***Assignment Soft Copy Email to “[email protected]” All students are advised to keep a duplicate copy of all work submitted for reference. Please keep this cover and any marked pages! 學生姓名 Student Name : 聯絡電話 Contact Number : 電郵地址 Email Address : 課程名稱 Program Name :  Please  HND in BSE HND in Cons HND in Civil 科目名稱及編號 Module Code & Name : B5U03 Applied Mathematics for Construction and the Built Environment 講師姓名 Lecturer : Mike Chan/Dr. Peter Kwan 第一次上課日期 1st lesson Date: 派發日期 Issue Date: 遞交限期 Submission Deadline : 遞交日期 Submission Date :2 功課交收紀錄 Assignment Submission Records Attention  All assignments need to be submitted within 90days after distribution.  If needed, students can apply for a 30-day extension to the college’s staffs. (ONLY 1 extension per module)  Deferral application form should be handed in 10 days before deadline.  To be efficient, please keep this cover and the marked pages after amendment.  Late submission is not allowed. Any late submission will be charged HK$500 administration fee and students need to redo the new term’s assignment in the next intake.  All assignments must be submitted in both hard and soft copies (USB or Email to “[email protected]).  No plagiarism is allowed. If there is any plagiarism found, we will follow the procedures stated in the admission pack. If you have any enquiries, please feel free to contact our staffs. Submission Requirement Font Times New Roman Font Size 12 Spacing Single Line Spacing Margin 2 centimeters (Left-side of page only) Printing Double-sided Number of Words (Approx.) 7,500 words & at least 3 pages of answers to each questions 學生 / 導師交回功課 Submission or Take Away 日期 Date 負責職員簽處 Staff Signature 1. Student – 1st Submission 2. Lecturer – 1st Take Away 3. Lecturer – 1st Marking Completed 4. Student – 1st Take Away (Amendment) 5. Student – 1st Amendment Completed 6. Lecturer – 2nd Take Away 7. Lecturer – 2nd Marking Completed 8. Student – 2nd Take Away (Amendment) 9. Student – 2nd Amendment Complete 10. Lecturer – 3rd Take Away 11. Lecturer – 3rd Marking Completed 12. Student – 3rd Take Away ( Amendment) 13. Student – 3rd Amendment Completed 14. Lecturer – 4th Take Away 15. Lecturer – 4th Marking Completed3 Assessor's comments Qualification HND Assessor name Mike Chan/ Dr. Kwan Second Assessor Unit number B5U03 Learner name Assignment title Applied Mathematics for Construction and the Built Environment Marking *FOR REFERENCE ONLY Task Subtask 1 1.1 1.2 1.3 1.4 1.5 Comment: 2 2.1 2.2 2.3 2.4 2.5 Comment: 3 3.1 3.2 3.3 3.4 3.5 Comment: 4 4.1 4.2 4.3 4.4 4.5 Comment: 5 5.1 5.2 5.3 5.4 5.5 Comment: 6 6.1 6.2 6.3 6.4 6.5 Comment: 7 7.1 7.2 7.3 7.4 7.5 Comment: *Please  below if achieved. M1 M2 M3 D1 D2 D3 Overall Grade Marker Signature * Grading will not be accepted if there is no signature by the Marker.4 Grading criteria Achieved? Learner feedback Assessor feedback Action plan Assessor signature Date Learner signature Date5 INTERNAL VERIFICATION – ASSESSMENT DECISIONS Award HND Assessor Mike Chan / Dr. Kwan Unit(s) Unit 3 Applied Mathematics for Construction and the Built Environment Assignment title: Applied Mathematics for Construction and the Built Environment Learner’s name: Which criteria has the assessor awarded? Pass Merit Distinction Do the criteria awarded match those targeted by the assignment brief? Y/N* Details Has the work been assessed accurately? Y/N* Details Is the feedback to the learner:  Constructive  Linked to relevant grading criteria  Identifying opportunities for improved performance Y/N* Details Does the grading decision need amending? Y/N* Details Remedial action taken: Internal Verifier name Internal Verifier signature Date Confirm Action completed Assessor signature Internal verifier signature6 Assignment front sheet Learner name Assessor name Mike Chan / Dr. Kwan Date issued Completion date Submitted on Qualification Unit number and title HND in Construction and the Built Environment HND in Construction and the Built Environment (Building Services Engineering) HND in Construction and the Built Environment (Civil Engineering) Unit 3 Applied Mathematics for Construction and the Built Environment Assignment title Applied Mathematics for Construction and the Built Environment In this assessment you will have opportunities to provide evidence against the following criteria. Indicate the page numbers where the evidence can be found. Criteria referenc e To achieve the criteria the evidence must show that the student is able to: Task no. Evidenc e P1.1 Determine resource requirements for construction projects. 1.1 P1.2 Perform calculations for project planning and cost analysis. 1.2 P2.1 Solve surveying problems. 2.1 P2.2 Perform calculations to support setting out procedures. 2.2 P3.1 Compile construction data for statistical purposes. 3.1 P3.2 Present construction data in appropriate formats. 3.1 and 3.2 P3.3 Use statistical methods to solve problems involving estimation, prediction and quality control. 3.2 and 3.3 P4.1 Solve engineering problems using vector analysis. 4.17 P4.2 Solve engineering problems using calculus. 4.2 M1 Identify and apply strategies to find appropriate solutions. 1.2 M2 Select/design and apply appropriate methods/techniques. 