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ASME SI-2-1976 — SI Units in Strength of Materials (Second Edition)
📐 ASME SI-2-1976 is the second booklet in the ASME International System (SI) of Units series, dedicated to SI units in strength of materials, published in its Second Edition in July 1976. Developed as part of the Society’s policy to promote the adoption and use of SI (metric) units, the booklet serves students, teachers, and engineers in practice as a primer and as a supplement to existing textbooks that use U.S. Customary units.
💡 The philosophy of the series: problems whose input is in SI terms should be worked in SI — do not convert back to U.S. Customary and solve there. Once the “feel” for SI units is acquired, calculations in SI become simpler and faster. The Second Edition incorporates suggestions received from readers of the First Edition.
1. Overview and Scope 📌
Strength of Materials is the discipline that investigates the effect of applied forces upon bodies and is concerned with the resulting deformations. It follows logically after the rigid-body treatments of classical statics and dynamics. Four basic types of external loading are frequently encountered in machine and structure design: axial tension, axial compression, bending, and torsion. The objective is to design machines and structures that withstand the applied loads within acceptable limits of stress, deflection, and deformation, which requires understanding the internal stress-strain relations in a given geometry under a specified loading and knowing certain basic physical properties of the materials involved.
The booklet contains five sections: (1) Introduction; (2) Units and Conversion Factors; (3) Solved Problems; (4) Practice Problems with Answers; and four tables covering principal quantities and their units, derived units, commonly used conversion factors, and average physical properties of common materials.
⚠️ The booklet is a primer and is not a substitute for a textbook: it supplements current U.S. Customary textbooks, so it should be used together with formal statics and strength-of-materials courses.
2. Principal Quantities and Unit Systems 🔧
The principal quantities encountered in strength of materials, in both U.S. Customary and SI (metric) units, are listed below. The recommended SI unit for stress and pressure is the pascal (Pa), with MPa favored in engineering practice.
| Quantity | U.S. Customary Unit (Symbol) | SI Unit (Symbol) |
|---|---|---|
| Force | pound force (lbf) | newton (N) |
| Stress / pressure | lbf/in² (psi) | pascal (Pa); MPa preferred |
| Length | foot (ft), inch (in) | meter (m), millimeter (mm) |
| Energy / work | foot-pound force (ft·lbf) | joule (J) |
| Power | horsepower (hp) | watt (W) |
| Area | square inch (in²) | square meter (m²), mm² |
| Area moment of inertia | in⁴ | mm⁴ |
| Section modulus | in³ | mm³ |
| Torque / bending moment | lbf·ft | N·m |
| Measured temperature | degree Fahrenheit (°F) | degree Celsius (°C) |
| Rotational frequency | rev/s, rad/s | s⁻¹, rad/s |
Key derived SI units follow from the base units: energy J = N·m = m²·kg·s⁻²; force N = m·kg·s⁻²; power W = J/s = m²·kg·s⁻³; stress Pa = N/m² = m⁻¹·kg·s⁻².
🚨 In SI, loads are often given as masses in kilograms — the most frequent source of error. Multiply the mass by the gravitational acceleration g ≈ 9.8 m/s² to obtain the force in newtons. For example, a 10 kg mass hanging from a wire of 4 mm² cross section produces a stress of (10 × 9.8) N / 4 mm² = 24.5 N/mm² = 24.5 MPa. Never confuse mass with force!
3. Commonly Used Conversion Factors ⚖️
The booklet tabulates conversion factors using the “number plus E exponent” notation (a number between 1 and 10 followed by E, a sign, and two digits giving the power of ten):
| Quantity | Conversion | Factor |
|---|---|---|
| Area | in² to m² | 6.4516 × 10⁻⁴ |
| Area | ft² to m² | 9.290304 × 10⁻² |
| Bending moment / torque | lbf·ft to N·m | 1.355818 |
| Energy / work | ft·lbf to J | 1.355818 |
| Force | lbf to N | 4.448222 |
| Length | in to mm (exact) | 2.54 × 10¹ |
| Length | ft to m (exact) | 3.048 × 10⁻¹ |
| Plane angle | degree to rad | 1.745329 × 10⁻² |
| Power | hp (550 ft·lbf/s) to W | 7.456999 × 10² |
| Stress / pressure | lbf/in² to Pa | 6.894757 × 10³ |
| Stress / pressure | lbf/ft² to Pa | 4.788026 × 10¹ |
| Temperature interval | °F to °C (interval) | 5.555556 × 10⁻¹ |
For instance, 1.745329 E-02 means 1.745329 × 10⁻² = 0.01745329, the exact radian value of one degree. Factors marked with an asterisk (e.g., in to mm, ft to m) are exact relationships in terms of base units.
💡 In strength-of-materials work, the modulus of elasticity is conveniently expressed in GPa (steel ≈ 200 GPa, aluminum ≈ 70 GPa) while allowable stresses are in MPa. Remember 1 GPa = 1000 MPa, and keep units consistent when substituting into formulas such as δ = PL/(AE).
