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Strength of Materials (Mechanics of Materials)
174 topics across 7 chapters
Chapter 1
Foundations for Mechanics of Materials
1
Engineering Math Essentials (for Strength of Materials)
4 subtopics
2
Vectors, moments, and basic tensor notation used in stress/strain
3
Calculus you’ll use: derivatives/integrals for load, shear, moment, deflection
4
Compute centroid and second moment of area (I) for common sections
5
Dimensional analysis & unit consistency checks on formulas
6
Statics Equilibrium Refresher
3 subtopics
7
Solve 2D/3D rigid-body equilibrium problems (ΣF=0, ΣM=0)
8
Moments, couples, and moment of a force about a point/axis
9
Replace distributed loads with equivalent resultants (location & magnitude)
10
Free-Body Diagrams (FBDs) & Reaction Forces
3 subtopics
11
Draw correct free-body diagrams for beams/frames/members
12
Identify support types and the correct reaction components
13
Use internal cuts: what forces/moments must appear on a cut section
14
Internal Resultants (N, V, M, T) & Sign Conventions
3 subtopics
15
Compute N, V, M, T using the method of sections
16
Draw shear-force and bending-moment diagrams (SFD/BMD)
17
Use relationships between load, shear, and moment (dV/dx=-w, dM/dx=V)
18
Stress & Strain Definitions (Normal/Shear, Engineering vs Tensor View)
3 subtopics
19
Differentiate normal vs shear stress; traction on a plane conceptually
20
Strain measures: axial strain, shear strain; engineering vs true strain (overview)
21
Interpret stress/strain components as a tensor (what σx, τxy, etc. mean)
Chapter 2
Material Behavior (Constitutive Relations)
↗ Stress & Strain Definitions (Normal/Shear, Engineering vs Tensor View) (see Chapter 1)
22
Stress–Strain Curve & Material Properties
3 subtopics
23
Extract E, yield strength, UTS from a stress–strain curve
24
Compute ductility and energy measures (resilience, toughness)
25
Compare tension vs compression behavior and typical failure modes
26
Linear Elasticity (Hooke’s Law, Isotropic Relations)
3 subtopics
27
Apply Hooke’s law in 1D and 3D (concept + common forms)
28
Use elastic constants relations (E, G, ν, K) for isotropic materials
29
Recognize plane stress vs plane strain and when each assumption applies
30
Thermal Expansion & Thermoelastic Stress
3 subtopics
31
Compute free thermal strain using coefficient of thermal expansion (αΔT)
32
Compute thermal stress for constrained expansion (compatibility + Hooke’s law)
33
Understand temperature gradients and why they can induce bending/warping (intro)
34
Plasticity Basics & Yield Onset
3 subtopics
35
Define yielding and distinguish yielding vs fracture at a high level
36
Hardening concepts (isotropic/kinematic) and what they change in response
37
Convert engineering stress–strain to true stress–strain (conceptual + basic calc)
38
Viscoelasticity & Creep (Intro)
3 subtopics
39
Identify creep stages and key design concerns (time, temperature, stress)
40
Understand Maxwell and Kelvin-Voigt models qualitatively (springs/dashpots)
41
Stress relaxation vs creep: recognize scenarios and implications
Chapter 3
Stress Analysis for Common Load Cases
42
Axial Loading of Members (Bars)
4 subtopics
43
Compute axial stress (σ=P/A) and interpret sign (tension/compression)
44
Solve stepped/segmented bar problems (internal force in each segment)
45
Eccentric axial loading (intro): combined direct + bending stress idea
46
Composite bars: load sharing using compatibility (same deformation) + stiffness
47
Torsion of Circular Shafts
3 subtopics
48
Use torsion formula (τ=Tr/J) and polar moment for circular sections
49
Power transmission: relate torque, power, and rotational speed
50
Thin-walled torsion basics: shear flow idea for open/closed sections (intro)
51
Bending of Beams: Normal Stress (Flexure)
3 subtopics
52
Apply flexure formula (σ=My/I) and locate max stress in a section
53
Use section modulus (S=I/c) for quick bending stress sizing
54
Unsymmetric bending (intro): bending about non-principal axes concept
55
Transverse Shear Stress in Beams
3 subtopics
56
Compute beam shear stress using τ=VQ/(It) for common shapes
57
Compute shear flow q=VQ/I and use it for built-up/thin-walled sections
