# Limit State Method,Working Stress Method and Ultimate Load Method

Limit State Method,Working Stress Method and Ultimate Load Method

# 1) Limit States Method (LSM)

• A limit state is a state of impending failure, beyond which a structure ceases to perform its intended function satisfactorily, in terms of either strength or serviceability; i.e., it either collapses or becomes unserviceable.
• Unlike WSM, which bases calculations on service load conditions alone, and unlike ULM, which bases calculations on ultimate load conditions alone, LSM aims for a comprehensive and rational solution to the design problem, by considering safety at ultimate loads and serviceability at working loads.
• LSM is described as a ‘semi-probabilistic’ method or a ‘Level 1 reliability’ method

Partial load and material safety factor

Ultimate limit states – partial load factors:

UL = 1.5 (DL + LL)

UL = 1.5 (DL + QL) or (0.9DL + 1.5 QL)

UL = 1.2 (DL + LL + QL)

Ultimate limit states – material safety factors:

Concrete:      gamma   = 1.5

Steel:              gamma  = 1.15

Code Recommendations for   Limit States Design

Characteristic Strength

• 5 percentile strength
• to be taken as ‘specified yield strength’ in case of steel.

• the load that “has a 95 percent probability of not being exceeded during the life of the structure”
• In the absence of statistical data regarding loads, the nominal values specified for dead, live and wind loads are to be taken from IS 875 (Parts 1–3) : 1987 and the values for ‘seismic loads’ (earthquake loads) from IS 1893 : 2002

Ultimate limit states – partial load factors:

UL = 1.5 (DL + LL)

UL = 1.5 (DL + QL) or (0.9DL + 1.5 QL)

UL = 1.2 (DL + LL + QL)

Serviceability limit states – partial load factors:

SL = 1.0 (DL + LL)

SL = 1.0 (DL + QL)

SL = 1.0 DL  + 0.8 (LL + QL)

# 2) Working Stress Method (WSM)

• Simple conceptual basis: The structural material behaves in a linear elastic manner, and that adequate safety can be ensured by suitably restricting the stresses in the material induced by the expected ‘working loads’ (service loads) on the structure.
• As the specified permissible (‘allowable’) stresses are kept well below the material strength (i.e., in the initial phase of the stress-strain curve), the assumption of linear elastic behaviour is considered justifiable.
• The ratio of the strength of the material to the permissible stress is often referred to as the factor of safety.
• Still in use for the design of bridges, chimneys, water tanks etc.

Points in WSM

• Modular ratio is not a constant: increases with time due to creep of concrete.
• Assumption of linear elastic behaviour not always justifiable.
• WSM does not account for behaviour under loads that exceed service loads.
• Uneconomical section design

• Evolved in the 1950s and became an alternative to WSM
• Also called the load factor method or the ultimate strength method
• The stress condition at the state of impending collapse of the structure is analysed, and the non-linear stress-strain curves of concrete and steel are made use of.
• No need for ‘modular ratio’.
• The safety measure in the design is introduced by an appropriate choice of the load factor, defined as the ratio of the ultimate load (design load) to the working load.

• This method generally results in more slender sections, and often more economical designs of beams and columns (compared to WSM), particularly when high strength reinforcing steel and concrete are used.

Points in ULM

• Satisfactory performance at ultimate loads does not guarantee serviceability at working loads (reduced stiffness due to slender sections).
• The use of the non-linear stress-strain behaviour for the design of sections becomes truly meaningful only if appropriate non-linear limit analysis is performed on the structure (significant inelastic behaviour and redistribution of stress resultants takes place at ultimate loads).

Voids in Hydrated cement paste

TRANSITION ZONE IN CONCRETE

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• November 28, 2017 at 6:16 PM