WORKING STRESS METHOD (WSM)

This is the traditional method of design, used not only for reinforced concrete but

also for structural steel and timber. Close to about hundred years old, the method is based on linear elastic theory or the classical elastic theory. This method of design was evolved around 1900 and was the first theoretical method accepted by National Codes of Practice for the design of reinforced concrete sections. This method ensures adequate safety by suitably restricting the stresses in the materials (i.e. concrete and steel) induced by ' the expected working loads on the structure. The assumption of linear elastic behaviour is considered

justifiable since the specified permissible (or allowable) stresses are kept well below the ultimate strength of the material. The ratio of yield stress of the steel reinforcement or the cube strength of the concrete to the corresponding permissible or Working stress is usually called the factor of safety. The WSM uses a factor of safety of about 3 with respect to the cube strength of concrete and a factor of safety of about 1.8 with respect to the yield strength of steel.

Reinforced concrete is a composite material. The WSM assumes strain compatibility, whereby the strain in the reinforcing steel is assumed to be equal to that in the adjoining concrete to which it is bonded. Consequently the stress in steel in linearly related to the stress in adjoining concrete by a constant factor, called the modular ratio defined as the ratio of the modulus of elasticity of steel to that of concrete. The WSM is therefore also known as the modular ratio method.

Demerits of WSM

Most structures designed in accordance with WSM have been generally performing satisfactorily for many years. However, the method has the following demerits :

1. The WSM does not show the real strength nor gives the true factor of safety

of the structure under failure.

2. The modular ratio design results in larger percentage of compression steel than

that given by the limit state design, thus leading to un-economic design.

3. Because of creep and non-linear stress-strain relationship. concrete does not have definite modulus of elasticity.

4. The WSM fails to discriminate between different types of loads that act simultaneously but have different uncertainties.

Merits of WSM

Inspire of the above defects, the WSM has the advantage of its simplicity. both in

concept as well as in application. The design usually results in relatively large sections of structural members, compared to the ULM. Due to this, structures designed by WSM give better serviceability performance (i.e. less det1ection. less crack width etc.) under working loads. WSM is the only method available when one has to investigate the R.C. section for service stresses and for the serviceability states of detlection and cracking. It is essemial to have a knowledge of WSM since it forms a part of Limit state design (LSD) for a serviceability condition.

ULTIMATE LOAD METHOD (ULM)

The ultimate load method (ULM) was evolved in 1950 as an alternative to the WSM. The method is based on the ultimate strength of reinforced concrete at ultimate Load. The ultimate load is obtained by enhancing the service load by some factor referred to as load factor for giving a desired margin of safety. Hence the method is also referred to as the Load factor method or the ultimate strength method. The ULM was introduced as alternative to WSM in the ACI Code in 1956, the British Codes in 1957 and the Indian Code in

1964.

In the ULM method, stress condition at the state of impending collapse of the structure is analysed, thus using the non-linear stress-strain curves of concrete and steel. The safety measure in the design is obtained by the use of proper Load factor. This makes it possible to use different load factors under combined loading conditions. It is to be carefully noted that satisfactory strength performance at ultimate Loads does not guarantee satisfactory serviceability performance at normal service Loads. Since the method utilizes a large reserve of strength

in plastic region (inelastic region) and of ultimate strength of member, the resulting section is very slender or thin. This gives rise to excessive deformation and cracking. Also, the method does not take into consideration the effects of creep and shrinkage. -

Merits of ULM

1. While the WSM uses only the nearly linear part of stress-strain curve, the U LM

uses fully the actual stress-strain curve. In other words, the stress block parameters are defined by the actual stress-strain curve.

2. The load factor gives the exact margin of safety against collapse.

3. The method allows to use different load factors for different types of loads and

the combination thereof.

4 . The failure load computed by ULM matches with the experimental results.

5. The method is based on the ultimate strain as the failure criteria.

6. The method utilises the reserve of strength in the plastic region.

Demerits of ULM

1. The method does not take into consideration the serviceability criteria of deflection and cracking.

2. The use of high strength reinforcing steel and concrete results in increase of detlection and crack width.

3. The method does nor rake into consideration the effects of creep and shrinkage.

4. In the ULM, the distribution of stress resultants at ultimate load is taken as the

distribution at service loads magnified by the load factor(s). This is erroneous since significant redistribution of stress resultants takes place as the loading is increased from service loads

to ultimate loads.

LIMIT STATE METHOD (LSM)

We have seen that while the WSM gives satisfactory performance of the structure

at working loads, it is unrealistic at ultimate state of collapse. Similarly, while the ULM provides realistic assessment of safety, it does not guarantee the satisfactory serviceability requirements at service loads. An ideal method is the one which takes into account not only the ultimate strength of the structure but also the serviceability and durability requirements. The newly emerging 'limit state method' of design is oriented towards the simultaneous satisfaction of all these requirements. In the limit state method. a structure is designed for safety against collapse (i.e. for ultimate strength to resist ultimate load) and checked

for its serviceability at working loads, thus rendering the structure fit for its intended use. Thus, the LSM includes consideration of a structure at both the working and the ultimate load levels with a view to satisfy the requirements of safety and serviceability.

The European Committee for Concrete (CEB) and the International Federation for Prestressing (FIP) were amongst the earliest to introduce the philosophy of limit state. method which is reliability-based in concept. 'Recommendations for an International Code of Practice for Reinforced Concrete' known as the blue book was published in 1963 by CEB and the complimentary report ' International Recommendations for the Design of Concrete Structures known as red book, was published in 1970 by CEB along with FIP. These were subsequently revised by CEB-FIP as the 'Model Codes for Concrete Structures· as model for national

Codes to follow. The LSM was introduced in the British Code in 1973 and the Indian

Code in 1978. However, in United States, it was introduced in ]971 in a slightly different format of 'strength and serviceability design'.

The acceptable limit of safety and serviceability requirements, before failure occurs. is called a limit state. 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 or serviceability. i.e. it either collapses or becomes unserviceable. The aim of design is to achieve acceptable probabilities that the structure will nor become unfit for the use for which it is intended. that is. it will not reach a limit stare. As per IS 456 : 2000. all limit states (see * 2. 5) shall be considered in design to ensure an adequate degree of safety and serviceability. In general, the structure shall be designed on the basis of the most critical Limit State and shall be checked for other limit stares.

For ensuring the above objectives, the design should be based on characteristic values for material strengths and applied loads, which take into account the variations in the material strengths and in the loads to be supported. The characteristic values should be based on statistical data if available; where such data are not available. they should be based on experience. The 'design values' are derived from the characteristic values through the use of partial safety factors, one for material strengths and the other for loads.

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