58
Shear center (intro): why some sections twist under transverse loading
59
Thin-Walled Pressure Vessels
3 subtopics
60
Thin-walled cylinder stresses: hoop and longitudinal stress formulas
61
Thin-walled spherical vessel stress formula and comparisons to cylinders
62
Thick-walled cylinder overview (Lame’s equations concept + when needed)
63
Stress Transformation, Principal Stresses & Mohr’s Circle
4 subtopics
64
Use 2D stress transformation equations to find stress on a rotated plane
65
Construct Mohr’s circle for plane stress and read off key values
66
Compute principal stresses and maximum shear stress (plane stress)
67
Recognize 3D stress ideas: invariants and the role of principal stresses (intro)
68
Combined Stresses & Superposition (Axial, Bending, Torsion)
3 subtopics
69
Combine axial + bending stress at a point (superposition + sign)
70
Combine bending + torsion in shafts to get a multiaxial stress state
71
Work typical combined-loading examples end-to-end (identify loads → stress)
Chapter 4
Deformation, Deflection & Indeterminacy
72
Axial Deformation (Including Temperature Effects)
3 subtopics
73
Compute axial deformation using δ=∫(N/(AE)) dx for variable loading/area
74
Use compatibility for temperature change in bars (free strain vs constrained)
75
Axial indeterminacy (intro): solve with equilibrium + compatibility + stiffness
76
Torsional Deformation (Angle of Twist)
2 subtopics
77
Compute angle of twist using φ=∫(T/(JG)) dx (uniform and stepped shafts)
78
Indeterminate torsion (intro): multiple shafts/segments with compatibility
79
Beam Deflection by Integration (Elastic Curve)
3 subtopics
80
Set up the elastic curve: EI v''(x)=M(x) and integrate to get slope/deflection
81
Apply boundary conditions correctly (supports, symmetry, continuity)
82
Memorize/derive common deflection cases (cantilever/SS beams; point & UDL)
83
Energy & Virtual Work Methods for Deflection
3 subtopics
84
Compute strain energy in axial, torsion, and bending members
85
Use Castigliano’s theorems to get deflections/rotations from strain energy
86
Use the unit-load method to compute deflections efficiently
87
Statically Indeterminate Members & Compatibility
3 subtopics
88
Write compatibility equations and choose redundants systematically
89
Use superposition and flexibility/stiffness ideas to solve indeterminate cases
90
Account for temperature change/settlement in indeterminate members (intro)
91
Shear Deflection & Nonprismatic/Curved Members (Intro)
3 subtopics
92
Shear deflection (intro): Timoshenko beam concept and correction factors
93
Deflection with variable EI (tapered/nonprismatic members) using integration
94
Curved beams (intro): why curved geometry changes stress distribution
Chapter 5
Failure, Fatigue & Strength Design
↗ Plasticity Basics & Yield Onset (see Chapter 2)
↗ Stress Transformation, Principal Stresses & Mohr’s Circle (see Chapter 3)
95
Yield/Failure Criteria (Tresca, von Mises)
3 subtopics
96
Apply Tresca (maximum shear) criterion to multiaxial stress states
97
Apply von Mises criterion and interpret equivalent stress
98
Use principal stresses (from Mohr’s circle/transformation) inside failure checks
99
Stress Concentration & Notch Effects
3 subtopics
100
Use theoretical stress concentration factor Kt from charts/handbooks (practice)
101
Notch sensitivity (q) and fatigue notch factor (Kf) concept + basic use
102
Design mitigations: fillets, holes, surface finish, and load path smoothing
103
Fatigue Design
4 subtopics
104
Read S–N curves; define endurance limit (when applicable) and fatigue strength
105
Apply mean-stress corrections (Goodman/Gerber/Soderberg) in design problems
106
Apply Miner’s rule for cumulative fatigue damage (simple spectrum)
107
Account for modifiers: size, surface, temperature, reliability (intro level)
108
Fracture Mechanics (Intro)
3 subtopics
109
Crack modes and stress intensity factor K (interpretation + basic calculations)
110
Griffith energy balance idea and why cracks can cause brittle failure
111
Fracture toughness (KIC) testing concept and conservative design use
112
Factor of Safety, Reliability & Code-Based Allowables
3 subtopics
113
