Mechanical Engineering Design: Key Concepts and Formulas

Material Properties and Heat Treatment

• 2.1: Toughness
• 2.2: 14 × 10⁴, 90 × 10⁴
• 2.3: Stiffness
• 2.4: Toughness
• 2.5: Hardness
• 2.6: Malleability
• 2.7: 3–4% Carbon
• 2.8: Grey cast iron with ultimate tensile strength 300 N/mm²
• 2.9: Plain carbon steel (0.35–0.45% C, 0.7–0.9% Mn)
• 2.10: Mild steel
• 2.11: Less than 0.3% carbon
• 2.12: Sulphur
• 2.13: Chromium
• 2.14: Chromium
• 2.15: Above upper critical temperatures, cooled in still air
• 2.16: Case-hardening
• 2.17: Cyaniding
• 2.18: Case-carburising

Manufacturing and Tolerances

• 3.1: Aluminium
• 3.2: Fibre lines arranged in a predetermined way
• 3.3: Very small fillet radius
• 3.4: Easy removal of forged part from die cavities
• 3.5: Tolerances given on both positive and negative sides
• 3.6: Tolerance zone of hole and shaft overlap
• 3.7: Tolerance zone of hole is entirely above shaft
• 3.8: Upper deviation is zero
• 3.9: Designation of fit for 50 mm basic size
• 3.10: Clearance fit

Stress and Structural Analysis

• 4.1: Shear and bending
• 4.2: Ry = 775.4 N and Rx = 0
• 4.3: W/2 + Pℓ/2a
• 4.4: 300 kg
• 4.5: P(3L + 4b) / 4b
• 4.7: Poisson's modulus and Poisson's ratio
• 4.8: Bars AB and BC subjected to bending
• 4.9: μ < 0.5
• 4.10: 150
• 4.11: 1/12
• 4.12: 2/3
• 4.13: P(E₁−E₂)/(A(E₁+E₂))
• 4.14: 100 kN
• 4.15: Difference of normal stresses
• 4.16: 11 MPa

Fatigue, Failure Theories, and Columns

• 5.1: Ratio of peak stress to nominal stress
• 5.2: Components made of cast steel
• 5.3: 3
• 5.4: 5
• 5.5: Fluctuating stress
• 5.6: Reversed stress
• 5.7: Distortion energy theory
• 5.8: Ratio of endurance limit to ultimate stress
• 5.9: Decreases
• 5.10: Cold working
• 5.11: q = (Kt−1)/(Kf−1)
• 5.12: 400
• 5.13: 1.75
• 5.14: 7 × 10⁶
• 5.15: Both ends hinged
• 5.16: Rankine's equation
• 5.17: (L/k)² = 30
• 5.18: 400
• 5.19: Ends hinged in one plane, fixed in perpendicular
• 5.20: None of the above
• 5.21: 40 kN
• 5.22: Both ends fixed
• 5.23: π²EI / 4L²
• 5.24: √2 π²EI / L²

Thread Mechanics and Power Screws

• 6.1: Square threads
• 6.2: One direction
• 6.3: Trapezoidal threads
• 6.4: Buttress threads
• 6.5: Acme
• 6.6: High mechanical advantage
• 6.7: Buttress threads
• 6.8: WR tan(φ+α) / d
• 6.9: η = tan α / tan(φ+α)
• 6.10: φ < α
• 6.11: Less than 50%
• 6.12: π/4
• 6.13: Equal to 50%
• 6.14: (1−sinφ)/(1+sinφ)
• 6.15: Lead angle
• 6.16: 33%
• 6.17: To prevent rotation of load
• 6.18: One end fixed, other free

Fasteners and Threaded Joints

• 7.1: Threaded on full length of shank
• 7.2: Used on one end only
• 7.3: Small shank diameter
• 7.4: Split pin passed through bolt and nut
• 7.5: Metric threads (36 mm pitch diameter, 2 mm pitch)
• 7.6: Metric coarse threads (20 mm outside diameter)
• 7.7: Effective diameter
• 7.8: 55°
• 7.9: 60°
• 7.10: 60°
• 7.11: h = 0.5d
• 7.12: h = 0.4d
• 7.13: Tensile stress
• 7.15: 424.5 and 42.4
• 7.16: 159 MPa
• 7.17: Left-hand threads on both ends
• 7.18: Sum of initial tension and external load
• 7.19: External load
• 7.20: Increasing shank diameter

Welded and Riveted Joints

• 8.1: Throat
• 8.2: 60° and 30°
• 8.3: Tensile strength
• 8.4: Shear strength
• 8.5: P/(2hl)
• 8.6: 0.707
• 8.7: 2T / (πd²t)
• 8.8: Snap head
• 8.9: Bending moment
• 8.10: Low mild steel
• 8.11: d = 6√t
• 8.12: 1.5 d
• 8.13: Free from residual stresses
• 8.14: Single shear
• 8.15: 1.875 times resistance in single shear
• 8.16: 0.75
• 8.17: Double-strap butt joint
• 8.18: Quadruple-riveted

Shafts, Keys, and Couplings

• 9.1: 2T / πd³
• 9.2: 0.25 θ
• 9.3: Tensile yield strength (Sy)
• 9.4: 40 MPa
• 9.5: 4.5
• 9.6: σ₁
• 9.7: 16
• 9.8: 1/2
• 9.9: (dA/dB)³
• 9.10: √(Mb² + Mt²)
• 9.11: Mb + √(Mb² + Mt²)
• 9.12: (shaft diameter)⁴
• 9.13: σb/2 + √((σb/2)² + τ²)
• 9.14: Parabola
• 9.15: Tension
• 9.16: Feather key
• 9.17: Four times shear stress
• 9.18: Friction force
• 9.19: Flexible bush coupling
• 9.20: Shear force and bending moment