UPSC ESE Mechanical Engineering Engineering Mechanics Syllabus

Engineering Mechanics 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 in UPSC ESE Mechanical Engineering, not a summary of it.

1. 1

   Statics

   3 topics

   • Equilibrium of Forces
   • Trusses and Frames
   • Friction
2. 2

   Dynamics

   3 topics

   • Kinematics
   • Kinetics
   • Work and Energy
3. 3

   Vibrations

   3 topics

   • Free and Forced Vibrations
   • Damping
   • Resonance

Engineering Mechanics flashcards for UPSC ESE Mechanical Engineering

20 of 50 cards from the Engineering Mechanics deck — real questions with worked answers.

1. State the necessary and sufficient conditions for the equilibrium of a coplanar (2D) system of forces.

   The vector sum of all forces and the sum of moments about any point must vanish: $\sum F_x = 0$, $\sum F_y = 0$, and $\sum M_z = 0$.

2. How many independent equilibrium equations are available for a general three-dimensional rigid body?

   Six: $\sum F_x = 0$, $\sum F_y = 0$, $\sum F_z = 0$ and $\sum M_x = 0$, $\sum M_y = 0$, $\sum M_z = 0$.

3. State Lami's theorem for three concurrent coplanar forces in equilibrium.

   If three forces keep a particle in equilibrium, each force is proportional to the sine of the angle between the other two: $\dfrac{P}{\sin\alpha} = \dfrac{Q}{\sin\beta} = \dfrac{R}{\sin\gamma}$.

4. What is the moment of a force about a point, expressed as a vector?

   $\vec{M} = \vec{r} \times \vec{F}$, where $\vec{r}$ is the position vector from the point to any point on the line of action of $\vec{F}$. Its magnitude is $M = F d$, with $d$ the perpendicular distance.

5. Define a couple and give the magnitude of its moment.

   A couple is a pair of equal, opposite, non-collinear parallel forces. Its moment $M = F \times d$ (force times perpendicular separation) is a free vector, the same about every point.

6. State Varignon's theorem (principle of moments).

   The moment of a resultant force about any point equals the algebraic sum of the moments of its component forces about the same point: $\vec{r}\times\vec{R} = \sum \vec{r}\times\vec{F_i}$.

7. What is a free-body diagram and why is it essential in statics?

   A free-body diagram isolates a body and shows all external forces and reactions acting on it, with the body removed from its supports. It is essential for correctly applying the equilibrium equations.

8. Define a two-force member and state a key property.

   A member loaded by forces at only two points (and no moments). For equilibrium the two forces must be equal, opposite, and collinear along the line joining the two points (purely axial).

9. What is a perfect (statically determinate) plane truss? Give the relation between members $m$ and joints $j$.

   A truss with just enough members to be rigid and solvable by statics alone: $m = 2j - 3$. If $m > 2j-3$ it is redundant (indeterminate); if $m < 2j-3$ it is deficient (a mechanism).

10. List the standard assumptions made in the analysis of an ideal pin-jointed truss.

    Members are straight and connected by frictionless pins; loads and reactions act only at joints; member weight is neglected (or split to joints); each member carries only axial force (tension or compression).

11. Describe the method of joints for truss analysis.

    Isolate each joint as a particle in equilibrium and apply $\sum F_x = 0$ and $\sum F_y = 0$ (two equations per joint). Start at a joint with at most two unknown member forces and proceed sequentially.

12. Describe the method of sections for truss analysis and its advantage.

    Cut the truss through the members of interest (ideally three) and apply $\sum F_x=0$, $\sum F_y=0$, $\sum M=0$ to one part. Advantage: it directly gives the force in a specific interior member without solving every joint.

13. What is a zero-force member, and give two rules for identifying one by inspection?

    A member carrying no axial force. (1) At an unloaded joint with only two non-collinear members, both are zero-force. (2) At an unloaded joint with three members where two are collinear, the third (non-collinear) member is zero-force.

14. How do you determine static determinacy of a plane frame (rigid jointed) with $m$ members, $r$ reactions, and $j$ joints?

    Degree of static indeterminacy $D_s = 3m + r - 3j$. If $D_s = 0$ it is determinate, $D_s > 0$ indeterminate, $D_s < 0$ unstable.

15. State the laws of static (Coulomb) dry friction.

    Friction opposes impending/relative motion; $F \le \mu_s N$ with limiting value $F_{max} = \mu_s N$; it is independent of the apparent contact area; and it depends on the nature of the surfaces in contact.

16. Define the coefficient of static friction and write the limiting friction relation.

    $\mu_s = \dfrac{F_{max}}{N}$, the ratio of the limiting friction force at impending motion to the normal reaction. At impending motion $F_{max} = \mu_s N$.

17. Define the angle of friction $\phi$ and relate it to $\mu$.

    The angle between the resultant reaction and the normal at impending motion: $\tan\phi = \mu$. The resultant lies on a cone of semi-angle $\phi$ (the cone of friction).

18. Define the angle of repose and state its relation to the angle of friction.

    The maximum inclination of a plane at which a body just begins to slide under its own weight. The angle of repose equals the angle of friction: $\theta_{repose} = \phi$, so $\tan\theta = \mu_s$.

19. For a body on an incline of angle $\theta$ on the verge of sliding down, what is the friction force in terms of weight $W$?

    $F = W\sin\theta$ and $N = W\cos\theta$; at impending motion $\mu_s = \tan\theta$. The minimum force along the plane to prevent sliding is $W(\sin\theta - \mu_s\cos\theta)$.

20. State the belt friction (capstan) equation for a flat belt about to slip.

    $\dfrac{T_1}{T_2} = e^{\mu\beta}$, where $T_1$ is the tight-side tension, $T_2$ the slack-side tension, $\mu$ the coefficient of friction, and $\beta$ the angle of wrap in radians.

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