--- title: "Define structural steel; resistance after yielding" subject: "Design of Steel and Timber Structure" chapter: 1 key: "semester_6/design_of_steel_and_timber_structure:steel-resist-after-yielding" source: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/steel-resist-after-yielding site: BCT Engineering --- # Define structural steel; resistance after yielding Design of Steel and Timber Structure · Chapter 1: Steel Structures and their Analysis and Design - Asked in: 2074 Bhadra, 3+3 marks - Video: [Design Steel Structures Lecture - 3 Steel Structure Specifications & Design Loads as per LRFD](https://www.youtube.com/watch?v=K6ppZV_gcGk) — Any Tech Key - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/steel-resist-after-yielding - Whole chapter: https://www.bctengineer.com/md/semester_6/design_of_steel_and_timber_structure/chapter-1 ## Question Define the terms structural steel, factor of safety and partial safety factor. Explain briefly, how structural steel can resist loads even after local yielding. ## Short answer Structural steel is rolled steel alloy per IS 2062. Factor of safety is fy/σperm in WSM; partial safety factors γf and γm are used in LSM. After local yielding, ductile steel redistributes stress: yielded fibers carry fy and transfer load to surrounding elastic fibers, relieving stress concentrations and allowing plastic hinge formation. ## Answer #### Structural steel Structural steel is rolled steel (iron + 0.15-0.25% carbon and alloying elements such as Mn) of grades covered by IS 2062 that is used as the load-carrying material in buildings, bridges and towers. #### Factor of safety It is the ratio of the failure (or yield) stress of the material to the permissible (working) stress, $FOS = f_y/\sigma_{perm}$. In working stress design a single factor (about 1.67 on yield, i.e. $\sigma_{perm}=0.6f_y$) covers all uncertainties in loads and material. #### Partial safety factor In limit state design separate factors are used: $\gamma_f$ multiplies characteristic loads (e.g. 1.5 for DL and LL) and $\gamma_m$ divides characteristic material strength (e.g. $\gamma_{m0}=1.10$ for yielding, $\gamma_{m1}=1.25$ for ultimate strength, 1.25 for bolts, 1.25/1.5 for shop/field welds). Each factor reflects the uncertainty of one particular quantity. #### Resistance after local yielding Mild steel is ductile, with a long yield plateau (strain about 10-15 times the yield strain) and then strain-hardening up to $f_u$. - At stress concentrations (holes, notches, welds) the local stress may reach $f_y$ and the fibre yields, but it keeps carrying the stress $f_y$ while the strain increases. - The extra load is transferred to the adjoining elastic fibres, so stresses redistribute and the stress concentration is relieved. - Residual stresses and bending stresses at connections also redistribute in this way, and a section can go on to form a plastic hinge and resist moment up to $M_p$. - Hence local yielding does not lead to failure; the structure gives large deformation as warning before collapse. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is the factor of safety defined in working stress design? A. Ratio of permissible stress to yield stress B. Ratio of yield (failure) stress to permissible stress C. Ratio of factored load to working load D. Ratio of ultimate load to yield load Answer: B. FOS = fy / permissible stress, about 1.67 for sigma = 0.6fy. (Key point: Factor of safety) 2. How are partial safety factors applied in limit state design? A. One factor multiplies the permissible stress B. gamma_f multiplies characteristic loads and gamma_m divides characteristic material strength C. gamma_f divides loads and gamma_m multiplies strength D. Both factors multiply the loads Answer: B. Loads are multiplied by gamma_f and material strengths divided by gamma_m, each reflecting its own uncertainty. (Key point: Partial safety factor) 3. What property lets steel keep carrying load after local yielding at a stress concentration? A. Brittleness B. A long yield plateau where the fibre keeps carrying fy while strain increases C. Very low ductility D. Reduction of modulus E to zero at the start Answer: B. Ductile mild steel holds stress fy over a long strain range, so yielding fibres do not fail immediately. (Key point: Yield plateau) 4. What happens to the extra load when a fibre yields locally? A. It is transferred to adjoining elastic fibres, relieving the stress concentration B. It causes immediate fracture C. It is carried by the yielded fibre at higher than fy D. It disappears Answer: A. Stresses redistribute to neighbouring elastic fibres, so local yielding does not cause failure and large deformation warns before collapse. 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