(a) The plate is subjected to the two forces at A and B as shown in the Figure below. If ?= 45°, determine the magnitude of the resultant of these two forces and its direction measured clockwise from the horizontal. (5 marks) (b) Determine the angle of for connecting member A to the plate so that the resultant force of FA and FB is directed horizontally to the right. Also, determine the magnitude of the resultant force. (5 marks)
48321 ENGINEERING MECHANICS (Autumn 2021) ASSIGNMENT 2 Due date: 16 April 2021, 11:59 PM Note: • The submission should show all the detailed working or calculation steps not just short answers, otherwise full marks will not be awarded even if the answers are correct. • If you are submitting a scanned copy or an image file, the work sheet should be clear and legible otherwise full marks may not be awarded. • Wherever applicable, all the solutions should first start with the FBD. Without FBD, full marks will not be awarded. • Use the same nomenclature for calculations as given in the questions. For example: the notation for support reactions should be Ax, Ay, Az, Bx, By, Bz etc as used in the question. Do not use notations of your own to be consistent for markings. • The report must be submitted by including Assignment Cover Page. Question 1 (10 marks) (a) The plate is subjected to the two forces at A and B as shown in the Figure below. If θ= 45⁰, determine the magnitude of the resultant of these two forces and its direction measured clockwise from the horizontal. (5 marks) (b) Determine the angle of for connecting member A to the plate so that the resultant force of FA and FB is directed horizontally to the right. Also, determine the magnitude of the resultant force. (5 marks) Question 2 (10 marks) Determine the magnitude of the vertical force acting on the tower (along z-axis) due to the three cable forces FAB, FAC, and FAD using unit vector in Cartesian coordinate system. Question 3 (10 marks) Determine the force (F) in each member of the Pratt truss, and state if the members are in tension or compression. Show FBD and calculation steps for all the calculations. Question 4 (10 marks) Determine the force in members BC, CH, GH and CG of the truss, and state if the members are in tension or compression. Show appropriate FBD and calculation steps. Question 5 (10 marks) Determine the force in members KJ, NJ, ND, and CD of the K truss. Indicate if the members are in tension or compression. Hint: Use sections aa and bb. Question 6 (10 marks) Determine the force in each member of the truss if the load P=10 kN and state if the members are in tension or compression. Question 7 (10 marks) a) Determine the force required to hold the 250 kg mass in equilibrium. (5 marks) b) The principles of a differential chain block are indicated schematically in the figure. Determine the magnitude of force P needed to support the 5000 N force. Also, find the distance x where the cable must be attached to bar AB so the bar remains horizontal. All pulleys have a radius of 60 mm. (5 marks) Question 8 (10 marks) The Figure below shows a bent beam supporting a staircase with pin support at A and roller support at D. Determine the support reactions, axial force, shear force and bending moments. Question 9 (10 marks) The dimensions of the dam storing a water to a height of 10 m is shown in the Figure. Determine the following: a) Magnitude of the resultant force due to water pressure Fp, location of the Fp from the base of the dam and the overturning moment caused by the Fp about O. b) Calculate the stabilising moment caused by the weight of the dam about O. c) Is the dam safe from over-turning? If the dam does not meet the minimum factor of safety of 3.0 then, what are your suggestions to increase the stability of the dam to over 3.0 with reasons? Assumed concrete density of 2,500 kg/m3 and water density of 1,000 kg/m3. Question 10 (10 marks) Determine the support reactions of the beam shown in the figure below. Draw the shear and bending moment diagrams for the compound beam. The beam is pin-connected at E and F.