llow structural member manufactured from a high grade tensile strength steel, forms part of a large piece of lifting equipment and is shown in the figure. The cross-section of the member has an outer diameter of 100 mm and a wall thickness of 15 mm. The member is supported on a knife edge and by a pin support as shown. During a particular loading situation, the structural member is subjected to lateral loading: three point loads and two uniformly distributed loads as shown. Also, during service, the member is subjected to an axial force of 110 kN and a torque of 5.75 kNm. The member also contains hydraulic fluid operating at a pressure of 7.5 MN/m2. i) Calculate the reactions and hence draw scaled diagrams of the thrust, shear force and bending moments acting on the member, highlighting and/or calculating all significant points.
Design Against Fluctuating Loads
Machine elements are subjected to varieties of loads, some components are subjected to static loads, while some machine components are subjected to fluctuating loads, whose load magnitude tends to fluctuate. The components of a machine, when rotating at a high speed, are subjected to a high degree of load, which fluctuates from a high value to a low value. For the machine elements under the action of static loads, static failure theories are applied to know the safe and hazardous working conditions and regions. However, most of the machine elements are subjected to variable or fluctuating stresses, due to the nature of load that fluctuates from high magnitude to low magnitude. Also, the nature of the loads is repetitive. For instance, shafts, bearings, cams and followers, and so on.
Design Against Fluctuating Load
Stress is defined as force per unit area. When there is localization of huge stresses in mechanical components, due to irregularities present in components and sudden changes in cross-section is known as stress concentration. For example, groves, keyways, screw threads, oil holes, splines etc. are irregularities.
A hollow structural member manufactured from a high grade tensile strength steel, forms part of a large piece of lifting equipment and is shown in the figure. The cross-section of the member has an outer diameter of 100 mm and a wall thickness of 15 mm. The member is supported on a knife edge and by a pin support as shown. During a particular loading situation, the structural member is subjected to lateral loading: three point loads and two uniformly distributed loads as shown. Also, during service, the member is subjected to an axial force of 110 kN and a torque of 5.75 kNm. The member also contains hydraulic fluid operating at a pressure of 7.5 MN/m2.
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i) Calculate the reactions and hence draw scaled diagrams of the thrust, shear force and bending moments acting on the member, highlighting and/or calculating all significant points.
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ii) Calculate all the component stresses set-up in the member material at the point of maximum bending moment due to the loading conditions. (Note: assume that thin cylinder theory applies).
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iii) Produce the 2D complex stress system for the member at the point of maximum stress and hence determine the magnitude and nature of the principal stresses, the maximum shear stress (analytically and graphically), and the angle of the planes on which the major principal stresses act.
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iv) Evaluate the minimum factor of safety for the member and compare with the required factor of safety of 3.
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v) A delta strain gauge is attached to the member at point ‘X’ as highlighted in the figure. During a particular stage of a lifting process, strain readings are recorded as detailed. Determine the magnitude and nature of the principal stresses acting on the member at point ‘X’, the maximum shear stress, and the angle of the principal planes.
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vi) Using Macauley’s method, determine the deflection of the member at the locations where the 25 kN, 20 kN and 50 kN point loads are applied. Comment on how the maximum deflection of the member could be determined.
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