Static Engineering Systems - Assignment Example

QIA) A uniform cross- section beam of length 7m is simply supported at its ends and carries three point loads of l5kN at 2mfrom the left, 25kN at 5m from the left and 35kN at 6m from the left hand side of the beam. a) Calculate the reaction forces. b) Draw shear force and bending moment diagrams and determine the maximum bending moment. Maximum bending moment At A=0 Therefore Q2A) In Q1A, the cross — section of the beam is as follows. Determine the second Moment of area (in m4) and the maximum Bending stress in the beam. LO 1.1, 1.2 Q3A) A solid square section steel column has dimensions of 100mm x 100mm x 6m length. The modulus of elasticity of the steel is 2IOGN/m2. The column is fixed at one end and pined on the other end. Determine: a) The second moment of area, the radius of gyration, the effective length and the Slenderness ratio. Comment on your answer whether the column is classified as short, intermediate or long. b) Calculate the critical compressive load, the critical stress and the allowable stress. Assuming the yield stress of the steel column is 450MN/m2. Q4A) A hollow circular shaft has internal diameter of 60mm and thickness of 10mm. The shaft is delivering a power output of 130kW at 900RPM. The length and the modulus of rigidity of the shaft are 1.2m and 8OGNIm2 respectively. Calculate: a) The polar second moment of area of the shaft (in m4). b) Calculate the maximum and the minimum shear stresses in the shaft (give your answers in MN/rn2). c) Calculate the angle of twist in the shaft (give your answer in degree). 5.A motor rotating at 800 RPM and accelerates uniformly until it reaches a speed of 1800 RPM. During this period it makes 565 complete revolutions. Determine: a The angular acceleration of the motor and the time taken from 800 RPM to 1800 RPM. b The number of revolutions from stationary to 1800RPM, assuming the Angular acceleration is same as part (a). And Q6A) An experimental solid disc flywheel has a mass of 120 kg and an outside diameter of 300 mm. When the flywheel is at rest, a constant torque of 10 Nm is applied for a period of 2 seconds. Assuming for flywheel the radius of gyration K = r I’J2. Calculate: a The moment of inertia and the angular acceleration b The angular velocity, the angular Kinetic Energy and the power required. Q7A) A solid flywheel on a machine has a mass of 900kg and 800mm in diameter. The wheel is rotating at 150RPM. For solid flywheel, the radius of gyration K r[J2. Calculate: a Store of Kinetic Energy in the flywheel. b Decrease in speed of flywheel (in RPM) if 1.5 kJ of energy is transferred from the wheel to do work in a process carried out by the machine. Q8A) An object of mass 0.3 kg oscillates with S.H.M of frequency 25 Hz (mass —spring system). Determine: a The periodic time and restoring force acting on the object when it is at displacement of 50mm. b The stiffness of the spring 9a. A flywheel has 700mm inside and 800mm outside diameters. The thickness of the wheel is 60mm and it is made of steel with density 7800kgm/m3. The flywheel accelerates from stationary and reaches 1500 rpm after 280 complete revolutions by uniform torque. There is an opposing torque. There is a opposing torque of 30 NM due to friction (output load). Assuming the radius of gyration K=rm/√2 (rm is the mean radius). Calculate: a) The moment of inertia of the flywheel and change in kinetic energy b) The value of the driving torque c) The power input and power output d) The efficiency of the flywheel 10. For the following symmetrical (I) section horizontal beam: a) Calculate the reaction forces c Draw shear force and bending moment diagrams and for the diagrams determine the maximum bending moment d Calculate the second moment of the area and the maximum bending stress. Give your answer in MN/M2. e Suggest a solid square section of the beam of the beam if the maximum bending moment and bending stress remain the same. What is the factor of safety if the maximum yield stress of the beam material is 400 NM/M2. Read More