Limit State, Working Stress and Ultimate Load Method of Structural Design
Gopal Mishra
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There are three methods of structural design, i.e. working stress, limit state and ultimate load method of structural design. These design methods are used for reinforced concrete as well as steel structure design.
This was the traditional method of design not only for reinforced concrete, but also for structural steel and timber design.
The method basically assumes that the structural material behaves as 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” on the structure.
As the specified permissible stresses are kept well below the material strength, the assumption of linear elastic behavior is considered justifiable. The ratio of the strength of the material to the permissible stress is often referred to as the factor of safety.
However, the main assumption linear elastic behavior and the tacit assumption that the stresses under working loads can be kept within the ‘permissible stresses’ are not found to be realistic.
Many factors are responsible for this such as a long term effort of creep and shrinkage, the effects of stress concentrations, and other secondary effects. All such effects resulting significant local increases in a redistribution of the calculated stresses.
The design usually results in relatively large sections of structural members, thereby resulting in better serviceability performance under the usual working loads.
2. Ultimate load method (ULM)
With the growing realization of the shortcomings of WSM in reinforced concrete design, and with increased understanding of the behavior of reinforced concrete at ultimate loads, the ultimate load of design is evolved and became an alternative to WSM.
This method is sometimes also referred to as the load factor methods are the ultimate strength. In this method, the stress condition at the site of impending collapse of the structure is analyzed, and the nonlinear stress-strain curves of concrete and steel are made use of.
The concept of ‘modular ratio’ and its associated problems are avoided entirely in this method. The safety measure design is introduced by an appropriate choice of the load factor, defined as the ratio of the ultimate load to the working load.
The ultimate load method makes it possible for different types of loads to be assigned different load factors under combined loading conditions, thereby overcoming the related shortcoming of WSM.
This method generally results in more slender sections, and often economical designs of beams and columns, particularly when high strength reinforcing steel and concrete are used. However, the satisfactory ‘strength’ performance at ultimate loads does not guarantee satisfactory ‘serviceability’ performance at the normal service loads.
The designs sometimes result in excessive deflections and crack-widths under service loads, owing to the slender sections resulting from the use of high strength reinforcing steel and concrete.
The distribution of stress resultants at ultimate load is taken as the distribution at the service loads, magnified by the load factor(s); in other words, analysis is still based on linear elastic theory.
3. Limit state method (LSM)
The philosophy of the limit state method of design represents a definite advancement over the traditional design philosophies.
Unlike WSM which based calculations on service load conditions alone, and unlike ULM, which based 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.
The LSM philosophy uses a multiple safety factor format which attempts to provide adequate safety at ultimate loads as well as adequate serviceability at service loads, by considering all possible ‘Limit State’.
Limits States
A limit state is a state of impending failure, beyond which a structure ceases to perform its intended function satisfactorily, in terms of either safety of serviceability i.e. it either collapses or becomes unserviceable.There are two types of limit states:
Ultimate limit states (limit states of collapse):- which deal with strength, overturning, sliding, buckling, fatigue fracture etc.
Serviceability limit states: - which deals with discomfort to occupancy and/ or malfunction, caused by excessive deflection, crack width, vibration leakage etc., and also loss of durability etc.
