Why this topic is important for ECET?
In ECET, questions from Design of Machine Elements are highly scoring because they are formula-based and concept-driven. Shafts and keys are fundamental components in mechanical systems, transmitting power and torque in machines. Mastering this topic improves your ability to solve design, stress, and failure questions in exams quickly.
📘 Concept Notes
🔹 Shafts
- A shaft is a rotating machine element that transmits power from one part to another (e.g., motor to gearbox, turbine to generator).
- Shafts are subjected to torsional, bending, and axial loads.
- Types:
- Transmission shafts – transmit power (e.g., line shafts).
- Machine shafts – integral part of machine (e.g., crankshaft).
Stresses on Shafts:
- Shear stress due to torque.
- Bending stress due to transverse load.
- Combined stress (torsion + bending).
🔹 Keys
- A key is a machine element inserted between the shaft and hub to prevent relative motion (slip).
- Keys transmit torque between shaft and machine component (gear, pulley, coupling).
Types of Keys:
- Sunk keys – Half fits in shaft, half in hub. (Rectangular, Square, Gib-head).
- Saddle keys – Only rest on shaft, not sunk.
- Tangent keys – Used in heavy-duty applications, placed in pairs.
- Woodruff keys – Small semicircular key, used for taper shafts.
Key Failure Modes:
- Shearing across section.
- Crushing failure due to compressive stress.
🔹 Example (Real-Life Application)
- Automobile crankshaft: Shaft transmits torque, and flywheel hub is fixed using a key.
- If key design is weak → slippage, failure.
⚙️ Formulas
1. Torque transmitted by shaft:
where τ\tauτ = allowable shear stress, DDD = shaft diameter.
2. Bending stress in shaft:
where MMM = bending moment.
3. Equivalent twisting moment (Combined bending + torsion):
4. Equivalent bending moment:
5. Shear stress in shaft (torsion):
6. Shear stress in key (due to torque):
where ddd = shaft dia, lll = length of key, ttt = thickness.
7. Crushing stress in key:
🔟 10 MCQs
Q1. A shaft is primarily used to transmit:
a) Axial force
b) Power
c) Bending force
d) Vibration
Q2. The shear stress in a solid shaft under torque is maximum at:
a) Centre
b) Surface
c) Half radius
d) Along the axis
Q3. A 40 mm diameter shaft is subjected to torque of 500 Nm. The shear stress is:
a) 20 MPa
b) 25 MPa
c) 30 MPa
d) 40 MPa
Q4. The torque transmitted by a shaft is proportional to:
a) D²
b) D³
c) D⁴
d) D⁵
Q5. A key transmits torque by:
a) Friction
b) Shear and crushing action
c) Riveting action
d) Welding
Q6. A rectangular key has width = 18 mm, thickness = 12 mm, length = 80 mm. If shaft dia = 50 mm, torque transmitted = 1000 Nm, find shear stress in key.
a) 12 MPa
b) 15 MPa
c) 18 MPa
d) 20 MPa
Q7. Which key is preferred for taper shaft?
a) Square key
b) Woodruff key
c) Saddle key
d) Tangent key
Q8. For combined bending and torsion, equivalent twisting moment is:
a) M2+T2\sqrt{M^2 + T^2}M2+T2
b) M+TM + TM+T
c) MT\frac{M}{T}TM
d) M+T2\frac{M+T}{2}2M+T
Q9. A shaft of 60 mm diameter is subjected to 100 Nm torque. Find max shear stress.
a) 0.7 MPa
b) 1.5 MPa
c) 2.0 MPa
d) 2.5 MPa
Q10. Crushing stress in a key is:
a) Twice the shear stress
b) Half the shear stress
c) Equal to shear stress
d) Independent of shear
✅ Answer Key
| Q | Ans |
|---|---|
| 1 | b |
| 2 | b |
| 3 | b |
| 4 | c |
| 5 | b |
| 6 | d |
| 7 | b |
| 8 | a |
| 9 | b |
| 10 | a |
🧠 Explanations
Q1: Shaft transmits power via torque → (b).
Q2: Max shear stress in torsion = outer surface → (b).
Q3: Use 
. Substituting → ~25 MPa → (b).
Q4: Torque ∝ D³ → (c).
Q5: Keys work by resisting shear & crushing → (b).
Q6: 
≈ 20 MPa → (d).
Q7: Woodruff key used for taper shafts → (b).
Q8: Formula for equivalent twisting moment = 
→ (a).
Q9: 
≈ 1.5 MPa → (b).
Q10: Crushing stress = twice shear stress → (a).
🎯 Motivation / Why Practice Matters
Design problems in ECET are direct formula-based – if you know the correct relation, you can solve in seconds. Practicing shafts & keys improves speed and confidence, especially for numerical-heavy questions.
👉 In a competitive exam, fast recall of formulas + practice with stress calculations = clear advantage over others.
📲 CTA
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