The Ultimate FE Mechanical Exam Cheat Sheet:
Essential Formulas and Concepts to Memorize
Introduction
The FE Mechanical Exam covers assorted topics, including Mechanics of Materials, Mathematics and Advanced Engineering Mathematics, Thermodynamics, Materials Science, and Machine Design and Analysis.
Knowing where to focus your study efforts can be difficult with so much ground to cover. However, one thing can help you immensely: memorizing formulas and concepts.
Essential Formulas and Concepts for the FE Mechanical Exam
To help you prepare for the FE Mechanical Exam, we have compiled a list of essential formulas and concepts you need to know. We have organized the material into the topics covered on the exam, so you can easily find the necessary information.
Mechanics of Materials
The Mechanics of Materials section of the FE Mechanical Exam covers topics such as stress and strain, axial loading, bending, and torsion. Here are some essential formulas and concepts to memorize:
Stress = Force / Area
Strain = Change in length / Original length
Young's modulus = Stress / Strain
Moment of inertia = (1/12) * b * h^3 (for a rectangular crosssection)
Shear stress = Force / Area (for shear)
Maximum bending stress = (My / I) * c (where M is the bending moment, I is the moment of inertia, and c is the distance from the neutral axis to the point in question)
Mathematics and Advanced Engineering Mathematics
The Mathematics and Advanced Engineering Mathematics section of the FE Mechanical Exam covers calculus, differential equations, linear algebra, and numerical methods. Here are some essential formulas and concepts to memorize:
Derivative of a function f(x) = df/dx
Integral of a function f(x) = ∫f(x)dx
Taylor series expansion: f(x) = f(a) + f'(a)(x-a) + (1/2)f''(a)(xa)^2 + ...
Eigenvalues and eigenvectors: Ax = λx
Thermodynamics
The Thermodynamics section of the FE Mechanical Exam covers thermodynamic laws, cycles, and properties. Here are some essential formulas and concepts to memorize:
The first law of thermodynamics: ΔU = Q - W
The second law of thermodynamics: ΔS = Q/T
Carnot cycle efficiency = (T_H - T_C) / T_H
Ideal gas law: PV = nRT
Enthalpy = U + PV
Materials Science
The Materials Science section of the FE Mechanical Exam covers topics such as crystal structures, defects, and mechanical properties of materials. Here are some essential formulas and concepts to memorize:
Young's modulus = Stress / Strain
Shear modulus = Shear stress / Shear strain
Poisson's ratio = -Transverse strain / Axial strain
Yield strength = Stress at which plastic deformation begins
Ductility = measure of how much a material can deform before breaking
Machine Design and Analysis
The Machine Design and Analysis section of the FE Mechanical Exam covers topics such as stress analysis, machine elements, and vibration analysis. Here are some essential formulas and concepts to memorize:
Stress = Force / Area
Strain = Change in length / Original length
Young's modulus = Stress / Strain
Moment of inertia = (1/12) * b * h^3 (for a rectangular crosssection)
Natural frequency of a simple harmonic oscillator: f = (1/2π) * √(k/m)
Critical speed of a rotating shaft: N = (π/2) * (D/d) * √(E/ρ)
Conclusion
Memorizing formulas and concepts is essential for success on the FE Mechanical Exam. By focusing your study efforts on these areas outlined on this cheat sheet, you will be prepared to pass the exam.
Remember to practice regularly, use mnemonic devices, make flashcards, and use visual aids to reinforce your memory. With these tips and our cheat sheet, you will be well on your way to passing the FE Mechanical Exam.
For more information: https://www.schoolofpe.com/femechanical/
