UPSC IES/ESE (Engineering Services) Engineering Mechanics, Strength of Materials and Theory of Machines Syllabus

Engineering Mechanics, Strength of Materials and Theory of Machines 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, Strength of Materials and Theory of Machines in UPSC IES/ESE (Engineering Services), not a summary of it.

1. 1

   Statics and Dynamics of Rigid Bodies

   4 topics

   • Force systems, equilibrium and free body diagrams
   • Trusses, frames and analysis of forces in members
   • Friction, centroid and moment of inertia
   • Kinematics and kinetics of particles and rigid bodies
     • Work-energy and impulse-momentum principles
     • D'Alembert's principle
2. 2

   Stress, Strain and Elastic Behaviour

   4 topics

   • Simple stresses and strains, elastic constants
   • Compound stresses and Mohr's circle
   • Thermal stresses and strain energy
   • Theories of failure
3. 3

   Bending, Shear and Torsion

   4 topics

   • Shear force and bending moment diagrams
   • Bending stresses and shear stresses in beams
   • Torsion of circular shafts and power transmission
   • Deflection of beams by various methods
     • Double integration and Macaulay's method
     • Moment-area and conjugate beam
4. 4

   Columns, Springs and Pressure Vessels

   4 topics

   • Euler and Rankine theories of columns
   • Springs in series and parallel, leaf and helical springs
   • Thin and thick cylinders and spheres
   • Buckling and stability considerations
5. 5

   Kinematics and Dynamics of Machines

   4 topics

   • Mechanisms, kinematic pairs and inversions
   • Velocity and acceleration analysis of mechanisms
   • Cams, gears and gear trains
   • Flywheels and governors
6. 6

   Vibrations and Balancing

   4 topics

   • Free and forced vibrations of single degree of freedom systems
   • Damped vibrations and resonance
   • Whirling of shafts and critical speed
   • Static and dynamic balancing of rotating and reciprocating masses

Engineering Mechanics, Strength of Materials and Theory of Machines flashcards for UPSC IES/ESE (Engineering Services)

24 of 60 cards from the Engineering Mechanics, Strength of Materials and Theory of Machines deck — real questions with worked answers.

1. What three scalar equations express the equilibrium of a coplanar (2D) force system?

   $\sum F_x = 0$, $\sum F_y = 0$, and $\sum M_z = 0$ (the sum of forces along each axis and the sum of moments about any point all vanish).

2. What is a free body diagram (FBD) and why is it drawn?

   A sketch of a single isolated body showing all external forces, reactions, and moments acting on it (with the body removed from its supports). It is drawn to systematically apply the equilibrium equations and solve for unknown forces.

3. State the necessary and sufficient conditions for equilibrium of a rigid body in 3D.

   The resultant force and resultant couple must both be zero: $\sum \vec{F} = 0$ and $\sum \vec{M} = 0$, giving six scalar equations ($\sum F_x=\sum F_y=\sum F_z=0$ and $\sum M_x=\sum M_y=\sum M_z=0$).

4. For a plane truss with $m$ members, $j$ joints and $r$ reactions, what condition makes it statically determinate?

   $m + r = 2j$. If $m + r > 2j$ the truss is statically indeterminate; if $m + r < 2j$ it is a mechanism (unstable).

5. What key assumptions underlie the analysis of an ideal pin-jointed truss?

   Members are straight and connected by frictionless pins, loads and reactions act only at joints, member weights are neglected (or applied at joints), so each member carries only an axial force (pure tension or compression).

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

   A member carrying no force under a given loading. Rule: at an unloaded joint where only two non-collinear members meet, both are zero-force members; if three members meet with two collinear and no external load, the non-collinear member is zero-force.

7. Compare the method of joints and the method of sections for truss analysis.

   Method of joints applies $\sum F_x=0,\ \sum F_y=0$ at each joint (good for finding all member forces, max 2 unknowns per joint). Method of sections cuts the truss and uses $\sum F$ and $\sum M$ on a portion (good for finding a few specific member forces directly, up to 3 unknowns per cut).

8. State the laws of dry (Coulomb) friction including the limiting friction relation.

   Limiting friction $F = \mu_s N$ is independent of contact area, proportional to normal reaction $N$, and acts opposite to impending motion. Once sliding, kinetic friction $F_k = \mu_k N$ with $\mu_k < \mu_s$. The angle of friction $\phi$ satisfies $\tan\phi = \mu$.

