ME626 Advanced Mechanics of Materials Formula Sheet Factor ...me626.cankaya.edu.tr/uploads/files/Formula Sheet Quiz 4.pdf · Mohr’s Circle in 3-D (1.45) (1.46) (1.47) Boundary Conditions

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)


2

(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

(1.31)

(1.32)

(1.33) (1.34a)

(1.34b)

(1.34c)

Principal Stresses in 2-D

(1.35)

Stresses on an Oblique Plane

(1.36) (1.37)

(1.38a)

(1.38b)

(1.39)

(1.40)

(1.41)

(1.42)

Octahedral Stresses

(1.43)

(1.44)

Mohr’s Circle in 3-D

(1.45)

(1.46)

(1.47)

Boundary Conditions i.t.o. Surface Forces

(1.48)

Strain Defined (2.1)

Normal Strain

(2.2)

Plane Strain (2.3a)

(2.3b)


3

3-D Strain

(2.4)

(2.5a)

(2.5b)

(2.6)

(2.7)

Plane Strain (Approximate) (2.8)

Large Strains

(2.9)

(2.10a)

(2.10b)

(2.10c)

Equations of Compatibility 2-D

(2.11)

3-D

(2.12)

Transformation of 2-D Strain

(2.13a)

(2.13b)

(2.14a)

(2.14b)

Principal Strains in 2-D

(2.15)

(2.16)

(2.17)

Transformation of 3-D Strain

(2.18a)

(2.18b)

(2.18c)

(2.18d)

(2.18e)

(2.18f)

(2.19a)

(2.19b)

Principal Strains (2.20)


4

in 2-D

(2.21)

Displacement Field in 3-D (2.22)

Specimen Geometry Change

(2.23a)

(2.23b)

True Strain

(2.24)

True Stress (2.25)

Hooke’s Law 1-D (2.26)

(2.27)

Poisson’s ratio

(2.28)

Unit Volume Change

(2.29)

Deformation of a Tension Bar

(2.30)

(2.31a)

(2.31b)

Hooke’s Law

Generalized

(2.32)

Indicial (2.33)

Isotropic & Homegenous

(2.34)

(2.35)

(2.36)

(2.37)

(2.38)

Bulk Modulus of Elasticity

(2.39)

Hooke’s Law Orthotropic

(2.40)

(2.41)


5

(2.42)

(2.43)

Strain Rosette

Normal Strains

(2.44)

(2.45)

Maximum Shearing Strain

(2.46)

Strain Rosette (Rectangular/450)

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)

(2.51)

(2.52)

(2.53)

(2.54)

(2.55)

(2.56)

Strain Energy

Common Structural Member

(2.57)

Axially Loaded Bar

(2.58)

(2.59)

(2.60)


6

Circular bar in Torsion

(2.61)

(2.62)

Beam in Bending

(2.63)

Dilatational per Unit Volume

(2.64)

Distortional per Unit Volume

(2.65)

Octahedral Shearing Stress (2.66)

Plane Strain Solutions

(3.1)

(3.2)

(3.3)

(3.4)

(3.5)

(3.6)

(3.7)

(3.8)

(3.9)

Plane Stress Solutions

(3.10)

(3.11a)

(3.11b)

(3.12)

Orthotropic

(3.13)

(3.14)

(3.15)

Airy’s Stress Function

Plane Stress (3.16)

(3.17)


7

Plane Strain

(3.18)

(3.19)

Polynomial Stress Functions

(3.20)

(3.21)

(3.22)

(3.23)

End Loaded Cantilever Beam

(3.24)

Equations of Thermoelasticity

(3.25)

(3.26a)

(3.26b)

(3.27)

(3.28)

(3.29)

(3.30)

Basic Relations in Polar Coordinates

(3.31)

(3.32)

(3.33a)

(3.33b)

(3.33c)

Plane Stress

(3.34)

Plane Strain

(3.35)

Transformation Equations

(3.36)

(3.37)

Compatibility Equations

(3.38)

(3.39)


8

(3.40)

