Fundamentals of Engineering Exam (FE) Engineering Mechanics and Materials Syllabus

Engineering Mechanics and Materials syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Engineering Mechanics and Materials in Fundamentals of Engineering Exam (FE), not a summary of it.

1. 1

   Statics

   5 topics

   • Force Systems and Resultants
     • Concurrent and coplanar forces
     • Resultants and moment of a force
     • Couples and equivalent systems
   • Equilibrium
     • Free-body diagrams
     • 2D and 3D equilibrium equations
   • Trusses and Frames
     • Method of joints
     • Method of sections
     • Frames and machines
   • Centroids and Moments of Inertia
     • Centroids of areas and volumes
     • Area and mass moments of inertia; parallel-axis theorem
   • Friction
     • Dry (Coulomb) friction
     • Wedges, belts and screws
2. 2

   Dynamics

   4 topics

   • Kinematics of Particles
     • Rectilinear and curvilinear motion
     • Normal-tangential and polar coordinates
     • Relative and projectile motion
   • Kinetics of Particles
     • Newton's second law
     • Work-energy principle
     • Impulse-momentum and impact
   • Rigid Body Motion
     • Rotation about a fixed axis
     • General plane motion
   • Vibrations
     • Free vibration and natural frequency
     • Damped and forced vibration
3. 3

   Mechanics of Materials

   4 topics

   • Stress and Strain
     • Normal, shear and bearing stress
     • Hooke's law and Poisson's ratio
     • Thermal stress and strain
   • Axial, Torsion and Bending
     • Axial deformation
     • Torsion of circular shafts
     • Shear and bending moment diagrams
     • Flexural and shear stresses in beams
   • Combined Loading and Stress Transformation
     • Combined axial, torsional and bending stress
     • Mohr's circle and principal stresses
   • Beam Deflection and Stability
     • Deflection by integration and superposition
     • Euler buckling of columns
4. 4

   Materials Science

   3 topics

   • Atomic Structure and Bonding
     • Crystal structures and defects
     • Bonding types
   • Mechanical Properties and Testing
     • Stress-strain behavior, ductility, toughness
     • Hardness, fatigue and creep
   • Material Classes and Processing
     • Metals, polymers, ceramics, composites
     • Phase diagrams and heat treatment
     • Corrosion and degradation

Engineering Mechanics and Materials flashcards for Fundamentals of Engineering Exam (FE)

23 of 51 cards from the Engineering Mechanics and Materials deck — real questions with worked answers.

1. What is the resultant of a coplanar concurrent force system, and how is its magnitude computed from components?

   The resultant $\vec{R}$ is the single force equivalent to all the forces, found by summing components: $R_x=\sum F_x$, $R_y=\sum F_y$. Its magnitude is $R=\sqrt{R_x^{2}+R_y^{2}}$ and direction $\theta=\tan^{-1}\!\left(\frac{R_y}{R_x}\right)$.

2. How is the moment of a force about a point computed using the vector (cross-product) method?

   $\vec{M}=\vec{r}\times\vec{F}$, where $\vec{r}$ is the position vector from the point to any point on the line of action of $\vec{F}$. The scalar magnitude is $M=Fd$, where $d$ is the perpendicular distance from the point to the force's line of action.

3. What is a couple, and what is the magnitude of the moment it produces?

   A couple is two equal, opposite, parallel forces separated by a distance $d$. It produces a pure moment (no net force) of magnitude $M=Fd$. The couple moment is a free vector—it is the same about every point.

4. State the three scalar equations of equilibrium for a rigid body in two dimensions.

   $$\sum F_x=0,\quad \sum F_y=0,\quad \sum M_z=0$$ All forces balance in both directions and the net moment about any point is zero.

5. How many independent equilibrium equations exist for a rigid body in three dimensions?

   Six: $\sum F_x=\sum F_y=\sum F_z=0$ (force balance) and $\sum M_x=\sum M_y=\sum M_z=0$ (moment balance).

6. What distinguishes a statically determinate structure from a statically indeterminate one?

   A statically determinate structure has exactly enough reactions/members to be solved by equilibrium equations alone (equations = unknowns). Indeterminate structures have more unknowns than equilibrium equations and require compatibility/material relations to solve.

7. What are the two key assumptions of the method of joints for analyzing a simple truss?

   (1) Members are two-force members carrying only axial load (tension or compression), and (2) loads and reactions act only at the joints (pins). Each joint is in equilibrium under concurrent forces, giving $\sum F_x=0$ and $\sum F_y=0$ per joint.

8. What is a zero-force member in a truss, and give one rule for identifying one.

   A zero-force member carries no load under the given loading. Rule: at a joint with only two non-collinear members and no external load or reaction, both members are zero-force. Also, at a joint of three members where two are collinear and unloaded, the third is zero-force.

