EDEXCEL NATIONALS UNIT 18 ADVANCED MECHANICAL PRINCIPLES. ASSIGNMENT No. 1 - THE AFFECTS OF STRESS

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1 EDEXCEL NATIONALS UNIT 18 ADVANCED MECHANICAL PRINCIPLES ASSIGNMENT No. 1 - THE AFFECTS OF STRESS NAME: I agree to the assessment as contained in this assignment. I confirm that the work submitted is my own work. Signature Date submitted FEEDBACK COMMENTS This assignment assesses P1, P2, P3 and M2 and D1. Grade Awarded: Assessor Signature Date: Internal verifier Signature Date:

2 Grading criteria To achieve a pass grade the evidence must show that the learner is able to: P1 determine the dimensional effects of uniaxial loading on a plain structural component and two-dimensional loading on a rectangular plate P2 determine the maximum stress due to bending, factor of safety in operation and minimum radius of curvature for a simply supported beam carrying a given concentrated load and a uniformly distributed load P3 determine the maximum shear stress, factor of safety in operation and angle of twist for a mechanical power transmission shaft when transmitting given power at a given speed P4 determine the resultant velocity of an object when moving simultaneously with velocities in two different directions and its velocity relative to a second object moving in the same plane in a third direction Tick Achieved To achieve a merit grade the evidence must show that, in addition to the pass criteria, the learner is able to: M1 determine the dimensional effects and change in volume for a given element of an engineering component when subjected to threedimensional loading M2 compare the effects on a rectangular section beam s load carrying capacity of increasing the breadth, and increasing the depth by given amounts M3 determine the output velocity of a given quickreturn mechanism for given input conditions M4 evaluate the output motion of the slider in a slider-crank mechanism with uniform input motion of the crank, for compliance with the conditions necessary for it to describe simple harmonic motion. Tick Achieved To achieve a distinction grade the evidence must show that, in addition to the pass and merit criteria, the learner is able to: D1 evaluate and compare the saving in weight and the reduced torque transmission capacity for a hollow power transmission shaft as its internal diameter is increased D2 determine from test data the effective contributory mass of the spring in an oscillating mass-spring system. Tick Achieved P5 determine the output motion of a slider-crank mechanism and a four-bar linkage mechanism for given input conditions P6 determine the periodic time and the displacement, velocity and acceleration at a given instant of the simple harmonic motion generated by circular motion of given parameters P7 determine the circular frequency, natural frequency of vibration and the maximum velocity and acceleration for a mass-spring system and a simple pendulum with given parameters. D.J.Dunn 2

3 DETAILS This assignment is in 3 parts. You should write a technical report that shows how you conducted the tasks outlined below and arrived at your answers. You should show the appropriate calculations clearly and make use of correct units and multiples. Analyse and comment on your work as appropriate. You should where possible check your answers by some alternative method. PART 1- LATERAL STRAIN A flat rectangular sheet of metal has width W, Length L and thickness t. It is subjected to a force F 1 as shown spread evenly all along the edge W. You will be allocated a set of data from the table below. Determine the following. The stress in the direction of F The strain in the direction of F The changes in the values of L and t The sheet of metal is now stretched in the direction parallel to edge W with a force F 2 as shown. Determine the following. The changes in W, L and t The change in the area of the plate. You should find the appropriate values of the elastic constants required for the metal from the table. STUDENT L (mm) W (mm) t (mm) F 1 (kn) F 2 (kn) METAL MILD STEEL ALUMINIUM /30 BRASS COPPER D.J.Dunn 3

4 TYPICAL PHYSICAL PROPERTIES OF COMMON METALLIC SOLIDS Name ρ density kg/m 3 σ Tensile Strength MPa σ y Yield Strength MPa E Elastic Modulus GPa 1 Aluminium Aluminium strong alloy Antimony Bismuth Brass (70Cu/30Zn) Bronze (90Cu/10Sn) 7 Cobalt Constantan Copper German silver (60Cu125Zn/15Ni) 11 Gold lnvar(64fe/36ni) Iron, pure Iron, cast grey Iron, white Iron, wrought Lead Magnesium Manganin Monel (70Ni/30Cu) Nickel Nickel,strong alloy ν Poisson's Ratio 23 Phosphor bronze Platinum Silver Sodium Solder, soft (50Pb/50Sn) 28 Stainless Steel (18Cr/8Ni) 29 Steel, mild Steel, piano wire Tin Titanium Zinc

5 PART 2 - BENDING OF A BEAM Each student will be given a separate data set for this problem to ensure individual solutions are produced. A steel box girder spans two walls and rests on roller as shown with the shorter edge (D) vertical. A traversing pulley moves along the girder. The maximum tensile stress allowed in the steel is 300 MPa. A safety factor of 2.0 is to be used. You should decide where the pulley will be on the length for maximum stress to occur. The modulus of elasticity for the steel is 205 GPa. Determine the following. The maximum load that can be lifted by the pulley. The radius of curvature at the beam at the load point. The beam is turned so that it rests on the other edge with B vertical. Re-calculate the answers. Which way up is the best? Explain the reasons for your answer. Your tutor will designate a set of data for you to use from the table below. STUDENT L (m) B (mm) D (mm) t (mm)

6 PART 3 TORSIONAL of a SHAFT A power transmission shaft is supported between two bearings as shown. The shaft delivers P kw of power to the pulley at N rev/min. The maximum allowable shear stress is 100 MPa and a safety factor of 1.8 is to be used. The modulus of rigidity G is 90 GPa. The density of steel is 7830 kg/m 3. You will be allocated a set of data from the table below. If the shaft is solid with diameter D determine the following. The maximum power that should be transmitted. The angle of twist over the length L at this condition. The mass of the shaft over the length L. Recalculate all your answers when the shaft is hollow with a wall thickness of t mm. Comment on the affect using a hollow shaft. Student L (m) D (mm) t (mm) N (Rev/min) D.J.Dunn 6