4.1 M3 Present and communicate appropriate findings. 3.1 D1 Use critical reflection to evaluate own work and justify valid conclusions. 3.3 D2 Take responsibility for managing and organizing activities. 1.2 D3 Demonstrate convergent/lateral/creative thinking. 1.1 Learner declaration I certify that the work submitted for this assignment is my own and research sources are fully acknowledged and agreed that once successfully submitted to Hong Kong College of Engineering, it is deemed the property of Hong Kong College of Engineering. Learner signature: Date:8 Assignment brief Qualification HND in Construction and the Built Environment HND in Construction and the Built Environment (Building Services Engineering) HND in Construction and the Built Environment (Civil Engineering) Unit number and title Unit 3 Applied Mathematics for Construction and the Built Environment Start date Deadline Assessor name Mike Chan / Dr. Kwan Assignment title Applied Mathematics for Construction and the Built Environment The purpose of this assignment is to: Outcome 1: Be able to apply analytical methods to construction problems. Outcome 2: Be able to apply analytical methods to surveying and setting out procedures. Outcome 3: Be able to apply statistics to construction problems. Outcome 4: Be able to apply analytical methods to engineering problems. For all the following tasks, please show all the steps clearly in the solution and justify the use of relevant theories, formulae, techniques, etc. Task 1 Scenario: In a construction project, the equipment and materials are some of the main resources. The equipment may include loaders, dozers, etc. and the material may include oil, tires, spare parts, etc. A construction project leader should determine the resource required, i.e. equipment and materials required. In the following cases, the calculations to determine resource (e.g. material) requirements are faced. Task 1.1 (P 1.1, D3) A bulldozer is estimated to cost $86,000 new and to have a useful life of 5 years with a salvage value of $14,000. The company believes that a realistic MARR would be 10%. Taxes, insurance, and storage should amount to an additional 8%, which results in an overall cost of money of 10 + 8, or 18%. To recover ownership cost, what is the appropriate amount per hour that must be charged for the equipment usage if the expected use rate of the equipment is 1,200 hours per year? For D3, you should assess whether the hourly charge for the bulldozer is appropriate, and provide an evaluation of how change in MARR, taxes, insurance, and storage cost, and yearly usage of the bulldozer can affect the ownership cost. You need to provide a detail evaluation for each factor. Scenario: In project planning, assuming that construction of a power station will take three years. The cost of construction is $1.2 million and it is equally spread over three years ($400,000 in year 1 and $400,000 in the following year 2 and year 3). We also assume that the power station has an operating life of 18 years. The entire project, therefore, spans 21 years. To simplify matters we assume that there is no inflation during the entire life of the project, and that all benefits and costs are certain as assumed. We also presume that during the 18 years of the power station operation the structure must be maintained at some costs. These9 operating costs are $50,000 per year. As for benefits, the power station project will produce 5,000 MWH of electricity each year (after construction) at a cost of $0.05 KWH. This cost represents a savings of $0.02 per KWH over the next best method of electricity generation. These savings in electricity cost constitute a benefit. The power station will also produce a reservoir for recreation. We assume that there will be 50,000 person days per year of recreation benefits and that the value of these recreation benefits is $1.00 per person per day. . Task 1.2 (P 1.2, M1, D2) Initially, the annual total benefits and total costs for the power station project should be calculated. You are also requested to perform calculations for cost analysis on Net Present Value (NPV) for the project whole life span of 21 years for annual interest rate is a) 8% b) Assuming the interest rate is 6% per annum, how much the cost of saving per KWH can the power company adjust such that she still maintain a profit on the NPV at the end of the 21 years span? The formula used to calculate the NPV is: where B represents benefits in the project C represents costs in the project r means the annual interest rate t refers to the number of year in the project life span For M1, you should identify and apply appropriate theories of cost analysis. Use the benefit-cost-ration (BCR) to determine what annual interest rate is justifiable to demonstrate the construction of the power station is a worthwhile project. It is assumed that the annual interest rate remains the same throughout the project life span. The formulae for the BCR is given as follow: where B represents benefits in the project C represents costs in the project r means the annual interest rate t refers to the number of year in the project life span BCR is larger than 1 implying the project is a worthwhile project. Because