Question

the analysis for the combined stresses consists of the following: (a) draw an element located at the position of gauges 7 and 8. take the top and bottom edges to be parallel to the axis of the tube. on the element, show all the stresses that act due to both bending and torsion. (b) for the state of stress from part (a), draw mohr's circle. use mohr's circle to compute the principal stresses and the direction in which each principal stress acts. draw the element on which the principal stresses act and indicate the angle op between the bottom edge of the element and the axis of the tube. (c) having determined the theoretical principal stresses, hooke's law may again be used to determine the associated normal strains. these strains correspond to those measured by gauges 7 and 8. (d) calculate the ratio of the measured strain to the predicted strain for each of gauges 7 and 8; see attached tables on page 5. 9.4 discussion 9.4.1 where was superposition used in this laboratory exercise? based on the results obtained, discuss the validity of the principle of superposition. as part of this discussion, indicate the limitations of this principle. 9.4.2 discuss the differences between measured and computed values of strain. for example, consider the significance of the observed difference and suggest possible reasons for analysis for the combined stresses consists of the following: (a) draw an element located at the position of gauges 7 and 8. take the top and bottom edges to be parallel to the axis of the tube. on the element, show all the stresses that act due to both bending and torsion. (b) for the state of stress from part (a), draw mohr's circle. use mohr's circle to compute the principal stresses and the direction in which each principal stress acts. draw the element on which the principal stresses act and indicate the angle op between the bottom edge of the element and the axis of the tube. (c) having determined the theoretical principal stresses, hooke's law may again be used to determine the associated normal strains. these strains correspond to those measured by gauges 7 and 8. (d) calculate the ratio of the measured strain to the predicted strain for each of gauges 7 and 8; see attached tables on page 5. 9.4 discussion 9.4.1 where was superposition used in this laboratory exercise? based on the results obtained, discuss the validity of the principle of superposition. as part of this discussion, indicate the limitations of this principle. 9.4.2 discuss the differences between measured and computed values of strain. for example, consider the significance of the observed difference and suggest possible reasons for them.

Answer 1

The question revolves around the stress analysis due to bending and torsion in an engineering context, requiring the drawing of Mohr's circle, application of Hooke's law, and comparison of theoretical and practical strain measurements to discuss the superposition principle.

Step-by-step explanation:

The analysis of combined stresses in an element situated at the location of gauges 7 and 8 is a multi-step process that involves understanding the stress states due to bending and torsion, drawing Mohr's circle, and utilizing Hooke's law to connect theoretical stresses to the corresponding strains. The superposition principle is applied throughout this process to combine the effects of different types of stresses, and the validity of this approach is evaluated by comparing the measured strain to the theoretical predictions.

In part (a), we examine the stresses on an element located where gauges 7 and 8 are placed, by considering both bending and torsional stresses. Part (b) involves using Mohr's circle to find the principal stresses and their respective directions, and aligning the drawn element with these directions. In part (c), we calculate the Normal strains using Hooke's Law based on the theoretical principal stresses obtained. For part (d), the ratio of the measured strain to predicted strain is calculated for both gauges to analyze the accuracy of the theoretical model.

During the discussion in 9.4.1, the application of superposition during the laboratory exercise is identified and critiqued, addressing the principle's limitations. For discussion point 9.4.2, the disparities between measured and computed strain values are discussed, considering the significance of these differences and possible explanations for discrepancies.