A simply supported beam of circular cross-section made up of hot rolled steel is subjected to a fluctuating load that varies from -F to +3F. Determine the minimum ultimate strength of the beam material which can withstand the fluctuating loads. The variable forces on the beam induce corresponding fluctuating stresses between + 82 N/mm2 to –42 N/mm2. Assume the following values: Yield strength = 0.55 ultimate strength, endurance stress = 0.45 ultimate strength. Take a factor of safety = 2. Use Soderberg relation in your design, i) Calculate the mean stress in N/mm2 and variable stress in N/mm2 ii) Calculate the Ultimate Strength in N/mm2 iii) Calculate the endurance strength in N/mm2
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 simply supported beam of circular cross-section made up of hot rolled steel is subjected to a fluctuating load that varies from -F to +3F. Determine the minimum ultimate strength of the beam material which can withstand the fluctuating loads. The variable forces on the beam induce corresponding fluctuating stresses between + 82 N/mm2 to –42 N/mm2. Assume the following values: Yield strength = 0.55 ultimate strength, endurance stress = 0.45 ultimate strength. Take a factor of safety = 2. Use Soderberg relation in your design,
i) Calculate the mean stress in N/mm2 and variable stress in N/mm2
ii) Calculate the Ultimate Strength in N/mm2
iii) Calculate the endurance strength in N/mm2
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