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Advanced Mechanics of Materials Formula Sheet, Cheat Sheet of Mechanical Engineering

Formula sheet in factor of safety, equations of equilibrium, normal stress and shearing stress, Principal of 2-D and 3-D stress, strain and strain energy.

Typology: Cheat Sheet

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ME626 Advanced Mechanics of Materials Formula Sheet
1
Factor of
safety
(1.1)
Equations of
Equilibrium
3-D
(1.2)
2-D
(1.3)
(1.4a)
(1.4b)
Normal
Stress &
Shearing
Stress
(1.5)
State of
Stress at a
Point
(1.6)
Equality of
Shearing
Stresses
(1.7a)
(1.7b)
2-D or Plane
Stress
(1.8)
Internal Force
Resultants
Stress Relations
(1.9a)
(1.9b)
Normal Stress
(1.10)
Stresses on
Inclined Sections
(Axially Loaded Bar)
(1.11a)
(1.11b)
(1.12)
Differential
Equations of
Equilibrium
2-D
(1.13)
3-D
(1.14)
Ind.
(1.15a)
(1.15b)
Plane Stress
Transformation
(1.16)
(1.17a)
(1.17b)
(1.17c)
(1.18a)
(1.18b)
(1.18c)
Principal
Stresses &
Maximum In-
Plane Shear
Stresses
(1.19)
(1.20)
(1.21)
(1.22)
(1.23)
Mohr’s Circle
for 2-D Stress
(1.24)
(1.25)
(1.26)
(1.27)
pf3
pf4
pf5
pf8
pf9
pfa
pfd
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Factor of safety

Equations of Equilibrium

3 - D (1.2)

2 - D

(1.4a) (1.4b) Normal Stress & Shearing Stress

State of Stress at a Point

Equality of Shearing Stresses (1.7a) (1.7b) 2 - D or Plane Stress

Internal Force Resultants – Stress Relations (1.9a) (1.9b) Normal Stress (1.1 0 ) Stresses on Inclined Sections (Axially Loaded Bar) (1.11a) (1.11b) (1.12) Differential Equations of Equilibrium

2 - D (1.13)

3 - D (1.14)

Ind. (1.15a) (1.15b) Plane Stress Transformation

(1.17a) (1.17b) (1.17c) (1.18a) (1.18b) (1.18c) Principal Stresses & Maximum In- Plane Shear Stresses

Mohr’s Circle for 2-D Stress

(1.28a) (1.28b) (1.28c) (1.28d) (1.28e) (1.28f) (1.29a) (1.29b) (1.29c) (1.30a) (1.30b) Principal Stresses in 3 - D

(1.34a) (1.34b) (1.34c) Principal Stresses in 2-D

Stresses on an Oblique Plane

(1.38a) (1.38b) (1.39) (1.40) (1.41) (1.42) Octahedral Stresses

Mohr’s Circle in 3 - D

Boundary Conditions i.t.o. Surface Forces

Strain Defined (2.1) Normal Strain (2. 2 ) Plane Strain (2.3a) (2.3b)

in 2-D (2.21) Displacement Field in 3 - D

Specimen Geometry Change (2.23a) (2.23b) True Strain (2. 24 ) True Stress (2. 25 ) Hooke’s Law 1-D

Poisson’s ratio (2. 28 ) Unit Volume Change

Deformation of a Tension Bar

(2.31a) (2.31b) Hooke’s Law Generalized (2.32) Indicial (2.33) Isotropic & Homegenous

Bulk Modulus of Elasticity

Hooke’s Law Orthotropic

Strain Rosette Normal Strains

Maximum Shearing Strain

Strain Rosette (Rectangular/45^0 ) Principal Strains (2.46a) Principal Stresses (2.46b) Principal Planes (2.46c) Strain Rosette (Delta/ 600 ) Principal Strains (2.47a) Principal Stresses (2.47b) Principal Planes (2.47c) Strain Energy Density (2.48) (for Normal Stress) Complementary^ (2.49) Strain Energy (for Shear Stress) Density (2.50) Strain Energy (for 3-D Stresses)

Strain Energy Common Structural Member

Axially Loaded Bar

Plane Strain

Polynomial Stress Functions

End Loaded Cantilever Beam (3.24) Equations of Thermoelasticity

(3.26a) (3.26b) (3.27) (3.28) (3.29) (3.30) Basic Relations in Polar Coordinate s

(3.33a ) (3.33b ) (3.33c) Plane Stress (3.34) Plane Strain (3.35) Transformatio n Equations

Compatibility Equations

Uniaxial Tension

Compression of a Wedge

Bending of a Wedge

Combined Compression & Bending of a Wedge

Straight Boundary of a (3.48) large Plate (3.49) (3.50) (3.51) poor

better

Stress Concentration Factors

Circular Hole in Tension (3.55a) (3.55b) (3.55c) Elliptic Hole in Tension

Contact Stresses Two Spheres in Contact

Theory Stress (4.11b) Coulomb-Mohr Theory (4.12a) (4.12b) (4.12c) (4.13) Torsion Bar

Fracture Mechanics Stress Intensity Factor

Fracture Toughness

Fatigue

Impact or Dynamic Loads

Pure Bending of Beams of Symmetrical Cross Section

(5.3a) (5.3b) (5.4) (5.5) (5.6) (5.7) (5.9a) (5.9b) (5.10) Pure Bending of Beams of Symmetrical Cross Section

Bending of cantilever of narrow Section (5.20a) (5.20b) (5.21) (5.22) (5.23) (5.24) (5.25a) (5.25b) (5.25c) Elementary Theory of

Bending (5.2 7 ) (5.28) (5.29) (5.30) (5.31) (5. 32 ) (5.33) (5.34) Displacements of a Cantilever Beam

Stresses in a Steel Crane Hook (5.7 5 a) (5.75b)