BEM PCE Part B Mechanical common mistakes
BEM PCE Part B Mechanical · Understand the traps and how to avoid them.
Treating every pressure vessel or piping question as a thin-wall problem and applying the hoop-stress formula sigma = pr/t without first checking that the radius-to-thickness ratio justifies it (r/t of roughly 10 or more).
The thin-wall formula is the only one most candidates memorise, so it becomes a reflex; when a thick-walled cylinder appears, the wall stress is under-predicted and the answer chosen is the thin-wall value.
What to do instead
Before any cylinder stress calculation, compute r/t explicitly and write it down. If r/t is below about 10, switch to Lame equations (thick-cylinder) and state the boundary conditions at the inner and outer surfaces. Practise three thick-cylinder problems until the check is automatic.
Selecting a fatigue or stress-concentration factor from memory and applying it to the wrong stress component, for example multiplying the mean stress by Kf as well as the alternating stress, or ignoring the notch sensitivity q.
Fatigue questions combine several modifiers (surface, size, load, reliability, notch) and candidates collapse them into one remembered number rather than deriving the effective factor Kf = 1 + q(Kt - 1).
What to do instead
Write the fatigue design equation in full before substituting: separate alternating and mean components, apply Kf only to the alternating term for ductile materials, and show each modifying factor as a separate line with its source value. Rehearse one fully worked shaft-fatigue problem per study session.
Using the wrong failure theory for a given material: applying von Mises (distortion energy) to a brittle cast iron or concrete component, or applying maximum principal stress to a ductile steel.
Von Mises is drilled in as the default, and the material description in the stem (brittle, cast, low ductility) is skimmed past.
What to do instead
At the start of every combined-stress question, underline the material and its ductility in the stem and write 'ductile -> von Mises / Tresca' or 'brittle -> maximum principal stress / Mohr' before calculating. Compare Tresca and von Mises results so the factor-of-safety difference is familiar.
Drawing the free-body diagram with friction, reaction, or cable forces in an assumed direction and then silently dropping the negative sign when reporting the magnitude, or omitting one reaction component entirely.
Candidates draw the diagram in a hurry and treat signs as bookkeeping rather than information; a negative result is then reported as positive, changing the direction of the answer.
What to do instead
Adopt a fixed sign convention, annotate assumed directions on the diagram, and carry signs through every equation to the final line. Explicitly state the direction of each reaction in the answer. Do a second pass checking that the number of unknown reactions matches the number of equilibrium equations available.
Mixing unit systems mid-calculation, for example inserting a diameter in millimetres into an equation expecting metres, or using g = 9.81 with masses given in lbm without converting to slugs.
Exam stems deliberately mix units (kW, mm, rpm, MPa) to test vigilance, and candidates convert only the first quantity they notice.
What to do instead
Convert every given quantity to a coherent base set (SI: m, kg, s, N, Pa) as the first step, writing the converted value beside the original. Keep a conversion line visible for each quantity, and sanity-check the final magnitude against physical intuition (e.g. a shaft torque in the kN.m range, not MN.m).
Applying a bearing-life or gear-rating formula with the wrong exponent or without converting speed and load to the reference conditions the formula assumes (e.g. using revolutions instead of millions of revolutions in the basic rating life equation).
Bearing and gear formulae have several variants (L10 = (C/P)^p in millions of revolutions; p = 3 for ball, 10/3 for roller) and the exponent and unit basis are easily transposed under time pressure.
What to do instead
Memorise the basic rating life equation with its unit basis and both exponents, and write the exponent choice and unit basis on the working page before substituting. Convert speed to the correct revolution count explicitly and check that the resulting life is expressed in the unit the question asks for (hours, revolutions, or millions).
Skipping the thermodynamic state check: applying the ideal-gas relation to a saturated mixture, or using the wrong specific heat (cp versus cv) in an energy balance for a closed versus open system.
Candidates pattern-match on 'gas' and reach for pV = mRT without checking whether the fluid is in the two-phase region, and they confuse the closed-system first law (Q - W = dU) with the steady-flow form (Q - W = dh).
What to do instead
Before any property calculation, state the phase (subcooled, saturated, superheated) and the system type (closed or open). For open systems use enthalpy; for closed systems use internal energy. Where a property table would be needed, state the assumption explicitly and flag it.
Answering a multi-part question in the order asked without allocating marks, so an early long calculation consumes the time needed for later, higher-value parts and the final part is left blank.
Candidates read the paper linearly and start writing immediately; they underestimate how long a full worked calculation takes under exam conditions.
What to do instead
In the first five minutes, scan the whole paper, note the marks per part, and budget minutes proportional to marks. Do the highest marks-per-minute parts first and leave a fixed reserve for the final part. Practise full papers against a timer to calibrate the budget.
Presenting a numerical answer with no working, no stated assumptions, and no units, so method marks are lost even when the final number is right.
Candidates assume the marker only checks the final value, or they run out of time and write only the result.
What to do instead
Structure every solution as: given data with units, stated assumptions, governing equation in symbols, substitution, result with units and a direction or sign where relevant. Even when short of time, write the governing equation and the substitution line, which carry method marks.
Failing to re-read the question's final line, so a question asking for the factor of safety, the power required, or the maximum allowable load is answered with an intermediate quantity such as stress or torque.
The stem's narrative and data dominate attention, and the actual requested quantity is buried in the last sentence.
What to do instead
Before starting the calculation, underline the requested quantity and write it at the top of the working page as a target (e.g. 'find: FoS'). After obtaining a number, check it against that target and against the units requested, and add a one-line interpretation of what the number means physically.