Analyse the statically determinate bar illustrated below by expressing the loading as a single function using Macaulay brackets and the Dirac delta, integrating to find th axial force and integrating again to find the displacements, applying the boundary conditions appropriately. Find the axial force in the bar at point A and the displaceme at point B. The cross section of the bar is constant with EA = 18000 kN. a = 4 m, b = 2 m, c = 2 m and d = 4 m. w1 = 12 kN/m, w2 = 17 kN/m,, P1 = 12 kN and P2 = 19kN. a W2 W1 A L/2 Multiple Choice Answers Multiple Choice Answer: Axial force at point A (kN, tension positive): a. 3.31 b. 31.97 c. 37.33 d. 31 Multiple Choice Answer: Displacement at point B (mm, positive to right): a. 0.0061 b. 0.0395 c. 0.0193 d. 0.0261 L/2 P1 P2

A petrol engine inlet valve is spring-loaded. The valve opens at 360 N closes at 220 N, while the corresponding lengths of springs when it is open is 41 mm and when it is closed is 49 mm. The maximum inside diameter of the spring is 25 mm. Assume the shear yield strength in steel as 400 MPa, shear ultimate strength is 643.2 MPa and shear modulus as 80 kN/mm². Assume the helical compression spring has squared and ground ends, minimum factor of safety, n = 1.5 and spring index, C = 5. Determine for shot-peened wires a) initial compression b) coil diameter d using Zimmerli data, Goodman theory and Langer theory. Select standard size of Washburn & Moen wire c) helical diameter D d) number of actual turns, Na and total turns, Nt e) free length