STRUCTURAL ANALYSIS
Structural analysis is necessary to find the internal forces developed in the members of the structures. The required internal forces for design are axial forces and moments.
IS code permits the following methods of analysis:
(a) Elastic Analysis
(b) Plastic Analysis
(c) Advanced Analysis
(d) Dynamic Analysis.
(a) Elastic Analysis. It is based on the assumption that - no fibre of a member has yielded for design load and stress is linearly proportional to strain. The analysis may be in 2 stages:-
Stage 1 Order Analysis: It is based on the loads acting on undeformed geometry of the structure. Redistribution of 15% of peak moment is permitted by code.
Stage 2-Second Order Analysis: It is based on the deformed (large deflection theory) shape of the structure. IS 800 permits use of amplification factors (as given under clause 4.4.3.2) instead of second order analysis.
(b) Plastic Analysis: In this method it is assumed that when every fibre at a section reaches yield stress a plastic hinge is formed. After hinge is formed, it is assumed that the member rotates freely at the plastic hinge without resisting any additional moment. However its resistance to moment remains constant (M,). This 1s called first order plastic analysis.
Code permits second order in elastic analysis by any of the following methods:
(i) Distributed plasticity method
(ii) Elastic — plastic hinge method
(iii) Modified plastic hinge method.
(c) Advanced Analysis: For a frame with full lateral restraints, an advanced structural analysis may be carried out, provided the analysis can be shown to accurately model the actual behaviour of that class of frames. The analysis shall take into account the following:
(i) Relevant material properties
(ii) Residual stresses
(iii) Geometric imperfections
(iv) Reduction in stiffness due to axial compressions
(v) Second order effects
(vi) Erection procedure
(vii) Interaction with foundation.
For further details Annexure B of IS 800-2007 may be referred.
(d) Dynamic Analysis: Dynamic analysis is to be carried out in accordance with IS 1893 (part I).
DESIGN PHILOSOPHY
The aim of design is to decide shape, size and connection details of the members so that the structure being designed will perform satisfactorily during its intended life. With an appropriate degree of safety the structure should
(a) Sustain all loads expected on it.
(b) Sustain deformations during and after construction.
(c) Should have adequate durability.
(d) Should have adequate resistance to misuse and fire.
(e) Structure should be stable and have alternate load paths to prevent overall collapse under accidental loading. Analytical method of design consists in idealizing the structure, quantifying expected loads, carrying analysis to find member forces and sizing the members based on possible failure criteria. Since there are limitations in precisely modelling the structure, working condition is kept as a fraction of failure condition.
The design philosophies used are listed below in the order of their evolution and they are briefly explained:
(i) Working Stress Method (WSM)
(ii) Ultimate Load Design (ULD) and
(iii) Limit State Design (LSD).
(i) WORKING STRESS METHOD: This is the oldest systematic analytical design method. Though IS 800-2007 insists for the limit state design, permits use of this method wherever LSD cannot be conveniently adopted.
In this method stress strain relation is considered linear till the yield stress. To take care of uncertainties in the design, permissible stress is kept as a fraction of yield stress, the ratio of yield stress to working stress itself known as factor of safety. The members are sized so as to keep the stresses within the permissible value. Thus
permissible stress = yield stress/factor of safety
The following load combinations are considered and increase of permissible stress by 33% is permitted
when DL, LL and WL are considered:
Stress due to DL+ LL less than and equal to permissible stress
Stress due to DL + WL less than and equal to permissible stress
Stress due to DL+ LL + WL less than and equal to 1.33 permissible stress.
The limitations of WSM:-
The limitations of working stress method are:
1. It gives the impression that factor of safety times the working load is a failure load, which is not true. Actually it is much more, because a material can resist the after yield appears at fibre. In the indeterminate structures just formation of a plastic hinges in not a failure criteria, since it can resist load till some more hinges are formed resulting into collapse mechanism. Thus the redistribution of moments gives rise to the additional load carrying capacity.
2. It gives uneconomical sections.
Advantages of WSM
1. This method is simple.
2. This is reasonably reliable.
3. As the working stress are low, the serviceability requirements are satisfied automatically.
(ii) ULTIMATE LOAD METHOD:
The limitation of working stress method to assess actual load carrying capacity, made researcher to develope ultimate load method, which is also known as load factor method(LFM). When applied to steel structure is referred as plastic design method. In this method a section is said to have formed plastic hinges when all the fibre yield.
After that it continues to resist load which has cause plastic hinges but will not resist any more load. But structure continues to resist further load till sufficient plastic hinges are formed to develope collapse mechanism.
In this method safety measures are introduced by suggesting a load factor, which is defined as the ratio of design load to working load. The suggested load factors as per IS 800:1984 were as shown
SI. No. Working Load Minimum Load Factor
l Dead Load 1.7
2 Dead Load + Imposed Load 1.7
3 Dead Load + Wind or Seismic Load 1.7
4 Dead Load + Imposed Load + Wind or Seismic Load 1.3
Advantages of ULD
1. Redistribution of internal forces is accounted.
2. It allows varied selection of load factors.
Disadvantages of ULD
It does not guarantee serviceability performance. To account for this IS 800:1984 suggested limitations on deflection. However it did not guarantee other serviceability limits like instability and fatigues etc. Finally it was felt to suggest more comprehensive method to take care of design requirements from strength and serviceability criteria.
(iii) LIMIT STATE DESIGN: It is the comprehensive method which will take care of both strength and serviceability requirements. IS 800:2007 suggests use of this method widely and restricts WSM only wherever LSD cannot be applied.
LIMIT STATES
Limit states are the states beyond which the structure no longer satisfied the Specified performance requirements. The various limit states to be considered in design may be grouped into a following two major categories:
(a) Limit state of strength
(b) Limit state of serviceability.
(a) Limit state of strength:
The limit states, prescribed to avoid collapse of structure which may endanger the safety of life and property, are grouped under this category. The limit state of strength includes:
(i) Loss of equilibrium of whole or part of the structure.
(ii) Loss of stability of structure as a whole or part of it.
(iii) Failure by excessive deformation.
(iv) Fracture due to fatigue.
(v) Brittle fracture.
(b) Limit state of serviceability:
The limit state of serviceability include:
(i) Deformations and deflections adversely affecting the appearance or effective use of structure or causing damage to finishings or causing improper functioning of equipment or services.
(ii) Vibrations in structures or any part of its component limiting its functional effectiveness.
(iii) Repairable damage or crack due to fatigue.
(iv) Corrosion.
(v) Fire.
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