the benefits of the project exceed the project cost when BCR > 1 at the minimum acceptable rate of return (MARR). For D2, Plan, manage and organize calculation, diagrams and substantial activities of organization a building of a power plant. The calculations and planning should include the depreciation, change in interest rate, change in operation costs, labor costs throughout the power plant life span, the net present value of all concerned items of the power plants, a thorough optimization plan on the plant evaluation and the developed statistical data supporting the sustainability of the plant operation. Interest10 Task 2.1 (P 2.1) (a) As an engineer, you are requested to solve this surveying problem. Calculate the area and side-widths of the cross-section in the following figure. Scenario: In the geometric design of roads, drains, etc., the setting out of curves is an important aspect of the engineer’s work. An engineer may use trigonometry to support setting out as follows. Task 2.2 (P 2.2) You need to perform calculations to support the setting out of a horizontal curve. Two straights intersecting at a point B have the following bearings, BA 270°, BC 110°. They are to be joined by a circular curve which must pass through a point D which is 150m from B and the bearing of BD is 260°. Determine (a) the required radius and (b) the tangent lengths. Task 3 Scenario: As for environmental protection measure to measure the efficiency of a gas combustion, thirty eight laboratory measurements are made of the work developed by combustion of gases within an enclosed container. Task 3.1 (P 3.1 and 3.2, M3) . The initial condition of a volume of 2,5 in3 is measured for each test. The test results of work developed by11 combustion of gas are provided as follows: 76, 78, 81, 82, 84, 84, 86, 86, 87, 88, 88, 88, 89, 91, 91, 92, 92, 92, 94, 94, 98, 101, 103, 103, 103, 104, 104, 106, 108, 108, 112, 113, 114, 116, 116, 118, 118, 119 (i) Develop histograms diagram for work by gas combustion using an appropriate cell size to present the data such that an acceptable shape of distribution can be obtained. (ii) Identify the relative frequency histogram of work by gas combustion. For M3, you should use properly statistical language and a range of methods of presentation such as tables and diagrams. Scenario: As an engineer, presentation of construction data and use of statistical methods to solve problems involving estimation are essential. Use probability functions such as mean, variance, standard of deviation, and covariance to solve the problem. Task 3.2 (P3.3) A sample of five tests was taken to determine the unconfined compression strength (in tons/foot2) of soil, with the test results shown in table 3.2. Table 3.2 Soil strength of sampled soil Sample number Strength of tested soil (Tons/foot2) 1 2.8 2 3.5 3 6.9 4 4.6 5 4.3 (i) Compute the variance and standard deviation of the soil strength. (ii) Use coefficient of variation to determine the safety of the soil when it is used in a site construction. Scenario: As an engineer, use of statistical methods to solve problems involving prediction and quality control is essential. Use probability estimation and confidence level in sampling distribution to answer task 3.3. Task 3.3 (P 3.3, D1) Analyse the probability distributions for discrete and continuous data with the following situations. a) Concrete blocks are tested and it is found that, on average, 7% fail to meet the required specification. To pick up 9 concrete blocks from a batch of concrete blocks in a construction site, , determine the probabilities that less than three blocks out from the chosen 9 concrete blocks will fail12 to meet the specification. b) A construction company wants to recruit a technical assistant to work in a new site and the offered salary is HK$11,500. Current research has indicated that the average monthly income for a technical assistant in construction industry is above 13K Hong Kong dollars. It is also known that the standard deviation of income is $9000. A random sample of 30 technical assistants’ income is shown in Table 3.3. Use sample data from the table to predict whether the construction company is able to recruit the assistant? Use the level of confidence to support your claim on this recruitment matter. i) Use z value to predict the chance of hiring a technical assistance using an offered salary of HK$11,500. ii)Applying the z value theorem, determine how much monthly income would be able to recruit a new technical assistance, by the construction company, to work in the new site with a chance of 90% successful. The formula for finding the z value is given as follows: is the sample mean. The z value table of normal sampling distribution is shown in Appendix 1. Table 3.3 Sample of monthly income of technical assistance 13800 16500 18500 12500 12000 11800 11200 9800 14500 14300 11800 16500 10050 13600 11500 12800 15500 10900 9600 13900 10800 8900 20000 15000 11300 11600 11800 12800 13500 12800 For D1 question – From the z value equation, discuss the difference of the sampling distribution if z value computed is to represent a large population while the sample size taken is 40. The degree of freedom of the