--- title: "Serviceability; short and long-term deflection" subject: "Design of RCC Structure" chapter: 8 key: "semester_7/design_of_rcc_structure:serviceability-short-and-long-term-deflection" source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/serviceability-short-and-long-term-deflection site: BCT Engineering --- # Serviceability; short and long-term deflection Design of RCC Structure · Chapter 8: Limit States of Serviceability: Deflection and Cracking - Asked in: 2082 Baisakh, 4 marks - Video: [024 CE342 Concrete Design - Serviceability : Deflections](https://www.youtube.com/watch?v=M6iE_aT0c3g) — JayThree Engineering - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/serviceability-short-and-long-term-deflection - Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-8 ## Question Define the limit state of serviceability. Differentiate between short-term and long-term deflection. ## Short answer The limit state of serviceability ensures satisfactory performance under working loads regarding deflection, cracking, vibration, and durability with γf = 1.0. Short-term deflection is immediate and elastic, using Ec = 5000√fck. Long-term deflection includes creep (effective modulus Ec/(1+θ), θ = 1.6) and shrinkage; total deflection is limited to span/250 and span/350 or 20 mm after partitions. ## Answer **Limit state of serviceability** is the state beyond which the structure, though safe against collapse, can no longer be used satisfactorily under service (working) loads because of excessive deflection, cracking or vibration, or because its durability is affected. IS 456 cl. 35 covers deflection, cracking, durability and vibration; deflection and cracking are checked in design with a partial safety factor $\gamma_f = 1.0$ on working loads. #### Short-term and long-term deflection | Basis | Short-term (immediate) deflection | Long-term deflection | |---|---|---| | Cause | Occurs as soon as the load is applied; elastic behaviour of the (cracked) section | Sustained load causes creep, plus shrinkage of concrete | | Modulus | $E_c = 5000\sqrt{f_{ck}}$ MPa | Effective modulus $E_{ce} = \dfrac{E_c}{1+\theta}$ ($\theta$ = creep coefficient, 1.6 for loading at 28 days) | | Occurs | Immediately; largely recovered when the load is removed | Slowly over months or years; not recovered | | Value | Smaller | Larger (typically 2 to 3 times the short-term value) | | Calculation | $a = \dfrac{5wl^4}{384E_cI_{eff}}$ (simply supported, UDL) with $I_{eff}$ from Annex C | $a_{total} = a_i + a_{cc} + a_{cs}$: short-term deflection under all loads plus creep deflection under permanent loads plus shrinkage deflection (shrinkage strain 0.0003) | The total deflection due to all loads, including creep and shrinkage, should not exceed span/250, and the part occurring after construction of partitions and finishes should not exceed span/350 or 20 mm, whichever is less (IS 456 cl. 23.2). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. The limit state of serviceability is the state beyond which A. Concrete crushes B. The structure is safe against collapse but unsatisfactory in use due to deflection, cracking or vibration C. Steel yields D. The structure collapses Answer: B. It concerns use under working loads. (Key point: Serviceability) 2. In serviceability checks the partial safety factor on loads is A. 1.5 B. 1.0 C. 1.2 D. 0.87 Answer: B. Working loads are used. (Key point: Partial factor) 3. Long-term deflection differs from short-term because A. Sustained load causes creep and shrinkage, so it is larger and not recoverable B. It is immediate and recoverable C. It is smaller than short-term D. It uses Ec = 5000 sqrt(fck) only Answer: A. Long-term includes creep and shrinkage. 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