UNIVERSITY OF BOLTON WESTERN INTERNATIONAL COLLEGE FZE BENG(HONS) MECHANICAL ENGINEERING SEMESTER ONE EXAMINATION 2015/2016 ENGINEERING PRINCIPLES 1

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1 UNIVRSITY OF BOLTON OC49 WSTRN INTRNATIONAL COLLG FZ BNG(HONS) MCHANICAL NGINRING SMSTR ON XAMINATION 2015/2016 NGINRING PRINCIPLS 1 MOUL NO: AM4052 ate: Saturda 16 Januar 2016 Time: 10:00 12:00 INSTRUCTIONS TO CANIATS: There are SIX questions. Answer Two Questions from Part A and Two Questions from Part B. All questions carr equal marks. Marks for parts of questions are shown in brackets. lectronic calculators ma be used provided the data and program storage memor is cleaned prior to the eamination. CANIATS RQUIR : Formula Sheet (attached)

2 Page 2 of 9 Western International College FZ Bng (Hons) Mechanical ngineering Semester One amination 2015/2016 ngineering Principles 1 Module no: AM4052 PART A Q1. In a mechanical sstem, acceleration, velocit and distance are related b the following simultaneous equations: = = = 0 a) press these equations in matri format and determine the inverse of the matri of the coefficients of, and. (12 marks) b) Use matrices method to solve the equations. (8 marks) Total 20 mark Q2. a )The velocit of a car, accelerating at uniform acceleration a m/s 2 between two points is given b v = u + at, where u is its velocit in m/s when passing the first point and t is the time in sec taken to pass between the two points. If v= 21 m/s when t=3.5s and if v=33m/s when t = 6.1s, Use eterminants method to find the values of u and a. (8 marks) Q2 continued over the page

3 Page 3 of 9 Western International College FZ Bng (Hons) Mechanical ngineering Semester One amination 2015/2016 ngineering Principles 1 Module no: AM4052 Q2 continued b) A.C. circuit comprises three closed loops. Appling Khirchoff s law to the closed loops gives the following equations for current flow in mill-amperes 2I 1 + 3I 2 4I 3 = 26 I 1-5I 2 3I 3 = -87-7I 1 + 2I 2 + 6I 3 = 12 Use the Gaussian elimination method to solve for I 1, I 2, I 3. Q3. a) Use partial fractions to epand: ( 2) (12 marks) Total 20 mark (6 marks) b) A drilling machine can have 3 speeds following an arithmetic progression. If the sum of speeds is 15 rev/min and their product is 80 rev/min, determine the net three speeds of the drilling machine. (6 marks) c) The 1 st, 12 th and last terms of arithmetic progression are 4, 31.5 and respectivel. etermine: (i) (ii) The number of terms in the series. The sum of all the terms. (8 marks) Total 20 marks Please turn the page

4 Page 4 of 9 Western International College FZ Bng (Hons) Mechanical ngineering Semester One amination 2015/2016 ngineering Principles 1 Module no: AM4052 PART B Q4. A weight of 400kN is supported b a short concrete column 25cm square. The column is strengthened in the corners b four steel bars of total cross sectional area 6000mm 2 as shown in Figure Q4. Figure Q4. etermine the following if s = 20 c. i) Stresses in the steel (7 marks) ii) Stresses in the concrete (7 marks) iii) If the stress in the concrete must not eceed 6MN/m 2, what area of steel is required in order that the column ma support a load of 650kN? (6 marks) Total 20 marks Please turn the page

5 Page 5 of 9 Western International College FZ Bng (Hons) Mechanical ngineering Semester One amination 2015/2016 ngineering Principles 1 Module no: AM4052 Q5 a) A steel bar which is 6m long,45mm wide and 30mm thick is subjected to an aial pull of 45kN in the direction of its length. The Young s modulus of lasticit and Poisson s ratio of steel bar is 2 X 10 5 N/mm 2 and 0.3. valuate the following: i) The changes in length, breadth and thickness of the given bar (5 marks) ii) Volumetric strain and final volume of the given steel bar. (5 marks) b) A stepped member ABC is subjected to point loads P 1 =65kN, P 2 = 120kN and P 4 = 160kN as shown in Figure Q5b.etermine the net elongation of the member. Assume =210GPa. FigureQ5b. (10 marks) Total 20 marks Please turn the page

6 Page 6 of 9 Western International College FZ Bng (Hons) Mechanical ngineering Semester One amination 2015/2016 ngineering Principles 1 Module no: AM4052 Q6. A simpl supported beam of length 10m, carries the uniforml distributed load and three point loads as shown in FigQ6.etermine: i. Reaction loads at the support ii. raw the shear force diagram for the beam iii. raw the bending moment diagram for the beam iv. Find the position of maimum bending moment. ( 5 marks) ( 5 marks) (5 marks) (5 marks) Total 20 marks N OF QUSTIONS Please turn the page

7 Page 7 of 9 Western International College FZ Bng (Hons) Mechanical ngineering Semester One amination 2015/2016 ngineering Principles 1 Module no: AM4052 FORMULA SHT eterminants - -1 Matrices 1 adja A 1 X A B Series U n = a + (n 1) d n S n = 2 [2a + (n 1) d] U n = ar n-1 S n = S n a(1 r ) 1 r a 1 r 1 U n = a + (n 1)d + 2 (n 1)(n 2)C Binomial (1 + ) n = 1 + n + n(n 1) 2! 2... Validit < 1

8 Page 8 of 9 Western International College FZ Bng (Hons) Mechanical ngineering Semester One amination 2015/2016 ngineering Principles 1 Module no: AM4052 Partial Fractions F() ( a)( b) A B ( a) ( b) F() ( a)( b)( c) A B C ( a) ( b) ( c) Stress Normal σ = P A A = -sectional area Shear τ = P A A = shear area Strain Normal Shear = (Angular isplacement in rads in direction of F) Compound Bars P = P 1 + P 2 P = 1 A A 2 σ 1 1 = σ 2 2, lastic Constants = σ ε, G = τ γ

9 Page 9 of 9 Western International College FZ Bng (Hons) Mechanical ngineering Semester One amination 2015/2016 ngineering Principles 1 Module no: AM4052 V V v v v 2 1