Limit state Frequency distribution curve

Structural Design Philosophies

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Limit state Frequency distribution curve
Limit state Frequency distribution curve

Designs are generally carried out under the guide of one philosophy or hybrid of philosophies; structural engineering field is no exception to this premise. In structural engineering over the years, three philosophies are well known for strength-based design, these are:

  1. Permissible Stress Method
  2.  Load Factor Method
  3. Limit State Method

Permissible Stress Method: 

In this method, the stress generated in a member is not allowed to exceed a certain stress which is called the permissible stress. The permissible stress is obtained by dividing the “failure stress” – the stress at which the member is assumed to fail – by a factor of safety.

If the “failure stress” of a beam is 5N/mm², to get the permissible stress this failure stress which is 5 is divided by a factor of safety, say 1.5.

i.e.: 5/1.5 = 3.33 5N/mm²

Hence the stress induced in the beam by working loads will not be allowed to exceed 3.33 5N/mm².

If the stress exceeds 3.33 5N/mm², the size of the beam will be increased until the stress falls below the permissible stress.

This method of design is also called the allowable stress design or working stress design.

 

Draw backs of permissible stress design

.               It is grossly uneconomical: Permissible stress design is uneconomical because what is deemed as the “failure stress” is sometimes exaggerated. This exaggeration is necessary so that a conservative “failure stress” is chosen such that the stress induced in the member will not come close to the ultimate strength of the member throughout its service life.  And In spite that an exaggerated failure stress has been chosen, this stress is divided by a factor of safety and then the resulting stress taken as the control parameter to guide the sizing of the member. This results to the member being unnecessarily big.

Due to this stark conservatism of limiting the stress members can be subjected, materials such as elasto-plastic and plastic with great strength potential beyond their yield strength are often underutilized. The permissible stress design ensures the stress developed in members are within elastic range, hence it is also called elastic design method. 

.           It lacks guidance on the behavior of Structures under Ultimate Load:  The permissible stress design does not consider how a structure behaves under ultimate load. The loads used in permissible stress design are not multiplied by a factor, so they are not necessarily designed to resist collapse. The method only considers the behavior of a structure under working load. All uncertainties in the structure is assumed to be have been taken care of by the Factor of Safety for the material strength.

 

 

Load Factor Design

This is a method where the forces acting on a structure are multiplied by a factor. By multiplying the loads by a factor (say 1.2 or 1.5) the structure can be designed against collapse such that it can withstand the most sever of loads that could possibly act on it during its service life. This method considers the behavior of a structure to be examined under collapse loads so that it can be sized accordingly.

 

Drawbacks of Load Factor Method

.               It disregards the performance of structure in service: The load factor does not examine the behavior of the structure in service (i.e. under un-factored load). The grim corollary of load factor method is that as long as the structure has not collapsed, it has not failed even if that means the structure becomes unfit for its intended purpose.

A practical aftereffect of this corollary is that if a slab deflects so much that one cannot walk or place furniture on it, it is still fine as long as it has not collapsed; if your water tank leaks such that all water is lost, it is fine as long as the tank itself has not collapsed. This liberal approach to understanding failure which preclude the performance of the structure in service is contrary to the basic objectives of a good structural design.

.              It lacks considerations for Secondary effects: The load factor method also does not take into consideration imperfection in material properties and error in construction.

 

Limit State Method.

The limit state method retains the advantages of both permissible stress method and load factor method and also overcomes their respective demerits. This method assesses structures base on their peculiar merits. The failure modes of a structure are studied and criteria that must be satisfied for the structure to be safe from those failures are proffered.  Generally, this method ensures the structure does not reach a limit state.

A limit state is a failure threshold which when a structure reaches it then the structure becomes unfit for the purpose for which it is intended. This failure could be buckling, rupture, bending, excessive vibration, etc. Each of the mentioned failure modes is a limit state which a structure must be prevented from and designed against if it could be susceptible to any of them in its life span.

The effect of reaching any of these limit states can be categorized broadly into two. The structure could either fail due to partial collapse or whole collapse, or the structure becomes unfit due to deficiency in its functionality and appearance. Hence, each of the limit states are broadly packed under either of these two categories:

  • Ultimate Limit State
  • Serviceability Limit State

 

 

Ultimate Limit State

The ultimate limit state is the limit state which when exceeded the structure wholly or partly becomes unsafe. There are different ultimate limit states such as ultimate limit states of strength, stability, buckling etc.

 

 

Serviceability Limit State

The serviceability limit state is the limit which when exceeded the aesthetics and functionality of the structure is affected. There are various serviceability limit states such as deflection, cracking, vibration etc.

 

 

Because of the comprehensive nature of the limit state method, it is the most widely used method currently and many codes of practice across state and regions have adopted and are still adopting it. It is also known as the Load and Resistance Factor Design according to some codes such as the ACI.

 

 

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