1) Can calculate the stresses and deflections that occur in a curved beam.
2) Can explain the fundamental equations for multi-axial stress condition.
3) Can apply the evaluation theories for multi-axial stress condition to some simple problems.
4) Can calculate stress and deformation of spherical and axisymmetric problems.
5) Can discuss material dynamics issues with others based on logical thinking.
Outline:
The aim is to be able to calculate the strength of structural and mechanical components and to evaluate the strength of these components, as well as to be able to independently and continuously learn related matters, and to conduct logical thinking and technical discussions. Based on the year 3 class Strength of Materials I and year 4 class Strength of Materials II, students will learn more advanced issues and prepare for Advanced Strength of Materials in the first year of the graduate study, and Fracture Mechanics in the second year of the graduate study.
Style:
Pre-study the textbook and example problems before classes. After the instructor explains the key points of the study material at the beginning of the class, students will have a group discussion. They are also expected to raise questions and unclear points to the instructor for explanation. Work in groups on the exercise assignments prepared by the instructor.
Notice:
This course's content will amount to 90 hours of study in total. These hours include the learning time guaranteed in classes and the standard study time required for pre-study / review, and completing assignment reports. Try to think and understand yourself. Actively participate in group discussions and contribute to the group's learning activities during class hours.
Students who miss 1/3 or more of classes will not be eligible for evaluation.
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Theme |
Goals |
| 1st Semester |
| 1st Quarter |
| 1st |
Curved beam (1) Stress of the curved beam |
Can explain the distribution of stresses in the virtual section of the curved beam, and can calculate its magnitude.
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| 2nd |
Curved beams (2) Deflection of curved beams, and thin beams |
Can calculate the deflection that occurs in curved and thin beams.
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| 3rd |
Multi-axial stress state |
Can explain what is multi-axial stress state and their stress and strain notations. Can calculate stresses in two dimensional stress state.
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| 4th |
Fundamental equation for multi-axial stress (1) Displacement-strain equation |
Can explain the unknown functions in a multi- axial stress state and the structure of the problem from the equations that relate them.Can explain the displacement-strain equations and the equations of compatibility, and can apply them to simple problems.
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| 5th |
Fundamental equation for multi-axial stress (2) Stress-strain relation |
Understand the stress-strain relation in a multi-axial stress state and, can calculate stresses and strains using it.
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| 6th |
Fundamental equation for multi-axial stress (3) Equilibrium equation |
Can derive equilibrium equations in a right-angle coordinate system, and can apply them to simple problems.
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| 7th |
Fundamental equation for multi-axial stress (4) The basis of the cylindrical coordinate system and the spherical coordinate system |
Can apply the fundamental equation in cylindrical and spherical coordinate systems. Can transform equations between rectangle and polar coordinate systems.
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| 8th |
Strength evaluation in multi-axial stress state (1) Principal stress and principal axes, fracture and failure conditions, principal stress and maximum shear stress |
Can calculate the stresses, principal stresses, and principal shear stresses acting on any slope at plane stress. Understand the strength evaluation method in a multi-axial stress state, and can design the strength in a plane stress state.
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| 2nd Quarter |
| 9th |
Strength evaluation in multi-axial stress state (2) Mohr's stress circle and a combination of bending and torsion |
Can explain how to use the Mohr's stress circle in a plane stress state, and can draw the circle for any plane stress. Can explain the meaning of equivalent bending and torsional moments in the combination of bending and torsional loads, and can calculate principal and maximum shear stresses.
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| 10th |
Strength evaluation in multi-axial stress state (3) Principal and maximum shear strains, stress measurements with strain gauges, and the relationship between the elastic modulus |
Can explain the coordinate transformation formula for strains in plane strain states, and can calculate the principal and maximum shear strains by using them. Can explain the principle of a resistive strain gauge, and can calculate the principal stresses of plane stresses from the measured values of the rosette gauge. Can explain the equations that are formed between the elastic modulus.
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| 11th |
Spherical symmetry and axisymmetric problems (1) Thick spherical shell |
Can explain the symmetry of thick spherical shells under which internal and external pressures act, and can calculate their stress and deformation.
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| 12th |
Spherical symmetry problem and axisymmetric problem (2) Thick cylinder, and thin pressure vessel |
Can explain the symmetry of thick cylinders under which internal and external pressures act, and can calculate their stresses and deformations. Can explain that the formula for stress in a thin-walled pressure vessel is an approximate solution.
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| 13th |
Spherical and axisymmetric problems (3) Combined cylinder and cylinder thermal stresses |
Can calculate stress and deformation of combined cylinders using stress and deformation solutions on thick cylinders. Can calculate the stresses and deformations for cylinders with temperature differences in the internal and external faces.
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| 14th |
Spherical symmetry and axisymmetric problems (4) Rotating circle, rotating circle plate, rotating cylinder |
Can explain the symmetry of revolving circles, revolving disks, and revolving cylinders, and can calculate their stresses and deformations.
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| 15th |
Total Review |
Deepen understanding on the structure of the problem and solving method for mechanics of solids in multi-axial stress.
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| 16th |
Final exam
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