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Working stress vs limit state method

Short answer

WSM is based on elasticity with working loads and a single safety factor on stress. LSM considers ultimate and serviceability limit states, uses factored loads and partial factors on loads and material, idealizing steel as elastic-perfectly plastic, achieving more uniform reliability and economy.

Differentiate between the working stress method of design and the limit state method of design (with sketches).

PointWorking Stress MethodLimit State Method
BasisElastic theoryBehaviour up to failure and at service
LoadsWorking (characteristic) loadsFactored loads γf×\gamma_f\times characteristic
SafetyOne factor of safety on material stressPartial factors γf\gamma_f and γm\gamma_m
Design checkStress ≤\le permissible stressFactored action ≤\le design strength
Stress-strainLinear elasticIdealised (elastic-plastic)
FailureFailure not consideredLimit states of strength and serviceability
Uniform safetyNot uniformNearly uniform reliability
EconomyGenerally heavierMore economical
CodeIS 800:1984IS 800:2007
 WSM                         LSM
 stress                      stress
  fy |      /                 fy |  ______ (plastic)
 0.6fy|----/  perm.           fd |-/
     |   /                       |/ design
     |__/____ strain             |________ strain

In WSM the structure is designed to keep stress below 0.6fy0.6f_y under working load; in LSM it is designed so that the factored load does not exceed the design strength fy/γm0f_y/\gamma_{m0} and deflection stays within limits.

✓ Answer checked by Claude Opus 5.5 (high effort)

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