UPSC ESE Mechanical Engineering Machine Design Syllabus

Machine Design syllabus — full chapter and topic list

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

1. 1

   Design of Machine Elements

   3 topics

   • Bolts and Nuts
   • Riveted and Welded Joints
   • Shafts, Keys and Couplings
2. 2

   Design for Static and Dynamic Loading

   3 topics

   • Fatigue Loading
   • Stress Concentration
   • Creep
3. 3

   Design of Gears and Bearings

   3 topics

   • Spur and Helical Gears
   • Rolling Contact Bearings
   • Lubrication

Machine Design flashcards for UPSC ESE Mechanical Engineering

23 of 50 cards from the Machine Design deck — real questions with worked answers.

1. In a bolted joint, what is the relationship between the nominal (major) diameter $d$ and the core (root) diameter $d_c$ used for, and which diameter is used to compute tensile strength?

   The core diameter $d_c$ is the smallest diameter at the thread root. Tensile (axial) strength of a bolt is based on the tensile stress area, which uses the core/minor diameter, since failure occurs at the weakest section: $\sigma_t = \frac{P}{\frac{\pi}{4}d_c^{2}}$.

2. State the empirical relation commonly used for the design tensile load capacity of a bolt of nominal diameter $d$ (in mm) subjected to fluctuating/initial tightening loads.

   $P = \sigma_t \cdot \frac{\pi}{4} d_c^{2}$, and an empirical initial tightening relation for fluid-tight joints is $P_i = 2840\,d$ (N), where $d$ is in mm.

3. For a bolt subjected to combined external load $P_{ext}$ and initial pre-tension $P_i$, write the resultant bolt load when the connected members and bolt have stiffnesses $k_b$ and $k_m$.

   $P_{bolt} = P_i + \frac{k_b}{k_b + k_m}\,P_{ext}$. The factor $\frac{k_b}{k_b+k_m}$ is the joint stiffness factor; the bolt carries only that fraction of the external load above pre-tension.

4. What is the purpose of a pre-load (initial tension) in a bolted joint subjected to fluctuating loads, in terms of fatigue?

   A high pre-load makes the bolt carry only a small fraction $\frac{k_b}{k_b+k_m}$ of the external fluctuating load, drastically reducing the alternating stress amplitude on the bolt and greatly improving its fatigue life, while also preventing joint separation.

5. Compare the eccentric loading of a bracket bolted joint: how is the primary and secondary shear load on each bolt determined?

   Primary shear $P_1 = \frac{P}{n}$ (load shared equally among $n$ bolts). Secondary shear due to moment $M=P\cdot e$ is $P_2 = \frac{M\,r_i}{\sum r_i^{2}}$, proportional to the bolt's distance $r_i$ from the centroid. The resultant is the vector sum of $P_1$ and $P_2$.

6. Classify the modes of failure of a riveted joint.

   (1) Tearing of the plate between holes, (2) Shearing of the rivet, (3) Crushing (bearing) of the rivet/plate, (4) Tearing of the plate at an edge (margin failure), and (5) Shearing of the plate edge (margin).

7. Write the formula for tearing strength, shearing strength, and crushing strength of a riveted joint per pitch length.

   Tearing: $P_t = (p-d)\,t\,\sigma_t$. Shearing: $P_s = n\,\frac{\pi}{4}d^{2}\,\tau$ (n = number of rivets per pitch, double for double shear). Crushing: $P_c = n\,d\,t\,\sigma_c$.

8. Define the efficiency of a riveted joint and write its expression.

   Efficiency is the ratio of the strength of the riveted joint to the strength of the solid (unriveted) plate: $\eta = \frac{\min(P_t,\,P_s,\,P_c)}{p\,t\,\sigma_t}$, where $p\,t\,\sigma_t$ is the strength of the solid plate per pitch.

9. State Unwin's formula relating rivet diameter $d$ to plate thickness $t$, and when it applies.

   Unwin's empirical formula: $d = 6\sqrt{t}$ (mm), valid for plates thicker than about $8$ mm. For thin plates, $d$ is found by equating shearing and crushing strengths.

10. Distinguish between lap joint and butt joint in riveting, and define single/double riveted.

    In a lap joint the two plates overlap and rivets pass through both. In a butt joint the plates are edge-to-edge and joined by one or two cover (strap) plates, with rivets in single or double shear. 'Single/double riveted' refers to the number of rivet rows on each side of the joint.

11. For a fillet weld of leg size $h$ (or $s$) subjected to load, what is the throat thickness and the formula for the shear stress?

    Throat thickness $t = 0.707\,h$. Shear stress $\tau = \frac{P}{t\,l} = \frac{P}{0.707\,h\,l}$, where $l$ is the weld length. Fillet welds are always designed for shear at the throat, regardless of load direction.

