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Mechanics of MAterials

These 57 tutorials cover typical material from a second year mechanics of materials course (aka solid mechanics). A solid understanding (pun intended?) of statics and calculus is necessary to properly learn and grasp the concepts of solid mechanics.

In order to gain a comprehensive understanding of the subject, you should start at the top and work your way down the list. That way you will start learning the most basic concepts first and build off of those as you progress through the course.
Mechanics of Materials

Stress

1. Normal stress
2. Normal stress in members with varying cross-sectional area
3. Shearing stress
4. Double shear
5. Bearing stress
6. Factor of safety
Practice Problems


​Strain

7. Normal strain
8. Stress strain diagram explained
9. Hooke's law
10. Normal strain in members with varying cross-sectional area
11. Use Hooke's law to find deflection in a statically determinate frame
12. Intro to statically indeterminate problems and the principle of superposition
13. Find the reactions of a statically indeterminate member with varying cross section
​14. Thermal expansion of material due to temperature change
Practice Problems


​Torsion

15. Torques and angle of twist
16. Angle of twist due to torsion in a shaft with varying cross section
17. Shearing strain due to torsion in a shaft
18. Shearing stress due to torsion in a solid circular shaft
19. Shearing stress due to torsion in a hollow circular shaft
20. Find the minimum diameter of a solid circular shaft in torsion
​21. Find the minimum inner diameter of a hollow circular shaft in torsion
22. Find the maximum permissible torque for a shaft of known dimensions
Practice Problems


​Pure Bending

23. Pure bending introduced
24. Geometry of pure bending problems
25. Stress and strain in the elastic range due to pure bending
26. Moment of inertia for composite shapes
27. Elastic section modulus demonstration
28. Pure bending in the elastic range example #1: rectangular beam
29. ​Pure bending in the elastic range example #2: T-beam
Practice Problems


​Pure Bending of Composite Materials

30. Pure bending of composite materials introduced
31. Pure bending of composite materials worked example #1
32. Pure bending of composite materials worked example #2
33: How to solve pure bending problems for reinforced concrete
34: Pure bending of reinforced concrete example #1
35: Pure bending of reinforced concrete example #2
Practice Problems


​Beam Deflection

36. Introduction to beam deflection and the elastic curve equation
37. Find deflection and slope of a cantilever beam with a point load
38. Find deflection of a simply supported beam with distributed load
39. Find deflection and slope of a simply supported beam with a point load
​40. Statically indeterminate beam deflection and slope example

Tutorials for the Method of Superposition, Moment Area Method, Displacement Method, Slope Deflection Method, 3 Moment Equation, and Force Method are located in the Structural Analysis course. 

Energy Methods

41. Strain energy and strain density introduced
42. Calculate elastic strain energy for a member with axial loading
43. Calculate elastic strain energy for a cantilever beam with a point load
44. Calculate elastic strain energy for a simply supported beam with a point load
45. Calculate elastic strain energy for a member in torsion
46.
Truss deflection under a single load example problem #1 (virtual work)
47. Truss deflection under a single load example problem #2 (virtual work)
48. How to apply Castigliano's theorem
49. Castigliano's theorem example #1: deflection at an applied point load
50. Castigliano's theorem example #2: deflection using a dummy load

Columns

51. Columns and buckling introduced
52. Effective length of columns with different end conditions
53. Column buckling example problem #1: both ends pinned
54: Column buckling example problem #2: both ends fixed 
55: Column buckling example problem #3: one fixed end, one free end
56. Column buckling example problem #4: one fixed end, one pinned end
57: Column buckling example problem #5: with bracing


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