Which is a disadvantage of WSM?

Single factor of safety, so the margin against collapse is unknown

Serviceability is not controlled at all

It requires partial factors on loads

It is too complex for routine use

Why does LSM give more rational and economical sections?

It uses different partial factors reflecting different uncertainties and ultimate strength

It uses a single large factor of safety

Which condition defines the balanced section in LSM?

x_u = x_u,max with concrete strain 0.0035 and steel yield reached together

Steel stress equals sigma_st only

What happens in an over-reinforced section?

Concrete crushes before steel yields, giving brittle failure

Steel yields first and the failure is ductile

The beam gives large cracks as warning

The neutral axis is above the balanced position

2071 Chaitra · 8 marks

WSM vs LSM advantages, section comparison

Short answer

WSM is simple and controls service stresses but gives unknown collapse margin and is uneconomical. LSM is realistic, economical, and checks serviceability. Under-reinforced sections yield first and are preferred; over-reinforced sections crush before steel yields and are brittle, so not permitted in LSM.

Discuss in detail the working stress method versus limit state method of design with their respective advantages and disadvantages. Compare balanced, under-reinforced and over-reinforced sections in limit state and working stress design methods.

Working stress method (WSM)

Stresses under working load are limited to permissible values, using linear elastic theory and the modular ratio $m$ .

Advantages

Simple, quick calculations, backed by long experience.
Stresses at service load are known, so deflection and cracking are reasonably controlled.
Suitable for liquid-retaining structures, where cracking governs.

Disadvantages

The real stress-strain behaviour is non-linear, so the method does not predict the true strength.
A single factor of safety is used; the margin against collapse is unknown and varies with the load combination.
It ignores creep, shrinkage and the different variability of dead and live loads.
Sections are uneconomical.

Limit state method (LSM)

The structure is designed for the limit states of collapse and serviceability using characteristic loads, partial safety factors and the non-linear stress-strain curves.

Advantages

Realistic: it uses the ultimate strength, so the margin against collapse is known.
Different partial factors for loads and materials reflect their different uncertainties.
Serviceability (deflection, cracking) is checked explicitly.
Sections are more economical.

Disadvantages

More complex, with separate checks for several limit states.
Serviceability checks may need trial and revision.

Comparison of balanced, under-reinforced and over-reinforced sections

Section	In WSM	In LSM
Balanced	$x = x_c = \dfrac{m\sigma_{cbc}}{m\sigma_{cbc}+\sigma_{st}}d$ ; concrete and steel reach $\sigma_{cbc}$ and $\sigma_{st}$ together	$x_u = x_{u,max}$ ( $0.48d$ for Fe415); concrete strain 0.0035 and steel strain $0.87f_y/E_s + 0.002$ are reached together
Under-reinforced	$x < x_c$ ; steel stress reaches $\sigma_{st}$ first, $M_r = \sigma_{st}A_{st}(d-x/3)$	$x_u < x_{u,max}$ ; steel yields first, $M_u = 0.87f_yA_{st}(d-0.416x_u)$ ; ductile failure, preferred
Over-reinforced	$x > x_c$ ; concrete reaches $\sigma_{cbc}$ first, $M_r = \tfrac12\sigma_{cbc}bx(d-x/3)$	$x_u > x_{u,max}$ ; concrete crushes before steel yields, brittle failure; not permitted (use $M_{u,lim}$ or add compression steel)

Under-reinforced sections are always preferred because they give warning (large deflection and cracks) before failure.

✓ Answer checked by Claude Opus 5.5 (high effort)

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