GATE Mechanical Engineering Applied Mechanics and Design Syllabus

Applied Mechanics and Design syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Applied Mechanics and Design in GATE Mechanical Engineering, not a summary of it.

1. 1

   Engineering Mechanics

   7 topics

   • Free-body diagrams and equilibrium
   • Friction and its applications
     • Rolling friction
     • Belt-pulley
     • Brakes
     • Clutches
     • Screw jack
     • Wedge
     • Vehicles
   • Trusses and frames
   • Virtual work
   • Kinematics and dynamics of rigid bodies in plane motion
   • Impulse and momentum (linear and angular) and energy formulations
   • Lagrange’s equation
2. 2

   Mechanics of Materials

   16 topics

   • Stress and strain
   • Elastic constants
   • Poisson's ratio
   • Mohr’s circle for plane stress and plane strain
   • Thin cylinders
   • Shear force and bending moment diagrams
   • Bending and shear stresses
   • Concept of shear centre
   • Deflection of beams
   • Torsion of circular shafts
   • Euler’s theory of columns
   • Energy methods
   • Thermal stresses
   • Strain gauges and rosettes
   • Testing of materials with universal testing machine
   • Testing of hardness and impact strength
3. 3

   Theory of Machines

   7 topics

   • Displacement, velocity and acceleration analysis of plane mechanisms
   • Dynamic analysis of linkages
   • Cams
   • Gears and gear trains
   • Flywheels and governors
   • Balancing of reciprocating and rotating masses
   • Gyroscope
4. 4

   Vibrations

   5 topics

   • Free and forced vibration of single degree of freedom systems
   • Effect of damping
   • Vibration isolation
   • Resonance
   • Critical speeds of shafts
5. 5

   Machine Design

   4 topics

   • Design for static and dynamic loading
   • Failure theories
   • Fatigue strength and the S-N diagram
   • Principles of the design of machine elements
     • Bolted joints
     • Riveted joints
     • Welded joints
     • Shafts
     • Gears
     • Rolling contact bearings
     • Sliding contact bearings
     • Brakes and clutches
     • Springs

Applied Mechanics and Design flashcards for GATE Mechanical Engineering

19 of 54 cards from the Applied Mechanics and Design deck — real questions with worked answers.

1. What is a free-body diagram (FBD)?

   A diagram of a single body or system isolated from its surroundings, showing all external forces and moments acting on it (applied loads, reactions, weight), used to apply equilibrium equations.

2. State the conditions for static equilibrium of a rigid body in 2D.

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

3. State the conditions for static equilibrium of a rigid body in 3D.

   $\sum F_x = 0,\ \sum F_y = 0,\ \sum F_z = 0$ and $\sum M_x = 0,\ \sum M_y = 0,\ \sum M_z = 0$ — six independent scalar equations.

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

   A member loaded at only two points with no other forces. For equilibrium the two forces must be equal, opposite, and collinear (directed along the line joining the two points).

5. State the laws of dry (Coulomb) friction.

   Friction opposes relative motion; the limiting friction is proportional to the normal reaction ($F = \mu N$); it is independent of the apparent contact area; and kinetic friction is slightly less than the maximum static friction.

6. Distinguish the coefficients of static and kinetic friction.

   $\mu_s$ relates to maximum friction just before sliding ($F_{max} = \mu_s N$); $\mu_k$ relates to friction while sliding ($F = \mu_k N$). Generally $\mu_s > \mu_k$.

7. Define the angle of friction $\phi$.

   The angle between the total reaction (resultant of $N$ and limiting friction $F$) and the normal at impending slip: $\tan\phi = \mu = \dfrac{F}{N}$.

8. Define the angle of repose and relate it to the angle of friction.

   The maximum inclination of a plane at which a body just begins to slide under gravity. It equals the angle of friction: $\tan\alpha = \mu$, so $\alpha = \phi$.

9. What is rolling friction (rolling resistance) and what causes it?

   The resistance to a body rolling on a surface, caused mainly by deformation of the body and surface at contact (hysteresis). It is much smaller than sliding friction and is characterized by a coefficient of rolling resistance (length) $b$, with resistive force $F \approx \dfrac{b}{R}W$.

10. For a flat belt, state the belt-friction (capstan) equation.

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

11. How is the belt-friction equation modified for a V-belt?

    $\dfrac{T_1}{T_2} = e^{\mu\theta/\sin\beta}$, where $2\beta$ is the included groove angle; the wedging action raises effective friction (so V-belts transmit more for the same $\mu$ and tension).

12. Give the power transmitted by a belt drive.

    $P = (T_1 - T_2)\,v$, where $v$ is the belt speed. Accounting for centrifugal tension $T_c = m v^2$ ($m$ = mass per unit length), effective tensions become $(T_1 - T_c)$ and $(T_2 - T_c)$.

13. State the condition for maximum power transmission by a belt.

    Maximum power occurs when centrifugal tension equals one-third of maximum tension: $T_c = \dfrac{T_{max}}{3}$, i.e. $T_{max} = 3 m v^2$, giving optimal belt speed $v = \sqrt{\dfrac{T_{max}}{3m}}$.

14. What is the function of a brake and how does it differ from a clutch?

    A brake absorbs the kinetic/potential energy of a moving system (converting it to heat) to slow or stop it relative to the frame. A clutch transmits power between two coaxial shafts, connecting/disconnecting driver and driven members.

15. For a simple band brake, give the braking torque.

    $T = (T_1 - T_2) r$, with $\dfrac{T_1}{T_2} = e^{\mu\theta}$, where $r$ is the drum radius, $T_1,T_2$ the band tensions, $\theta$ the wrap angle.

16. What is a self-energizing brake and when does it become self-locking?

    A self-energizing brake is one in which the friction force helps apply the brake (the moment of friction assists the actuating force). If the friction moment alone is enough to engage the brake with zero applied force, it is self-locking.

17. Give the torque transmitted by a single-plate clutch using the uniform-wear theory.

    $T = \mu W \dfrac{r_o + r_i}{2}$ (per friction surface), where $W$ is the axial force and $r_o, r_i$ are outer/inner radii. Uniform wear assumes $p\,r = \text{constant}$.

18. Give the torque transmitted by a single-plate clutch using the uniform-pressure theory.

    $T = \mu W \dfrac{2}{3}\,\dfrac{r_o^{3} - r_i^{3}}{r_o^{2} - r_i^{2}}$ (per friction surface), assuming uniform pressure over the contact area.

19. Why does uniform-wear theory give lower torque than uniform-pressure theory for clutches?

    Uniform wear concentrates pressure toward the inner radius (smaller effective radius), so for the same axial load it predicts a smaller mean radius and hence lower torque. Design uses uniform wear as the conservative (safer) basis.

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