Choose factor of safety/load factors consistent with uncertainty and consequences
114
Use material specifications (e.g., ASTM/ASME concepts) without misreading allowables
115
Document assumptions, traceability, and checks for strength calculations
116
Design of Beams & Shafts for Strength (Worked-Example Skills)
3 subtopics
117
Size a shaft for combined bending + torsion using a chosen failure criterion
118
Size a beam for bending/shear using allowable stress (and note critical sections)
119
Include serviceability: check deflection/rotation limits alongside strength
Chapter 6
Stability & Buckling
120
Euler Buckling of Columns
3 subtopics
121
Compute Euler critical load Pcr=π²EI/(KL)² and interpret sensitivity to L and I
122
Use slenderness ratio to judge Euler buckling applicability
123
Compare end conditions (pinned/fixed/free) and their effect on buckling load
124
Effective Length & Boundary Conditions (K-Factor)
2 subtopics
125
Use effective length factor K concept (what it represents and how it’s estimated)
126
Braced vs unbraced frames: how lateral stability changes column buckling risk
127
Inelastic Buckling & Column Curves
2 subtopics
128
Johnson (inelastic) buckling formula overview and when Euler overpredicts
129
Column curves and the role of imperfections/residual stresses (intro)
130
Lateral-Torsional Buckling of Beams (Intro)
2 subtopics
131
Understand lateral-torsional buckling (LTB) mechanism and critical moment idea
132
Use practical bracing strategies (reduce unbraced length; restrain compression flange)
133
Frame Stability, Bracing & Second-Order Effects (Intro)
2 subtopics
134
Sway vs non-sway frames and P–Δ second-order effect (conceptual intro)
135
Design intuition for bracing: load paths, constraints, and preventing instability
136
Buckling of Thin Plates/Shells (Intro)
2 subtopics
137
Plate buckling basics: critical stress form and buckling coefficient k (intro)
138
Local buckling in thin-walled members (intro): why width/thickness matters
Chapter 7
Experimentation, Computation & Engineering Practice
139
Mechanical Testing (Tension/Compression/Torsion)
3 subtopics
140
Tensile test workflow: specimen, extensometer/strain, and interpreting results
141
Torsion test workflow: obtaining shear modulus and comparing to theory
142
Hardness tests (Rockwell/Brinell/Vickers): what they do and limitations
143
Strain Measurement: Strain Gages & Rosettes
3 subtopics
144
Wheatstone bridge basics for strain gages (quarter/half/full bridge idea)
145
Gage factor, installation effects, and temperature compensation (intro)
146
Strain rosettes: convert measured strains to principal strains/stresses (practice)
147
Full-Field Stress/Strain Methods (DIC, Photoelasticity)
2 subtopics
148
Digital Image Correlation (DIC) basics: setup, outputs, and error sources
149
Photoelasticity basics: fringe patterns and qualitative stress interpretation
150
Intro Finite Element Analysis (FEA) for Solids
4 subtopics
151
FEA building blocks: element types, mesh density, and convergence idea
152
Apply loads and boundary conditions correctly; avoid rigid-body modes
153
Interpret stress results: peaks, averaging, and stress singularities near corners
154
Verify/validate FEA with hand calculations (sanity checks and benchmarks)
155
Reading Standards, Specs & Material Datasheets
3 subtopics
156
Read a material datasheet: conditions, heat treatment, and test standards
157
Distinguish typical vs minimum properties; allowables vs design values
158
Safety-critical documentation: revision control, traceability, and compliance (intro)
159
Case Studies & Failure Investigation
3 subtopics
160
Identify ductile vs brittle failure from fracture surface cues (intro checklist)
161
Recognize fatigue signatures (beach marks/striations concept) and typical origins
162
Root-cause analysis workflow: loads, environment, material, geometry, process
163
Reporting, Assumptions & Engineering Judgment
3 subtopics
164
Write a clear calculation package (given/assume/solve/check) for MoM problems
165
State assumptions and quantify uncertainty; use peer review as a control
166
Engineering ethics: communicating risk and limitations of analysis

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