School of Engineering \ Material Science and Nanotechnology Engineering
	
	
	
 
				
	Course Credit
	ECTS Credit
	Course Type
	Instructional Language
 
				
				
	Programs that can take the course
	
	
	
 
	Can be taken as faculty elective course by the other engineering departments
	
	
	
 
				
	Internal Forces and Section Effects Diagrams; Tension, Compression, Shear, and Bearing Stresses; Normal Stress and Strain; Stress-Strain Diagrams; Linear Elasticity and Hooke's Law; Shear Stress and Strain; Allowable Stress and Loads; Axially Loaded Members; Deformations in Axially Loaded Members; Stresses in Inclined Sections; Stress Concentrations; Effect of Temperature Change; Torsion; Torsion of Circular Shafts; Non-Uniform Torsion; Simple Shear Condition; Power Transmission in Circular Shafts; Mohr's Circle. 
	
	
	
 
				
	Textbook and / or References
	
	
	
 
	1] R. C. Hibbeler, Mechanics of Materials, Prentice-Hall Inc. , USA. [2] F. P. Beer and E. R. Johnston Mechanics of Materials, Mc-Graw Hill Comp. , England. [3] E. P. Popov ,Engineering Mechanics of Solids, Prentice-Hall Inc. , USA
	
	
	
 
				
	This course will help you solve many problems that you will frequently encounter in the industry. Systems are constantly subjected to different forces. The solution to these problems is possible through the knowledge gained in this course. 
	
	
	
 
				
	
					
						1. To acquire fundamental knowledge of Materials Science and Engineering.
					
						2. To select and apply mathematical, scientific, and engineering principles to Materials Science and Engineering.
					
						3. To utilize modern methods and tools in the field of Materials Science and Engineering.
					
						4. To analyze and interpret data related to material design and properties, as well as to design and conduct experiments.
					
						5. To calculate the stresses caused by forces on simple structures.
					
						6. To determine principal stresses resulting from combined forces on a system and use Mohr’s circle.
					
				
	
	
	
 
				
	Week 1: Course Objectives, Equilibrium, and Stress 
Week 2: Strain 
Week 3: Stress-Strain Diagrams, Hooke's Law, Poisson's Ratio 
Week 4: Axial Loading, Thermal Stress 
Week 5: Torsion 
Week 6: Power Transmission and Angle of Twist 
Week 7: Bending 
Week 8: Bending Deformations and Formulation 
Week 9: Shear Forces in Cross-Sections 
Week 10: Shear Force Formulation 
Week 11: Combined Loading 
Week 12: Mohr's Circle and Sectional Stresses
	
	
	
 
				
				
					
					
						
							
								
									| Tentative Assesment Methods | 
								
								
									| Activities | 
									Number | 
									Weight (%) | 
								
							
							
								
									
										| Course Attendance/Participation | 
										- | 
										- | 
									
								
									
										| Laboratory | 
										- | 
										- | 
									
								
									
										| Application | 
										- | 
										- | 
									
								
									
										| Homework | 
										- | 
										- | 
									
								
									
										| Project | 
										- | 
										- | 
									
								
									
										| Presentation | 
										- | 
										- | 
									
								
									
										| Field Work | 
										- | 
										- | 
									
								
									
										| Internship | 
										- | 
										- | 
									
								
									
										| Course Boards | 
										- | 
										- | 
									
								
									
										| Quiz | 
										25 | 
										10% | 
									
								
									
										| Midterm Exam | 
										1 | 
										45% | 
									
								
									
										| Final Exam | 
										1 | 
										55% | 
									
								
							
							
								
									 | 
									Total | 
									110% | 
								
							
						
						
						
							
								
									| Tentative ECTS-Workload Table | 
								
								
									| Activities | 
									Number/Weeks | 
									Duration (Hours) | 
									Workload | 
								
							
							
								
									
										| Course Hours (first 6 weeks) | 
										6 | 
										4 | 
										24 | 
									
								
									
										| Course Hours (last 6 weeks) | 
										6 | 
										3 | 
										18 | 
									
								
									
										| Laboratory | 
										- | 
										- | 
										- | 
									
								
									
										| Application | 
										- | 
										- | 
										- | 
									
								
									
										| Homework | 
										- | 
										- | 
										- | 
									
								
									
										| Project | 
										- | 
										- | 
										- | 
									
								
									
										| Presentation | 
										- | 
										- | 
										- | 
									
								
									
										| Field Work | 
										- | 
										- | 
										- | 
									
								
									
										| Internship | 
										- | 
										- | 
										- | 
									
								
									
										| Course Boards | 
										- | 
										- | 
										- | 
									
								
									
										| Preparation for Quiz | 
										25 | 
										2 | 
										50 | 
									
								
									
										| Preparation for Midterm Exam | 
										1 | 
										20 | 
										20 | 
									
								
									
										| Final Exam | 
										1 | 
										2 | 
										2 | 
									
								
									
										| Preparation for Final Exam | 
										1 | 
										20 | 
										20 | 
									
								
									
										| Study Hours Out of Class (preliminary work, reinforcement, etc.) | 
										12 | 
										2 | 
										24 | 
									
								
							
							
								
									| Total Workload |  |  | 
									158 | 
								
								
									| Total Workload / 30 |  |  | 
									158 / 30 | 
								
								
									 |  |  | 
									5.266667 | 
								
								
									| ECTS Credits of the Course |  |  | 
									5 | 
								
							
						
					
				
			
				
					
						
							 | 
							
								Program Outcome
								**
							 | 
						
						
							
								| 1 | 
							
								2 | 
							
								3 | 
							
								4 | 
							
								5 | 
							
								6 | 
							
								7 | 
							
								8 | 
							
								9 | 
							
								10 | 
							
								11 | 
							
						
					
					
						| 
							Course Outcome
						 | 
						
							
								| 1 | 
								
									
									
									
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B, C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B, C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
									
									
										
										
										
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												C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
									
									
										
										
											
												C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
							
						
							
								| 2 | 
								
									
									
									
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B, C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B, C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
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												C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
									
									
										
										
											
												C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
							
						
							
								| 3 | 
								
									
									
									
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B, C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B, C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
											
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
									
									
										
											
												
											 | 
										
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
									
									
									
										
										
											
												A
											 | 
										
										
									
								
							
						
							
								| 4 | 
								
									
									
									
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B, C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B, C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
									
									
									
										
										
											
												A
											 | 
										
										
									
								
							
						
							
								| 5 | 
								
									
									
									
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B, C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B, C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
									
									
									
										
										
											
												A
											 | 
										
										
									
								
							
						
							
								| 6 | 
								
									
									
									
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B, C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B, C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
									
									
										
										
											
												C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
										
											 |