4. Worked Examples and the SI Approach ✏️
The booklet solves the same two-bar series-load problem in both U.S. Customary and SI units to demonstrate the calculation flow in each system:
- U.S. Customary version: a 30 in bronze bar of 2 in² cross section and a 20 in steel bar of 1 in² cross section; allowable stresses 12,000 psi (bronze) and 20,000 psi (steel); total elongation limited to 0.0325 in; Ebr = 15×10⁶ psi, Est = 30×10⁶ psi; the governing load is P = 19,500 lb.
- SI version: a 750 mm bronze bar of 1300 mm² cross section and a 500 mm steel bar of 650 mm² cross section; allowable stresses 82.7 MPa (bronze) and 138 MPa (steel); total elongation limited to 0.8 mm; Ebr = 105 GPa, Est = 200 GPa; the governing load is P = 85.6 kN.
Another typical example: an aluminum bar 1500 mm long fixed between immovable supports A and B — after the bar is placed and the temperature drops 55 °C, find the stress in the bar. The free contraction is δt = α·L·ΔT = (22.5×10⁻⁶ °C⁻¹) × (1500 mm) × (−55 °C) ≈ −1.86 mm; the supports then supply the force that stretches the bar back, found through δ = PL/(AE). Well-posed SI examples like this one make the magnitudes far easier to visualize.
⚠️ Pay attention to the sign of forces and deformations: elongation is positive and contraction negative. Sign mistakes when combining thermal and load-induced strains are the most common error among beginners — always draw a free-body diagram and mark the positive direction.
5. Engineering Practice Essentials 🛠️
- 🔍 Stress unit choice: report and design in MPa (N/mm²) to avoid repeated conversions among N/m², kPa, and bar.
- 🔧 Section property naming: use mm⁴ for area moments of inertia and mm³ for section moduli, matching manufacturer tables for structural shapes.
- 📊 Separate mass and force: distinguish mass loads (kg) from force loads (N/kN) in the load catalogue; convert self-weight with g = 9.8 m/s² (the booklet’s average) or 9.81 m/s².
- 📋 Teaching practice: reconvert psi/ksi textbook exercises to SI (1 psi = 6.894757 kPa, 1 ksi ≈ 6.895 MPa) and re-solve them to build SI intuition.
✅ Suggested practice: rewrite every U.S. Customary problem in SI, and check that answer magnitudes (stresses of tens to hundreds of MPa, forces of tens to hundreds of kN) feel intuitively right — the most effective way to develop SI thinking.
6. Frequently Asked Questions ❓
❓ Q: Why does the booklet call MPa the preferred unit for stress?
A: Because 1 MPa = 1 N/mm², which pairs nicely with common cross sections (mm²) and forces (N, kN); using Pa alone would put steel strengths around 2×10⁸ and moduli around 2×10¹¹, making decimal errors easy.
A: Because 1 MPa = 1 N/mm², which pairs nicely with common cross sections (mm²) and forces (N, kN); using Pa alone would put steel strengths around 2×10⁸ and moduli around 2×10¹¹, making decimal errors easy.
❓ Q: What is a quick conversion factor from psi to MPa?
A: 1 psi ≈ 6.895 kPa ≈ 0.006895 MPa; for mental arithmetic remember 1 ksi ≈ 6.895 MPa. For example, 12,000 psi = 12 ksi ≈ 82.7 MPa.
A: 1 psi ≈ 6.895 kPa ≈ 0.006895 MPa; for mental arithmetic remember 1 ksi ≈ 6.895 MPa. For example, 12,000 psi = 12 ksi ≈ 82.7 MPa.
❓ Q: What units are used for spring stiffness and modulus of elasticity?
A: Spring stiffness in N/m (or N/mm); Young’s modulus in Pa, commonly GPa. Remember 1 GPa = 10⁹ Pa = 1000 MPa, and keep a consistent unit set when substituting into deformation formulas.
A: Spring stiffness in N/m (or N/mm); Young’s modulus in Pa, commonly GPa. Remember 1 GPa = 10⁹ Pa = 1000 MPa, and keep a consistent unit set when substituting into deformation formulas.
🔍 Q: How does this booklet relate to the rest of the SI series?
A: The ASME SI series comprises SI-1 (orientation guide), SI-2 (strength of materials), SI-3 (dynamics), SI-4 (thermodynamics), SI-5 (fluid mechanics), SI-6 (kinematics), SI-7 (heat transfer), SI-8 (vibration), SI-9 (energy conversion), and SI-10 (steam charts). SI-1 is the basic guide and should be used together with every field-specific booklet.
A: The ASME SI series comprises SI-1 (orientation guide), SI-2 (strength of materials), SI-3 (dynamics), SI-4 (thermodynamics), SI-5 (fluid mechanics), SI-6 (kinematics), SI-7 (heat transfer), SI-8 (vibration), SI-9 (energy conversion), and SI-10 (steam charts). SI-1 is the basic guide and should be used together with every field-specific booklet.
