BEM PCE Part B Mechanical study plan

Inventory the full Part B mechanical syllabus and map each topic to a confidence rating from 1 to 5, so the weakest areas are named explicitly rather than assumed.

Rebuild from memory the core statics toolkit: free-body diagrams, equilibrium equations in 2D and 3D, truss method of joints and sections, and friction on inclines.

Derive and apply stress and strain relationships for axial loading, including thermal expansion restraint and Poisson effect, working at least 20 hand-solved problems.

Set up a personal formula sheet and error log in a single document that will be maintained through all eight weeks.

Compute shear force and bending moment diagrams for determinate beams under point, uniformly distributed, and triangular loads without reference aids.

Calculate second moments of area for composite and built-up sections, including parallel axis theorem transfers.

Apply beam bending stress and deflection formulas, and identify where each formula's assumptions break down.

Solve combined loading cases by superposing axial, bending, and torsional stress components at a point.

Build and interpret Mohr's circle for plane stress, extracting principal stresses and maximum shear from arbitrary stress states.

Apply von Mises and Tresca yield criteria to decide failure under multiaxial stress and compare the two predictions.

Analyze thin-walled pressure vessels and combined torsion-bending shafts for critical stress locations.

Practice reading stress concentration factors from tabulated data described in words and apply them correctly.

Solve column buckling problems using Euler and Johnson parabolic formulas, selecting the correct regime by slenderness ratio.

Compute fatigue life estimates with S-N curves, Goodman and Gerber diagrams, and stress concentration and surface finish corrections.

Work through bolted and welded joint strength problems including eccentric loading and bolt group analysis.

Complete a timed 40-question mixed mechanics-of-materials set under exam pacing.

Analyze kinematic mechanisms using instant centers and relative velocity methods for linkages and cams.

Solve dynamic force problems with Newton-Euler equations for rotating and translating rigid bodies, including inertia referred to a pivot.

Balance rotating masses and evaluate flywheel energy fluctuation for a given coefficient of speed fluctuation.

Model single and multi-degree-of-freedom vibration, computing natural frequency, damping ratio, and resonance amplitude.

Compute gear train ratios for simple, compound, and planetary arrangements, including tooth-number and arm-speed relationships.

Analyze four-bar and slider-crank position, velocity, and acceleration at multiple crank angles and tabulate the results.

Evaluate belt, chain, and clutch torque capacity from friction and geometry parameters.

Review machine design selection logic for bearings, shafts, and keys using load and life criteria.

Work fluid mechanics fundamentals: continuity, Bernoulli with losses, Reynolds number, and friction factor selection by regime.

Solve pipe network and pump sizing problems using head, system curves, and NPSH reasoning.

Apply thermodynamic cycles and heat transfer basics to equipment-level problems likely to appear alongside mechanical content.

Revisit the week 1 confidence map and re-rate every topic, targeting the three lowest for concentrated review.

Take two full-length timed practice exams under realistic conditions and log pacing by question type.

Review every error from both exams and classify each as knowledge gap, formula recall, misread, or time pressure.

Drill only the top ten recurring error patterns until each is solved correctly twice in a row without notes.

Finalize a condensed one-page reference sheet and rehearse it from memory before exam day.