant has a weekly running cost of £420 and anticipated revenue of £980. Calculate the breakeven point and when a 16% profit is achieved in weeks.

e) Using Matrices check the outcomes for question 1a and 1d.



Task 2


a) The site has a section with a suspended pedestrian bridge with a span of 270m. The sag in the suspension cables (y) is calculated by the following equation


y =


If W = 0.16kN/m calculate y for H = 27.9kN, 54kN and 100kN














Above is the detail of a roof truss arrangement. AF and FE are 2.780m. CF is 3.450m with angles DFE 28° and FED 70°. Calculate the remaining members of the frames lengths


Task 3

a)  The table below shows 30 cube results from Month 2 of the project. Calculate the mean, mode & median of both x and y. Also calculate the standard deviation of the compressive strength of the cubes.

b) Present the data of month 2 density and strength in your chosen format from any software package

c) Calculate the Pearson Correllation Coefficent for the realtionship of compressive strength increasing with density and comment

d) Also test this Hypothesis to a confidence level of 90% by calculating the line of best fit

Compressive Strength (N/mm2)


Density (kg/m3)



41.2 2370
40.0 2350
34.0 2340
37.0 2350
38.7 2360
36.2 2340
39.1 2370
35.2 2350
41.2 2385
43.0 2390
37.1 2345
35.6 2305
36.2 2340
38.3 2400
37.3 2360
40.5 2375
41.2 2375
37.0 2380
36.3 2350
37.8 2335
38.2 2345
40.2 2375
36.7 2320
39.8 2360
39.6 2365
39.2 2350
42.3 2400
41.6 2395
42.3 2385
37.8 2350


Task 4


a) Your potential contracted  pilling company has summarised its quality over the last five years and found,

· 3% of piles fail integrity testing

· 1% of piles fail proof load testing

· 4% of piles are out of tolerance on plan location

Calculate the probability that,

1. A pile fails proof load and integrity testing

2. A pile is out of position and fails integrity testing

3. A pile fails all three tests

b) Your imported stone supplier has 5% non-compliance rate on stone grading’s analysis. From  a sample of 20 deliveries determine the probability that,

1. One sample is non-compliant

2. Two samples is non-compliant

3. All samples is non-compliant

4. All samples are compliant

c) Your materials testing logging system has a serial number with two letters and five digits. Calculate the number of permutations,

d) The movement joints for the project are being supplied by SJG Joints Ltd. In testing they have had 3 defective out of a 125 sampled. If 4 are selected ar random what is the probability of,

1. All four fault free

2. Only one defective

3. Two defective

4. Three Defective

5. All four defective

Task 5


Complete a final section report which evaluates both your analytical and statistical findings from the above questions completed and justifies the techniques adopted to solve such problems. The report should include all questions including research on how trigonometry, algebra and statistics are used in construction linking it to the above questions/solutions.








Plagiarism is a particular form of cheating. Plagiarism must be avoided at all costs and students who break the rules, however innocently, may be penalised.  It is your responsibility to ensure that you understand correct referencing practices.  As a university level student, you are expected to use appropriate references throughout and keep carefully detailed notes of all your sources of materials for material you have used in your work, including any material downloaded from the Internet. Please consult the relevant unit lecturer or your course tutor if you need any further advice.

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