ME POST study plan

Derive and apply the stress transformation equations and Mohr's circle for plane stress to compute principal stresses and maximum shear for combined loading cases

Compute axial, torsional, and bending stresses and superpose them for a shaft or bracket under combined loading

Calculate beam shear and bending moment diagrams for simply supported and cantilever beams with point, distributed, and moment loads

Solve column buckling problems using Euler and Johnson parabolic formulas and select the correct formula from slenderness ratio

Apply a static failure theory (von Mises, Tresca, or maximum normal stress) to a ductile or brittle component and justify the choice

Solve statics problems with friction, frames, and machines, including wedge and belt friction

Compute area moments of inertia and polar moments of inertia for composite sections and apply the parallel axis theorem

Analyze 2D particle and rigid-body equilibrium with distributed loads and equivalent resultant forces

Design a simple shaft for combined bending and torsion using the ASME or DE-Goodman approach and select a bearing from a catalog rating

Identify and size standard machine elements (keys, pins, bolts, welds) for shear and bearing failure

Differentiate and integrate standard functions and solve first- and second-order linear ODEs that arise in vibration and transient heat conduction

Solve linear systems and eigenvalue problems by hand and verify with a matrix tool

Apply dimensional analysis and the Buckingham Pi theorem to derive dimensionless groups for a fluid problem

Compute hydrostatic forces on plane and curved submerged surfaces and locate the center of pressure

Apply continuity, Bernoulli, and the momentum equation to pipe networks, nozzles, and bends with head loss

Compute friction and minor losses in series and parallel pipe systems and solve for flow rate or diameter iteratively

Classify pumps and fans and compute head, power, efficiency, NPSH available, and cavitation margin

Apply the affinity laws to predict flow, head, and power at changed speed or impeller diameter

Determine pump operating point by intersecting the system curve with the pump curve

Analyze drag and lift on immersed bodies using Reynolds-number-dependent drag coefficients and compute terminal velocity

Apply the first law to open systems (nozzles, turbines, compressors, heat exchangers) and compute work and heat transfer

Evaluate thermodynamic property changes for ideal gases and steam using tables and the Clausius-Clapeyron relation where needed

Analyze Rankine, Brayton, and vapor-compression refrigeration cycles and compute thermal efficiency or COP with component irreversibilities

Compute steady and transient conduction through plane walls, cylinders, and composite layers with convection boundary conditions using thermal resistance networks

Calculate heat exchanger duty and area using LMTD and effectiveness-NTU methods and select the appropriate method

Compare casting, forging, rolling, extrusion, and sheet-metal forming processes by capability, tolerance, and typical defects

Identify welding and joining processes and their characteristic defects and inspection methods

Apply the iron-carbon phase diagram and TTT curves to select heat treatment for a specified hardness and toughness

Compute machining parameters (cutting speed, feed, depth of cut, material removal rate, and machining time) and estimate tool life with Taylor's equation

Select materials using Ashby-style property indices for a strength-per-weight or stiffness-per-weight requirement

Specify and analyze measurement chains for temperature, pressure, flow, and strain, including sensor selection, range, and uncertainty propagation

Compute static and dynamic characteristics of instruments (sensitivity, linearity, hysteresis, time constant, bandwidth) and correct for loading effects

Derive transfer functions for first- and second-order systems and determine stability with Routh-Hurwitz and Bode criteria

Tune a PID controller for a first-order-plus-dead-time process using Ziegler-Nichols or Cohen-Coon and justify the chosen settings

Evaluate boiler, steam-turbine, and HVAC system performance, including boiler efficiency by losses and chilled-water and air-side load calculations

Compute present worth, annual worth, and internal rate of return for alternatives and select using a consistent basis

Perform depreciation, after-tax cash flow, and replacement analysis for equipment decisions

Apply the NCEES-style ethics framework to conflicts of interest, competence, sealing of documents, and public safety obligations

Identify professional practice issues including liability, standard of care, and contract basics

Complete two full-length timed practice exams and review every missed item to a root cause (concept, formula, or misread)