--- title: "Extension springs, ends and spring combinations" subject: "Machine Design II" chapter: 6 key: "semester_7/machine_design_ii:extension-spring-ends-series-parallel" source: https://www.bctengineer.com/q/semester_7/machine_design_ii/extension-spring-ends-series-parallel site: BCT Engineering --- # Extension springs, ends and spring combinations Machine Design II · Chapter 6: Spring design - Asked in: year not given, 6 marks - Video: [EXTENSION SPRING Design - Stresses and Initial Tension in Just Over 10 Minutes](https://www.youtube.com/watch?v=wKzU2s9bEA8) — Less Boring Lectures - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/machine_design_ii/extension-spring-ends-series-parallel - Whole chapter: https://www.bctengineer.com/md/semester_7/machine_design_ii/chapter-6 ## Question Differentiate between compression and extension springs with respect to end details. Explain the initial tension in an extension spring. Two springs of stiffness 20 N/mm and 30 N/mm are used in series and in parallel; find the equivalent stiffness in each case, and the extension of the series combination under 300 N. ## Short answer Compression spring ends are plain, ground, squared, or squared & ground; extension springs have hooks or loops and coils wound tight with initial tension. Initial tension provides a preload; no extension until load exceeds it. Equivalent stiffness: series 12 N/mm, parallel 50 N/mm. Series extension under 300 N is 25 mm. ## Answer #### Compression spring ends | End type | Description | Inactive coils | Solid length | |---|---|---|---| | Plain | Ends just cut off | 0 | $d(n+1)$ | | Plain and ground | Ends flat-ground | 1 | $d\,n_t$ with $n_t=n+1$ | | Squared (closed) | Ends turned to touch the next coil | 2 | $d(n+3)$ | | Squared and ground | Closed and ground flat | 2 | $d(n+2)$ | Squared and ground ends seat properly and give better load transfer and less buckling. #### Extension spring ends An extension spring works in tension, so its ends need **hooks or loops** (full loop, half loop, cross-over loop, extended hook, threaded plug). The stresses concentrate at the bend of the hook (bending and torsion), so a hook of larger radius lowers the stress and the hook is designed separately from the body. The body coils are wound tight (touching), unlike a compression spring where space is left between coils for deflection. #### Initial tension Extension springs are wound with coils pressed together, which stores a pretension $F_i$. No extension takes place until the applied load exceeds $F_i$. Then $$ F = F_i + k\,y $$ Initial tension keeps the spring tight, gives a definite starting load and reduces the length needed. It depends on spring index and manufacturing, and is usually limited so that the stress due to $F_i$ stays within the recommended band for the spring index. #### Springs in combination Series (same load, deflections add): $\dfrac{1}{k_s} = \dfrac{1}{k_1}+\dfrac{1}{k_2} = \dfrac{1}{20}+\dfrac{1}{30}$, so $k_s = 12$ N/mm. Parallel (same deflection, loads add): $k_p = k_1+k_2 = 20 + 30 = 50$ N/mm. Extension of the series combination under 300 N: $y = 300/12 = 25$ mm. **Answer:** $k_{series} = 12$ N/mm, $k_{parallel} = 50$ N/mm, extension $= 25$ mm. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How do extension spring ends differ from compression spring ends? A. They are squared and ground to seat properly B. They need hooks or loops, with stress concentrated at the hook bend C. They are plain cut-off ends D. They need no special end detail Answer: B. Extension springs work in tension, so ends are hooks/loops, and stress concentrates at their bend. (Key point: Extension spring ends) 2. What is the effect of initial tension F_i in an extension spring? A. Spring extends from the first newton, with F = k y B. Spring does not extend until applied load exceeds F_i, then F = F_i + k y C. It reduces the spring stiffness k D. It makes the coils spaced apart Answer: B. Coils wound tight store a pretension; no extension occurs until the load exceeds F_i. (Key point: Initial tension) 3. Springs of 20 and 30 N/mm in series have equivalent stiffness A. 50 N/mm B. 25 N/mm C. 10 N/mm D. 12 N/mm Answer: D. 1/k = 1/20 + 1/30 gives k = 12 N/mm; parallel gives 50 N/mm. (Key point: Series stiffness) 4. Extension of the series combination under 300 N is A. 25 mm B. 6 mm C. 15 mm D. 10 mm Answer: A. y = 300/12 = 25 mm. (Key point: Series extension) ## Related in Machine Design II - [Design of a helical compression spring](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Acompression-spring-design-static) — Machine Design II, chapter 6 - [Helical spring under fluctuating load](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Aspring-fatigue-soderberg-design) — Machine Design II, chapter 6 - [Surge and natural frequency of valve spring](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Aspring-surge-natural-frequency) — Machine Design II, chapter 6 - [Stress and deflection of helical spring](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Ahelical-spring-stress-deflection-derive) — Machine Design II, chapter 6 - [Spring materials and yield strength estimation](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Aspring-materials-yield-strength) — Machine Design II, chapter 6 ## Related in other subjects - [Natural frequency with series-parallel springs](https://www.bctengineer.com/question.md?key=semester_7%2Ftheory_of_mechanism_and_machine_ii%3Aseries-parallel-spring-mass-frequency) — Theory of Mechanism and Machine II, chapter 6 - [Hartnell governor spring force and stiffness](https://www.bctengineer.com/question.md?key=semester_7%2Ftheory_of_mechanism_and_machine_ii%3Ahartnell-governor-spring-stiffness) — Theory of Mechanism and Machine II, chapter 4 - [Equivalent inductance of two coupled coils in parallel](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Acoupled-coils-4h-6h-parallel-3h) — Basic Electrical Engineering, chapter 4 - [Equivalent T from Y parameters of series two-ports](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Aequivalent-t-parameter-two-y-networks) — Electrical Circuit Theory, chapter 7