OCD62 UNIVERSITY OF BOLTON WESTERN INTERNATIONAL COLLEGE FZE BENG (HONS) CIVIL ENGINEERING SEMESTER ONE EXAMINATION 2015/2016 ENGINEERING MATHEMATICS AND STRUCTURES MODULE NO. CIE5004 Date: Thursday 14 January 2016 Time: 10.00am to 01.00pm INSTRUCTIONS TO CANDIDATES: There are FIVE questions on this paper. Answer ALL questions. Answer Section A and Section B questions in separate answer books. All questions carry equal marks. Marks for parts of questions are shown in the brackets. This examination paper carries a total of 100 marks. All working must be shown. A numerical solution to a questions obtained by programming an electronic calculator will not be accepted.
Page 2 of 11 Question 1 SECTION A : STRUCTURES a) A three-pin frame is shown in Figure Q1 (a). The frame is supported at A and F by pins and a third pin is positioned at D. There is a vertical load of 15 kn acting at C i. Determine the magnitudes and directions of the vertical and horizontal reactions at A and F. ii. Draw the Bending Moment Diagram. iii. Draw the Shear Force Diagram. (2 marks) (5 marks) (5 marks) 3m 15kN 3m 3m B C D E 4m 4m A 9m F Figure Q1 (a) Question 1 Continued over the page
Page 3 of 11 Question 1 Continued b) Refer to Figure Q1(b). Reproduce the frames shown in the figure. Draw the bending moment diagram and sketch the deflected shape of the frames shown in Figure Q1(b). The relative sizes of the bending moments and deflections should be made clear in your sketches. i i ii. Figure Q1 (b) Frames (8 marks) Total 20 marks END OF SECTION A Please turn the page for SECTION B
Page 4 of 11 Question 2 SECTION B: MATHEMATICS a) The tensions, T1, T2 and T3 in a simple framework are given by the equations: 5T1 + T2 + 3T3 = 12 T1 + 4T2-3T3 = 25 6T1 - T2-7 T3 = 14. Détermine T1, T2 and T3 using Gaussian elimination (10 marks) b) Machines A, B and C make components of steel sections. Machine A makes 45% of the components and Machine B makes 30% of the components. Of those components made by Machine A, 96% are reliable, and of those made by Machine B, 91% are reliable, and of those made by Machine C, 93% are reliable. If a component is picked at random, calculate the probability that it is i. Made by Machine B and is unreliable ii. Made by either Machine A or Machine B iii. Reliable (4 marks) Total 20 marks Please turn the page
Page 5 of 11 Question 3 a) Define what is meant by discrete data with the help of an example (2 marks) b) Determine the mean and standard deviation of the grouped data shown below in the Table Q3 (b). (8marks) Table Q3 (b) Time (hrs.) Frequency(f) 20-24 9 25-29 13 30-34 15 35-39 9 40-44 4 Total 50 c) A service engineer is on call for 5 days out of 7. Whilst on call, the engineer has had to carry out maintenance on a machine on 3 days out of 10. The machine has also needed maintenance on 1 day out of 5 when the engineer has not been on call, this work being carried out by other staff. Calculate the overall probability that the machine requires maintenance on a given day, chosen at random. E1: the engineer is on call E2: the machine requires maintenance Question 3 continued over the page
Page 6 of 11 Question 3 continued Using Baye s Theorem find the probabilities that the engineer is: i. on call on a day when the machine requires maintenance ii. not on call on a day when the machine requires maintenance iii. on call on a day when the machine does not require maintenance iv. not on call on a day when the machine does not require maintenance (10 marks) Total 20 marks Question 4 a) A machine is producing a large number of bolts automatically. In a box of these bolts, 95% are within the allowable tolerance values with respect to diameter and the rest being outside of the diameter tolerance values. Seven bolts are drawn at random from the box. Determine the probabilities that i. No bolt is outside the tolerance value. ii. Two bolts are outside the tolerance value iii. Less than 3 bolts are outside the tolerance value. iv. More than 3 bolts are outside the tolerance value. (4 marks) (4 marks) Question 4 continued over the page
Page 7 of 11 Question 4 continued b) Calculate the number of permutations and combinations there are of: i. five distinct steel bars taken two at a time ii. four distinct steel bars taken two at a time Total 20 marks Question 5 a) The deposition of grit particles from the atmosphere is measured by counting the number of particles on 200 prepared cards in a specified time. The following distribution was obtained: Barriers in use 0 1 2 3 4 Number of instances 18 42 33 5 2 For the above scenario, i. Test the null hypothesis that the deposition of grit particles follows a Poisson distribution at a 0.01 level of significance,. ii. Determine whether the data is too good to be true at a level of confidence of 0.99. (12 marks) Question 5 continued over the page
Page 8 of 11 Question 5 continued b) The time taken to complete a job is known to be normally distributed with Mean 6.40 hours and Standard deviation 1.20 hours. What is the probability that a randomly chosen job will take. i. Less than 7 hours (4 marks) ii. Less than 6 hours (4 marks) Total 20 marks END OF QUESTIONS Please turn the page for the formula sheet
Page 9 of 11 Formula Sheet 1. Mean and Standard Deviation 2. Chi square test 2 ( O E) = E 2 v = (k-m) 3. Baye s theorem 4. Binomial expansion (q+p)ⁿ = qⁿ + nq ⁿ ¹p + n(n-1) qⁿˉ² p² + n(n-1)(n-2)qⁿ ³p³ +... 2! 3! 5. Permutation and Combination ⁿ P = n! ⁿ C = n! (n-r)! r! (n-r)! 6. Normal Distribution 7. Poisson Distribution Please turn the page for the standard tables
Page 10 of 11 Please turn the page
Page 11 of 11 END OF SECTION B END OF PAPER