12. For a parallel fillet weld vs a transverse fillet weld, which is stronger and why, in terms of design?

    In design both are taken to fail in shear through the throat, so strength per unit length is the same $0.707\,h\,l\,\tau$. In reality, a transverse fillet weld is stronger (loaded across the throat), but design conservatively assumes throat shear for both.

13. For eccentrically loaded fillet welds, how is the polar moment of inertia used to find the maximum stress?

    Treat the weld as a line of unit throat. Primary shear $\tau_1 = \frac{P}{A}$. Secondary (bending/torsion) shear $\tau_2 = \frac{M\,r}{J}$, where $J$ is the polar moment of the weld group. Resultant $\tau = \sqrt{\tau_1^{2}+\tau_2^{2}+2\tau_1\tau_2\cos\theta}$.

14. State the maximum shear stress (torsion) equation for a solid circular shaft of diameter $d$ transmitting torque $T$.

    $\tau = \frac{16\,T}{\pi\,d^{3}}$, derived from the torsion equation $\frac{T}{J} = \frac{\tau}{r}$ with $J = \frac{\pi}{32}d^{4}$ and $r=\frac{d}{2}$.

15. Write the relation between transmitted power $P$, torque $T$, and shaft speed $N$ (rpm).

    $P = \frac{2\pi N T}{60}$ (watts), where $T$ is in N·m and $N$ in rpm. Equivalently $T = \frac{60\,P}{2\pi N}$.

16. State the ASME code equation for a shaft under combined bending moment $M$ and torque $T$ (equivalent twisting moment).

    Equivalent twisting moment $T_e = \sqrt{M^{2}+T^{2}} = \frac{\pi}{16}\tau\,d^{3}$. Equivalent bending moment $M_e = \frac{1}{2}\left(M+\sqrt{M^{2}+T^{2}}\right) = \frac{\pi}{32}\sigma_b\,d^{3}$.

17. What are the standard proportions of a sunk key (rectangular) of width $w$ and thickness $t$ in terms of shaft diameter $d$?

    Width $w = \frac{d}{4}$ and thickness $t = \frac{d}{6}$ (so $t \approx \frac{2}{3}w$). The key length is found from shear and crushing strength considerations.

18. Derive the condition that makes a key equally strong in shear and crushing, relating its dimensions.

    Shear failure: $T = l\,w\,\tau\,\frac{d}{2}$. Crushing failure: $T = l\,\frac{t}{2}\,\sigma_c\,\frac{d}{2}$. Equating gives $\frac{w}{t} = \frac{\sigma_c}{2\tau}$. For $\sigma_c = 2\tau$, this gives $w = t$ (square key equally strong).

19. Classify couplings into rigid and flexible types, giving two examples of each.

    Rigid couplings (no misalignment allowed): muff/sleeve coupling, split-muff (clamp) coupling, flange coupling. Flexible couplings (accommodate misalignment): bushed-pin type flexible coupling, Oldham coupling (lateral), universal (Hooke's) joint (angular), gear coupling.

20. In a bushed-pin flexible coupling, why are rubber bushes provided around the pins?

    The rubber (or leather) bushes absorb shock and vibration and accommodate small angular, lateral, and axial misalignments between the shafts. The pins are designed for shear and bending, with the bush enlarging the effective bearing length.

21. State the basic equation of fatigue (S-N) behaviour and define the endurance limit.

    Fatigue is failure under fluctuating stress below the static yield. The S-N curve plots stress amplitude vs cycles to failure $N$. The endurance limit $\sigma_e$ (or $S_e$) is the stress amplitude below which a steel specimen survives infinitely many cycles (knee at about $10^{6}$ cycles).

22. Define mean stress, stress amplitude, stress ratio $R$, and amplitude ratio $A$ for a fluctuating load.

    $\sigma_m = \frac{\sigma_{max}+\sigma_{min}}{2}$, $\sigma_a = \frac{\sigma_{max}-\sigma_{min}}{2}$, stress ratio $R = \frac{\sigma_{min}}{\sigma_{max}}$, amplitude ratio $A = \frac{\sigma_a}{\sigma_m}$.

23. Write the Goodman equation for fatigue design with a factor of safety $n$.

    $\frac{\sigma_a}{\sigma_e} + \frac{\sigma_m}{\sigma_{ut}} = \frac{1}{n}$, where $\sigma_e$ is the endurance limit, $\sigma_{ut}$ the ultimate tensile strength, $\sigma_a$ the alternating and $\sigma_m$ the mean stress component.

See more Machine Design flashcards →

Planning Machine Design for UPSC ESE Mechanical Engineering

Machine Design (UPSC ESE Mechanical Engineering) FAQ