(3.41)

Uniaxial Tension

(3.42)

Compression of a Wedge

(3.43)

(3.44)

Bending of a Wedge

(3.45)

(3.46)

Combined Compression & Bending of a Wedge

(3.47)

Straight Boundary of a

(3.48)

large Plate

(3.49)

(3.50)

(3.51)

poor (3.52)

better (3.53)

Stress Concentration Factors

(3.54)

Circular Hole in Tension

(3.55a)

(3.55b)

(3.55c)

Elliptic Hole in Tension

(3.56)

(3.57)

Contact Stresses

Two Spheres in Contact

(3.58)

𝜈=0.3 (3.59)

(3.60)

(3.61)


9

(3.62)

(3.63)

Two Cylinders in Contact

(3.64)

(3.65)

(3.66)

Cylinder on a flat surface

(3.67)

Contact Stress Distrıbution

Two Spheres in Contact

(3.68a)

(3.68b)

(3.68c)

Two Parallel Cylinders in Contact

(3.69a)

(3.69b)

(3.69c)

(3.69d)

General Contact

(3.70)

(3.71)

(3.72)

(3.73)

(3.74)

Maximum Shearing Stress Theory

(4.1)

(4.2a)

(4.2b)

(4.3)

Maximum Distortion Energy Theory

(4.4a)

(4.4b)

plane stress (4.5a)

plane stress (4.5b)

Octahedral Shearing Stress (von Mises) Theory (4.6)

Combined Loading (Bending+Torsion)

(4.7)

Maximum Shearing Stress Theory

(4.8a

(4.8b)

Maximum Distortion Energy Theory

(4.9a)

(4.9b)

Maximum Principal Stress

(4.10)

Plane (4.11a)


10

Theory Stress

(4.11b)

Coulomb-Mohr Theory

(4.12a)

(4.12b)

(4.12c)

(4.13)

Torsion Bar (4.14)

(4.15)

Fracture Mechanics

Stress Intensity Factor

(4.16)

Fracture Toughness

(4.17)

(4.18)

(4.19)

Fatigue

(4.20)

(4.21)

(4.22)

(4.23)

(4.24)

(4.25)

Impact or Dynamic Loads

(4.26)

(4.28)

(4.29)

(4.30)

Pure Bending of Beams of Symmetrical Cross Section

(5.1)

(5.2)

(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

(5.11)

(5.12)

(5.13)

(5.14)

(5.15)


11

(5.16)

(5.17)

(5.18)

(5.19)

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

(5.26)

Bending

(5.27)

(5.28)

(5.29)

(5.30)

(5.31)

(5.32)

(5.33)

(5.34)

Displacements of a Cantilever Beam

(5.35)

(5.36)

(5.37)


12

Normal and Shear Stresses

(5.38)

(5.39)

(5.40)

(5.41)

(5.42)

(5.43)

Effect of Transverse Normal Stresses

(5.44a)

(5.44b)

Composite Beams

(5.45a)

(5.45b)

(5.46)

(5.47)

(5.47’)

(5.48)

(5.49)

(5.50)

(5.51)

(5.52)

(5.53)

Steel Reinforced Concrete Beam

(5.54)

(5.55)

Shear Center (5.56)

(5.57)

Displacements of a Propped Cantilever Beam

(5.58a)

(5.58b)

(5.58c)

(5.59)

(5.60)

(5.61)

Energy Method for Deflections

Bending stress only

(5.62)

Shearing stress only (5.63)

(5.64)

Elasticity Theory

(5.65)

(5.66)

(5.67)


13

(5.68)

(5.69)

(5.70)

(5.71)

(5.72)

(5.73)

(5.74)

Stresses in a Steel Crane Hook

(5.75a)

(5.75b)

Documents

ME626 Advanced Mechanics of Materials Formula Sheet Factor ...me626.cankaya.edu.tr/uploads/files/Formula Sheet Quiz 4.pdf · Mohr’s Circle in 3-D (1.45) (1.46) (1.47) Boundary Conditions