Mechanics of materials formula sheet, Cheat Sheet of Mechanical Engineering

Download Mechanics of materials formula sheet and more Cheat Sheet Mechanical Engineering in PDF only on Docsity! 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) ME626 Advanced Mechanics of Materials Formula Sheet 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) ME626 Advanced Mechanics of Materials Formula Sheet 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) ME626 Advanced Mechanics of Materials Formula Sheet 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) ME626 Advanced Mechanics of Materials Formula Sheet 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 Coordinate s (3.31) (3.32) (3.33a ) (3.33b ) (3.33c) Plane Stress (3.34) Plane Strain (3.35) Transformatio n Equations (3.36) (3.37) Compatibility Equations (3.38) (3.39) ME626 Advanced Mechanics of Materials Formula Sheet 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) ME626 Advanced Mechanics of Materials Formula Sheet 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) ME626 Advanced Mechanics of Materials Formula Sheet 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)