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Analytical Methods Arithmetical Techniques
This paper consists of three tasks, the first requests calculations to be made for a given area. The second task focuses on Centroids and the centre of gravity on certain shapes. The third task focuses more on volumes and costs for excavations.
Please find detailed information and guidance on how calculations are made and which formulas are used. This paper has been constructed in a used friendly manner.
This task uses the Simpson’s rule to calculate and area of land. The Simpsons rule formula is as follows;
Area = (Strip of width) x [ (Sum of First & Last Ordinates) + 4 (Sum of Even Ordinates) + 2 (Sum of Remaining Odd Ordinates) ]
Please turn overleaf for the calculations and answer.
For the second part of this task, a secondary method has been requested for the calculation of the area of land. The Trapezoidal rule is as follows;
Please turn overleaf for calculations and answer.
This task requests to determine the centre of gravity for two separate shapes. Using the measurements of each shape and an x and y axis graph, I will be able to establish the centre of gravity. The following formula will be used;
Please turn overleaf for calculations and answers for both axis. Also find on second page a graph of the shape and the centre of gravity.
For the second shape in this task the same formula will be used. Due to there being a hole in this shape of a diameter of 20m, the area calculations of this circle will be made and then deducted from the overall value of the shape.
To calculate the circle the following formula will be used;
Please turn overleaf for calculations and answers for both axis bearing in mind the deduction of the circle area. Also find on second page a graph of the shape and the centre of gravity for this shape.
This task request the calculation of the volume excavation needed for a given building shape. The ground slopes downwards at 1 in 20 from level A to level B. Furthermore, a further 1.25m of excavation is required below this drop.
For shape A, D and E the following formula has been used;
½ x W x L x H = Volume
For shape B and C the following formula has been used;
W x L x H = Volume
And for shape F the following formula has been used;
⅓ W x L x H = Volume
All shapes all
Please turn overleaf for calculations and answers for all shapes. Also find on second page the subtotal of the excavation volume needed.
The second part to this task is to determine the manual excavation costs of labour and transportation of the soil. The same formula will be used for both calculations. The following formula will be used;
Hours required =
Cost = Hours x Labourer cost p/h
Hours required =
Cost = Hours x Labourer cost p/h
Adding both values together gives me the total figure of cost for manual excavation. Please turn overleaf for calculations and answer.
The third part of this task requires me to determine the cost for excavating the given shape by a mechanical excavator. The same method and formula is used as above. a conclusion is made to which method is the most efficient economically.
The final part of this task requests the calculation of the entire volume of a concrete beam and two pillars that it rests on. To calculate the concrete beam the following formula is used;
Volume = W x H x L
To calculate the concrete pillars volume, the following formula is used;
Please turn overleaf for calculations and answer of total volume of all three objects.
The use of the Simpson’s rule has given me the ability to determine the areas of shapes of odd nature. This could be extremely helpful on predicting the amount of land available before the tender selection of a project.
I also found the calculations of labour and equipment cost very helpful even though the method of calculation was very simple. This has refreshed my ability to determine how much labour and time I would require for any given job.
The class notes and the ‘Mathematics for technicians’ book by A. Greer where very helpful in the process of calculations in this assignment.
I found task 3a very difficult as I had to visualise the given shape of excavation and also because I had to break the shape down into smaller shapes, it made it more confusing for me. One particular shape was the pyramid (Shape F). At first I calculated it as a Triangular Prism, dividing the volume by half. But after careful analysis I realised that the volume of this shape required division by.
- A. Greer (1983). Mathematics for Technicians. Cheltenham: Stanley Thornes. p59-65.
- Class Notes
- Class Handouts
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