How is safety provided in the limit state method compared with the working stress method?

Partial safety factors on loads and materials in LSM; a single factor of safety on material in WSM

One factor of safety on material strength in both methods

Partial factors on loads in WSM; one factor on materials in LSM

LSM uses no safety factors because it is based on failure

Which statement about the stress-strain assumption is correct?

WSM uses elastic linear behaviour; LSM uses the non-linear parabola-rectangle curve for concrete

Both use linear elastic behaviour

WSM uses the parabola-rectangle curve; LSM uses linear behaviour

Neither method considers the stress-strain curve of concrete

Which pair is correct for WSM and LSM respectively?

Modular ratio used; serviceability not checked explicitly in WSM, but checked explicitly in LSM

Modular ratio not used; deflection checked explicitly

Modular ratio used in both; serviceability checked in both

Modular ratio used in LSM only; serviceability checked in WSM only

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Working stress vs limit state method

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.

Differentiate between the working stress method and the limit state method of design (explain with stress and strain diagrams where needed).

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

   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 $0.87 f_y$ .

✓ Answer checked by Claude Opus 5.5 (high effort)

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