sampling distribution would be a main issue. Use data in Table 3.3 for discussion. Validate your conclusion when small sample of data is going to be applied to a large population which represents the whole technical assistance employment sector in construction industry in Hong Kong. Task 4 Scenario: In a construction project, vector analysis is required to solve problems in engineering mechanics.13 Task 4.1 (P 4.1, M2) Solve the following engineering problem using vector analysis. P4.1: The floor crane and the driver have a total weight of 1135 Kg with a center of gravity at G . (a) If the crane is required to lift a 227-Kg drum, determine the normal reaction on both the wheels at A and both the wheels at B when the boom is in the position shown. (b) Determine the largest weight of the drum that can be lifted without causing the crane to overturn when its boom is in the position shown. (Hint: Draw the free body diagram for the crane system first.) Figure 4.1 M2 – Apply relevant theories and techniques, with justification, analyze the shear forces and bending moments exerted on the base of the floor crane when the drum is at the position shown, then draw the shear forces and bending moment diagram14 Scenario: In a construction project, a slope excavation is shown by change of slope shape. Use calculus to find the area enclosed by curves represented the prior and final slope shape as shown in Figure 4.2 Task 4.2 (P 4.2) The two slope shapes were represented by two curves y=x2 and y2=8x. Use integral calculus to the area shown by the shaded lines in Figure 4.2. In this area is rotated 360°about the x-axis, determine the volume of the soil of revolution produced. The volume of revolution V, obtained by rotating area A through one revolution about the x-axis is given by the following expression: Figure 4.215 Appendix 1 – z value table16 Assignment Guideline Qualification HND in Construction and the Built Environment HND in Construction and the Built Environment (Building Services Engineering) HND in Construction and the Built Environment (Civil Engineering) Unit number and title Unit 3 Applied Mathematics for Construction and the Built Environment Assessor name Mike Chan / Dr. Kwan To achieve the different criteria, the student should fulfill the related requirement as shown: Pass Criteria and Related requirement – A pass grade is achieved by meeting all the requirements in the assessment criteria for pass for each task. Merit Criteria and Related requirement –A merit grade is achieved by meeting all the criteria for M1, M2 and M3 plus all pass criteria. Distinction Criteria and Related requirement–A distinction grade is achieved by meeting all the criteria for D1, D2 and D3 plus all pass criteria and all merit criteria. Outcome (Pass outcome - extract from Outcome from course document) Possible Evidence (Given by Lecturer to guide students how to meet the criteria of outcome & this evidence will be used for assessment of the assignment) Pass Criteria P1.1 Determine resource requirements for construction projects.  Estimate the lubricant oil required and tire cost. P1.2 Perform calculations for project planning and cost analysis.  Undertake cost analysis. P2.1 Solve surveying problems.  Estimate the cross sectional area and use trigonometry to determine the coordinates of a station. P2.2 Perform calculations to support setting out procedures.  Use trigonometry to analyze setting out problems. P3.1 Compile construction data for statistical purposes.  Compile data systematically for statistical purposes. P3.2 Present construction data in appropriate formats.  Present statistical data systematically and clearly in tables, diagrams, etc. P3.3 Use statistical methods to solve problems involving estimation, prediction and quality control.  Use statistical methods such as significance testing to solve problems involving estimation, prediction and quality control. P4.1 Solve engineering problems using vector analysis.  Use vector analysis to solve problems in engineering mechanics. P4.2 Solve engineering problems using calculus.  Use calculus to solve engineering problems. Merit Criteria M1. Identify and apply strategies to find appropriate solutions  Identify and apply appropriate theories of cost analysis and then compare and justify the17 choice from the three investment alternatives. M2. Select/design and apply appropriate methods/techniques  Select, with justification, and apply relevant theories and techniques of shear forces and bending moments on beams. M3. Present and communicate appropriate findings  Use properly statistical language and a range of methods of presentation such as tables and diagrams. Distinction Criteria D1. Use critical reflection to evaluate own work and justify valid conclusions  Make and test the relevant discrete or continuous data and then justify valid conclusions. D2. Take responsibility for managing and organizing activities  Plan, manage and organize calculation, diagrams and substantial activities. D3. Demonstrate convergent/lateral/creative thinking  Show that effective thinking has taken place in unfamiliar contexts, i.e. evaluating how change in different parameter can affect the ownership cost of a bulldozer.