9. Define the angle of repose and relate it to the coefficient of friction.

   The maximum inclination of a plane at which a body remains on the verge of sliding under its own weight. It equals the angle of friction $\phi$, so $\tan\alpha = \mu_s$.

10. Give the centroid location of a triangle, a semicircle, and a quarter circle.

    Triangle: at $\frac{h}{3}$ from the base (intersection of medians). Semicircle of radius $r$: $\bar{y} = \frac{4r}{3\pi}$ from the diameter. Quarter circle of radius $r$: $\bar{x} = \bar{y} = \frac{4r}{3\pi}$ from the straight edges.

11. State the parallel axis theorem for moment of inertia.

    $I = I_G + A d^{2}$, where $I_G$ is the second moment of area about the centroidal axis, $A$ is the area, and $d$ is the perpendicular distance between the parallel axes.

12. Give the area moment of inertia of a rectangle ($b\times h$) and a solid circle (diameter $d$) about their centroidal axes.

    Rectangle about centroidal axis parallel to base: $I = \frac{b h^{3}}{12}$. Solid circle: $I = \frac{\pi d^{4}}{64}$.

13. State the perpendicular axis theorem for plane areas.

    For a plane lamina, the polar moment of inertia about an axis perpendicular to the plane equals the sum of the moments of inertia about two perpendicular in-plane axes through the same point: $I_z = I_x + I_y$ (also written $J = I_{xx} + I_{yy}$).

14. Distinguish kinematics from kinetics.

    Kinematics studies motion (displacement, velocity, acceleration) without regard to the forces causing it. Kinetics relates the motion to the forces and masses producing it (e.g., via $\vec{F} = m\vec{a}$).

15. Write the equations of uniformly accelerated rectilinear motion.

    $v = u + at$, $\quad s = ut + \frac{1}{2}at^{2}$, $\quad v^{2} = u^{2} + 2as$, where $u$ is initial velocity, $v$ final velocity, $a$ acceleration, and $s$ displacement.

16. For a rigid body rotating about a fixed axis, relate linear and angular kinematic quantities.

    $v = r\omega$, tangential acceleration $a_t = r\alpha$, and normal (centripetal) acceleration $a_n = r\omega^{2} = \frac{v^{2}}{r}$, where $r$ is distance from the axis, $\omega$ angular velocity, $\alpha$ angular acceleration.

17. State the work-energy principle for a particle.

    The net work done by all forces equals the change in kinetic energy: $W_{net} = \Delta KE = \frac{1}{2}m v_2^{2} - \frac{1}{2}m v_1^{2}$.

18. State the impulse-momentum principle for a particle.

    The impulse of the resultant force equals the change in linear momentum: $\int F\,dt = m v_2 - m v_1$. For constant force, $F\,t = m(v_2 - v_1)$.

19. What is conserved in a collision and how is the coefficient of restitution defined?

    Linear momentum is conserved: $m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$. The coefficient of restitution $e = \frac{v_2 - v_1}{u_1 - u_2} = \frac{\text{relative velocity of separation}}{\text{relative velocity of approach}}$, with $e=1$ for perfectly elastic and $e=0$ for perfectly plastic impact.

20. State D'Alembert's principle.

    A moving body can be treated as in equilibrium by adding an inertia force $-m\vec{a}$ (and inertia couple $-I\alpha$) that is equal and opposite to the mass-times-acceleration term. Thus $\sum \vec{F} - m\vec{a} = 0$, reducing a dynamics problem to a statics-like equilibrium problem.

21. Define normal stress and longitudinal (axial) strain.

    Normal stress $\sigma = \frac{P}{A}$ (force per unit area). Longitudinal strain $\varepsilon = \frac{\delta L}{L}$ (change in length per original length); both are used in Hooke's law $\sigma = E\varepsilon$.

22. Write the formula for elongation of a prismatic bar under axial load $P$.

    $\delta = \frac{PL}{AE}$, where $L$ is the length, $A$ the cross-sectional area, and $E$ Young's modulus.

23. Define the three elastic constants $E$, $G$, and $K$, and Poisson's ratio $\nu$.

    $E$ = Young's modulus (axial stress/strain), $G$ = modulus of rigidity (shear stress/shear strain), $K$ = bulk modulus (volumetric stress/volumetric strain), $\nu$ = Poisson's ratio = $-\frac{\text{lateral strain}}{\text{longitudinal strain}}$.

24. State the relations among the elastic constants $E$, $G$, $K$ and $\nu$.

    $E = 2G(1+\nu)$, $\quad E = 3K(1-2\nu)$, $\quad E = \frac{9KG}{3K+G}$.

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