An 8-chapter interactive guide to core mechanical engineering calculations — opening with a fully worked chilled-water HVAC system example, then covering shaft torsion and shear stress theory, fillet weld throat shear design and weld distortion control, helical compression spring design, the ISO 286 limits-and-fits system, shell-and-tube heat exchanger LMTD sizing, and round duct sizing by the equal-friction method. Every topic gets its own reference figure on a dedicated, full-size slide so formulas, tables, and worked examples stay legible.
Chapter 1 walks through a complete worked example — a 6-story office building chilled-water system — from cooling load through pipe sizing, head loss, code references, an equipment schedule, and a design checklist. Chapters 2–4 cover mechanics of materials and welding: shaft torsion and shear stress distribution, fillet weld throat shear design per AWS D1.1/AISC 360, and weld distortion modes (shrinkage, angular distortion, bowing) and their control strategies. Chapter 5 covers helical compression spring design — spring rate, Wahl factor, and solid height per ASME B18.8.2. Chapter 6 covers the ISO 286 limits-and-fits system for hole-basis clearance, transition, and interference fits. Chapters 7–8 close with thermal/fluid systems: shell-and-tube heat exchanger sizing by the log mean temperature difference (LMTD) method, and round duct sizing versus airflow using the equal-friction method per SMACNA and the IMC.
Use the Prev / Next buttons at the bottom, or press the arrow keys on your keyboard. Click the ☰ menu button in the top-right to open the table of contents and jump to any section. Each chapter's reference figure follows immediately after its text as its own dedicated slide, so you can view the full diagram at a readable size before moving to the next chapter.
Mechanical engineers and designers who want a quick, visual refresher on core calculations spanning mechanics of materials, welding design, machine elements, fits and tolerances, and thermal/fluid systems; PE Mechanical exam candidates reviewing shaft design, weld design, spring design, and heat exchanger fundamentals; and engineering students building intuition for how these formulas connect to a real HVAC project deliverable.
Maximum shear stress occurs at the outer surface of the shaft: τmax = Tc/J, where T is the applied torque, c is the outer radius (d/2), and J is the polar moment of inertia (J = πd⁴/32 for a solid circular shaft). Shear stress varies linearly from zero at the centerline to τmax at the outer surface.
The effective throat area is At = 0.707wL, where w is the weld leg size and L is the effective weld length. Average shear stress is τ = V/At, and per AWS D1.1 and AISC 360 the design check is τ ≤ φFvw, where φ = 0.75 and Fvw is the design shear strength of the electrode (24,000 psi for E70XX).
In the hole-basis system, the hole tolerance zone is held fixed with its lower deviation at zero (an H-grade hole, such as H7), and the desired fit — clearance (H7/g6), transition (H7/h6), or interference (H7/p6) — is achieved by selecting the shaft tolerance class, since holes are typically produced with standard-sized tooling.
Tlm,cf = (ΔT1 − ΔT2) / ln(ΔT1/ΔT2), where ΔT1 = Th,in − Ts,out and ΔT2 = Th,out − Ts,in. Counterflow arrangements produce the highest LMTD for given inlet/outlet temperatures, maximizing heat transfer per unit of surface area (Q = U·A·Tlm,cf).
The equal friction method sizes every duct segment to the same friction rate per 100 ft (typically 0.08–0.12 in. w.g./100 ft) regardless of airflow, per SMACNA and the IMC. Duct size and resulting velocity are read directly from a friction-rate chart or table for each segment's CFM, then checked against a 700–1,500 fpm velocity band.
Disclaimer: This guide summarizes general mechanical engineering concepts and illustrative calculation examples for educational purposes only. Formulas and worked examples are simplified for teaching clarity and are not a substitute for a complete engineering analysis. Always consult a licensed professional engineer and the applicable codes and standards (ASME, AWS, AISC, ISO, SMACNA, IMC) for actual project design.