# Plastic Analysis Of a structure

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PLASTIC ANALYSIS OF

PLASTIC ANALYSIS OF A STRUCTURE

Presented byDipanjan Jana3rd yearCivil EngineeringRoll: 26301311039Regent Education and Research fundation

ContentsINTRODUCTIONSteel is very ductile material and from the stress strain curve it is observed that higher loads than in the elastic method can be applied over the structure. This is due to the fact that a major portion of the curve lies beyond the elastic limit. This extra strength is termed reserve strength and forms the basis of plastic design method.

This is an aspect of limit design, which confines the structural usefulness up to the plastic strength or ultimate load carrying capacity. this method is based on failure condition. In this method of design failure implies collapse or extremely large deformations, thus the structure fails at a much higher load, called the collapse load, than working load.Idealized stess strain curve for mild steel

Bending of beams

Redistribution of moments and reserve of strength

Shape factorFor a ductile material like structural steel a member reaching yield at the extreme fibers retains a reserve of strength that varies with the shape factor. Shape factor=plastic moment/yield momentIt is a function of the cross section form or shape.Load factorLoad is a factor defined as the ratio of collapse load to the working load. It is represented by F. F = Pu/ Pw = Mp/ Mw = fy Zp/f Ze = fy S /f = (F.O.S)SMECHANISM When a structure is subjected to a system of loads ,it is stable and hence functional until a sufficient number of plastics things have been formed to render the structure unstable. As soon as the structure reaches an unstable condition it is considered to have been failed. The segments of the beam between the plastic hinges are able to move without an increase of load. This condition in a member is called mechanism. The concept of mechanism formation in a structure due to loading beyond the elastic limit of a virtual work are used in plastic analysis has redundancy r,the collapse of number of plastic hinges required (r+1).

TYPES OF MECHANISM

Beam Mechanism Sway Mechanism Joint MechanismGable MechanismComposite Mechanism

PLASTIC COLLAPSE

The plastic collapse of a structure depends upon its redundancy .When a sufficient number of plastic hinges are formed to convert a structure into mechanism the structure collapse as such a stage, the deflection increases very fast at a constant load. The collapse of a structure can be partial, complete and over complete. This terms can be explained indeterminacy (r) . Number of Plastic hinges(N) The number of plastic hinges in collapse mechanism are less than (r+1).The collapse is called partial collapse.The number of plastic hinges in collapse mechanism are equal to (r+1).The collapse is called complete collapse.The number of plastic hinges in collapse mechanism are greater than (r+1).The collapse is called over complete collapse.

CONDITION IN PLASTIC ANALYSIS

Equilibrium condition Mechanism conditionYield condition

PRINCIPLE OF VIRTUAL WORK

If a system of forces in equilibrium is subjected to a virtual displacement the work done by the external forces equals the work done by internal forces. We=Wi It is to a object to express an equilibrium condition.THEOREMS OF PLASTIC ANALYSIS

Static or lower bound theoremKinematic or upper bound theoremUniqueness theoremMETHODS OF ANALYSIS

Static MethodKinematic MethodCONCLUSIONengineers and research workers have been stimulated to study the plastic strength of steel structures and its application to design for three principle reasons:a)it has a more logical design basis.b)it is more economical in the use of steel.c)it represents a substantial saving of time in the design.-[beedle,1960]the calculation of load carrying capacity by use of limit theorems is much easier than the calculation of stress .answer obtained are not only physically more meaningful but also simplier.The simplicity of limit analysis opens the way to limit design, to direct design as contrasted with the trial and error procedure normally followed in conventional design.-[chen,1982]

REFERENCELimit State Design of Steel Structures-[S.K.Duggal]Structural Design In Steel [Sarawar Alam Raz]Plastic Analysis and Design of Steel Structures-[M. Bill Wong]Collapse!: The Science of Structural Engineering Failures-[Kirstin Cronn-Mills]

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