9. When is the method of sections preferred over the method of joints for truss analysis?

   When the force in only one or a few specific members is needed (especially members far from supports). A cut is made through the member(s), and the three planar equilibrium equations are applied to one side of the section.

10. What is the difference between a truss and a frame?

    A truss consists entirely of two-force members carrying only axial forces, loaded at joints. A frame contains at least one multi-force member (loaded between joints or carrying bending), so members can carry shear, axial force, and bending moment.

11. Define the centroid of an area and give the formula for its $\bar{x}$ coordinate.

    The centroid is the geometric center (area-weighted average position). $$\bar{x}=\frac{\int x\,dA}{\int dA}=\frac{\sum \bar{x}_i A_i}{\sum A_i}$$ For composite shapes, sum each part's area times its centroidal coordinate, divided by total area.

12. State the parallel-axis theorem for the area moment of inertia.

    $$I=\bar{I}+A d^{2}$$ where $\bar{I}$ is the moment of inertia about the centroidal axis, $A$ is the area, and $d$ is the perpendicular distance between the centroidal axis and the parallel axis of interest.

13. Give the centroidal area moment of inertia of a rectangle (width $b$, height $h$) about its horizontal centroidal axis.

    $$\bar{I}_x=\frac{b h^{3}}{12}$$ and about the base, $I_x=\frac{b h^{3}}{3}$.

14. What is the polar moment of inertia $J$, and how does it relate to the rectangular moments of inertia?

    $J$ is the second moment of area about an axis perpendicular to the plane (through a point). By the perpendicular-axis theorem, $$J=I_x+I_y.$$ For a solid circle of radius $r$, $J=\frac{\pi r^{4}}{2}$.

15. State the relationship between the friction force and normal force at the point of impending slip (Coulomb friction).

    At impending motion, $$F_{max}=\mu_s N$$ where $\mu_s$ is the static coefficient of friction. Once sliding, $F=\mu_k N$ with kinetic coefficient $\mu_k<\mu_s$. Friction acts opposite to the (impending) motion.

16. What is the angle of friction (angle of repose), and how does it relate to $\mu_s$?

    The angle of friction $\phi_s$ is the angle the resultant of $N$ and $F_{max}$ makes with the normal at impending slip: $$\tan\phi_s=\mu_s.$$ On an incline, a block begins to slide when the incline angle equals $\phi_s$.

17. For a flat belt wrapping a fixed drum, give the belt-friction (capstan) equation.

    $$\frac{T_1}{T_2}=e^{\mu\beta}$$ where $T_1>T_2$ are the tensions on the tight and slack sides, $\mu$ is the friction coefficient, and $\beta$ is the contact (wrap) angle in radians.

18. Write the kinematic equations for particle motion under constant acceleration.

    $$v=v_0+at,\quad s=s_0+v_0 t+\tfrac{1}{2}a t^{2},\quad v^{2}=v_0^{2}+2a(s-s_0)$$ valid only when acceleration $a$ is constant.

19. For curvilinear motion described in normal-tangential coordinates, give the normal and tangential acceleration components.

    $$a_t=\frac{dv}{dt},\qquad a_n=\frac{v^{2}}{\rho}$$ where $\rho$ is the radius of curvature. Tangential acceleration changes speed; normal (centripetal) acceleration changes direction and points toward the center.

20. State Newton's second law for a particle in vector form and as applied along a path.

    $$\sum \vec{F}=m\vec{a}$$ Along a curved path in n-t coordinates: $\sum F_t=m a_t=m\frac{dv}{dt}$ and $\sum F_n=m a_n=m\frac{v^{2}}{\rho}$.

21. State the principle of work and energy for a particle.

    $$U_{1\to2}=\Delta T=\tfrac{1}{2}m v_2^{2}-\tfrac{1}{2}m v_1^{2}$$ The total work done by all forces equals the change in kinetic energy. Work of a force: $U=\int \vec{F}\cdot d\vec{r}$.

22. State the principle of impulse and momentum for a particle.

    $$\int_{t_1}^{t_2}\sum \vec{F}\,dt=m\vec{v}_2-m\vec{v}_1$$ The linear impulse of the net force equals the change in linear momentum. If $\sum\vec{F}=0$, momentum is conserved.

23. Define the coefficient of restitution $e$ for a direct central impact.

    $$e=\frac{v_{B}'-v_{A}'}{v_A-v_B}$$ the ratio of relative separation velocity to relative approach velocity along the line of impact. $e=1$ is perfectly elastic; $e=0$ is perfectly plastic (bodies move together).

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