--- title: "Working stress vs limit state method" subject: "Design of RCC Structure" chapter: 1 key: "semester_7/design_of_rcc_structure:working-stress-vs-limit-state-method" source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/working-stress-vs-limit-state-method site: BCT Engineering --- # Working stress vs limit state method Design of RCC Structure · Chapter 1: Concrete Structures and Design Methods - Asked in: 2081 Bhadra, 4 marks; 2079 Bhadra, 2 marks; 2074 Chaitra, 5 marks; 2072 Chaitra, 5 marks; 2066 Bhadra (old course), 5 marks; 2065 Shrawan (old course), 7 marks (asked 6 times) - Video: [Working Stress Method V/S Limit State Method | ReactionTest](https://www.youtube.com/watch?v=X00-ri4GmqQ) — Reaction Test - 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/working-stress-vs-limit-state-method - Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-1 ## Question Differentiate between the working stress method and the limit state method of design (explain with stress and strain diagrams where needed). ## Short answer WSM uses elastic theory, service loads, permissible stresses and a single factor of safety. LSM uses factored loads, partial safety factors, nonlinear concrete stress block, and explicitly checks collapse and serviceability; it is the main method in IS 456:2000. ## Answer The **working stress method (WSM)** designs a member so that stresses under working (service) loads stay within permissible elastic limits. The **limit state method (LSM)** designs a member so that it will not reach any limit state (collapse or serviceability) when factored loads act, using partial safety factors for loads and materials. | Point | Working stress method | Limit state method | |---|---|---| | Basis | Elastic theory, stress-strain linear for both materials | Inelastic behaviour; concrete uses parabolic-rectangular curve up to failure | | Loads | Service (working) loads | Characteristic loads multiplied by $\gamma_f$ (factored loads) | | Safety | Single factor of safety applied to material strength (permissible stress) | Partial safety factors: $\gamma_f$ on loads, $\gamma_m$ on materials (1.5 concrete, 1.15 steel) | | Stress in concrete | Linear, maximum $\sigma_{cbc}$ | Non-linear, $0.446 f_{ck}$ design stress block | | Modular ratio | Used ($m = 280/3\sigma_{cbc}$) | Not used | | Reserve strength | Not known; may be uneconomical or unsafe at failure | Known margin against collapse | | Serviceability | Not checked explicitly | Deflection and cracking checked explicitly | | Economy | Less economical for the same safety | More economical, rational | | Code status | Kept in IS 456:2000 Annex B (alternative) | Main method of IS 456:2000 | **Stress and strain diagrams at section level** ```text WSM (service load) LSM (collapse) strain stress strain stress |\ |\ 0.0035 0.446fck | \ | \ f_c<=σcbc |\ |========| x | \ x | \ xu | \ xu | | --+--- ----+--- ----+--- ----+--------+ | / | T=σst.Ast | / | T=0.87fy.Ast | / | | / | linear linear linear parabola+rectangle ``` In WSM, a triangular concrete stress block with $f_c \le \sigma_{cbc}$ and steel stress $\le \sigma_{st}$ is used. In LSM, the strain at the extreme concrete fibre is $0.0035$ and the compressive block is parabola plus rectangle (average stress $0.36 f_{ck}$, centroid at $0.416x_u$ from the top), with steel at $0.87 f_y$. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is safety provided in the limit state method compared with the working stress method? A. One factor of safety on material strength in both methods B. Partial safety factors on loads and materials in LSM; a single factor of safety on material in WSM C. Partial factors on loads in WSM; one factor on materials in LSM D. LSM uses no safety factors because it is based on failure Answer: B. WSM limits stresses to a fraction of strength with one factor of safety. LSM uses gamma_f for loads and gamma_m for materials. (Key point: Safety format) 2. Which statement about the stress-strain assumption is correct? A. WSM uses elastic linear behaviour; LSM uses the non-linear parabola-rectangle curve for concrete B. Both use linear elastic behaviour C. WSM uses the parabola-rectangle curve; LSM uses linear behaviour D. Neither method considers the stress-strain curve of concrete Answer: A. WSM is based on elastic theory with linear stress-strain. LSM uses the non-linear curve up to failure. (Key point: Basis of stress-strain behaviour) 3. Which pair is correct for WSM and LSM respectively? A. Modular ratio not used; deflection checked explicitly B. Modular ratio used; serviceability not checked explicitly in WSM, but checked explicitly in LSM C. Modular ratio used in both; serviceability checked in both D. Modular ratio used in LSM only; serviceability checked in WSM only Answer: B. WSM uses m = 280/(3 sigma_cbc) and does not check serviceability explicitly. LSM does not use m and checks deflection and cracking. (Key point: Modular ratio and serviceability) 4. In the LSM stress block, what are the extreme-fibre concrete strain and steel design stress? A. 0.002 and 0.87 fy B. 0.0035 and 0.87 fy C. 0.0035 and fy D. 0.0035 and 0.446 fck Answer: B. At collapse the extreme concrete strain is 0.0035 and steel stress is taken as 0.87 fy. 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