Mechanical Components and Assemblies

The applied components: pressure vessels and piping, hydraulic/pneumatic components, beams/trusses/frames, springs, vibrating systems, basic machines and mechanisms, and basic mechatronics. One of the heavier areas on the Machine Design & Materials depth.

What the problems look like

Component-level analysis across a broad set — pressure vessels (hoop/longitudinal stress, thin vs. thick wall); beams/trusses/frames (reactions, member forces by joints/sections); springs (rate, shear stress, deflection); vibrating systems (natural frequency, damping); hydraulic/pneumatic (cylinder force, flow). Calculation-based and wide-ranging.

By exam day you should be able to —

• pressure vessels: hoop σ = pr/t, longitudinal σ = pr/2t, thin- vs. thick-wall validity;
• beams/trusses/frames: reactions, method of joints/sections, member tension/compression;
• springs: spring rate k, corrected shear stress (K_s), deflection, series vs. parallel;
• vibrating systems: natural frequency ωn = √(k/m), damping ratio, resonance;
• hydraulic/pneumatic: cylinder force = p·A, continuity (flow = velocity × area).

Where people lose points

• Hoop vs. longitudinal stress — hoop is 2× longitudinal; and ignoring thin-wall validity (t < ~r/10).
• Spring shear stress — skipping the curvature correction (τ = K_s·8FD/πd³, with K_s = (4C + 2)/(4C − 3)); the uncorrected formula under-predicts.
• Damped vs. undamped frequency — ω_d = ω_n√(1 − ζ²), not ω_n.
• Truss method-of-joints sign errors (tension vs. compression).
• Springs in series vs. parallel — series springs are softer (compliances add), the opposite of the intuitive guess.
• Natural frequency — dropping the √, or using weight instead of mass (forgetting g).
• Cylinder force — gauge vs. absolute pressure, or the wrong area (rod side vs. cap side).

Have these at your fingertips

Hoop/longitudinal stress, spring k and the K_s correction, ωn = √(k/m), and the truss methods — plus where they sit in the Handbook.

Going deeper

• Pressure vessels
• Spring design
• Mechanical vibrations

Part of the Machine Design & Materials depth. Practice this area with exam-real problems — the tutor walks any one you miss. → Start your 7-day free trial — no card. Or take the free practice exam first.