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Dear Researchers, to get in touch with the recent developments in the technology and research and to gain free knowledge like , share and follow us on various social media. This video will guide authors to write their first research paper. Kindly check it and then prepare article Click Here. Plastic analysis offers several advantages over the traditional elastic analysis. With plastic analysis, a structure can be designed to form a preselected yield mechanism at ultimate load level leading to a known and predetermined response during ultimate condition.

In plastic analysis of a structure, the ultimate load of the structure as a whole is regarded as the analysis criterion. The term plastic has occurred due to the fact that the ultimate load is found from the strength of steel in the plastic range.

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Varition of stress distribution in Elastic, Elasto-Plastic, and Plastic section. It include advantages and disadvantages of Plastic method. Paper also explain about plastic hinge, plastic moment, shape factor, methods of plastic analysis. Add to Basket. Book Description Elsevier. Condition: NEW. End Chapter Exercises may differ.

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Seller Inventory FS Condition: New. Seller Inventory Book Description Elsevier, In doing so, we seek the relationship between applied moment and the rotation or more accurately, the curvature of a cross section.

We consider the cross section subject to an increasing bending moment, and assess the stresses at each stage. Stage 2 — Yield Moment The applied moment is just sufficient that the yield stress of the material is reached at the outermost fibre s of the cross-section. All other stresses in the cross section are less than the yield stress.

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This is limit of applicability of an elastic analysis and of elastic design. Stage 3 — Elasto-Plastic Bending The moment applied to the cross section has been increased beyond the yield moment.

Since by the idealised stress-strain curve the material cannot sustain a stress greater than yield stress, the fibres at the yield stress have progressed inwards towards the centre of the beam. Thus over the cross section there is an elastic core and a plastic region. The ratio of the depth of the elastic core to the plastic region is 1.

Since extra moment is being applied and no stress is bigger than the yield stress, extra rotation of the section occurs: the moment-rotation curve losses its linearity and curves, giving more rotation per unit moment i. Stage 4 — Plastic Bending The applied moment to the cross section is such that all fibres in the cross section are at yield stress. Also note that the full plastic moment requires an infinite strain at the neutral axis and so is physically impossible to achieve. However, it is closely approximated in practice.

Any attempt at increasing the moment at this point simply results in more rotation, once the cross-section has 8 Dr. Therefore in steel members the cross section classification must be plastic and in concrete members the section must be under-reinforced. Stage 5 — Strain Hardening Due to strain hardening of the material, a small amount of extra moment can be sustained. The above moment-rotation curve represents the behaviour of a cross section of a regular elastic-plastic material. However, it is usually further simplified as follows: With this idealised moment-rotation curve, the cross section linearly sustains moment up to the plastic moment capacity of the section and then yields in rotation an indeterminate amount.

Again, to use this idealisation, the actual section must be capable of sustaining large rotations — that is it must be ductile. This is termed a plastic hinge, and is the basis for plastic analysis. At the plastic hinge stresses remain constant, but strains and hence rotations can increase. In other words we want to find the yield moment and plastic moment, and we do so for a rectangular section.

Therefore the shape factor is a good measure of the efficiency of a cross section in bending. Thus the section must be ductile. Since this is impossible, we realise that the full plastic moment capacity is unobtainable.

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To demonstrate this last point, that the idea of the plastic moment capacity of section is still useful, we examine it further. These calculations are based on a ductility ratio of This is about the level of ductility a section requires to be of use in any plastic collapse analysis. Lastly, for other cross-section shapes we have the moment-curvature relations shown in the following figure.

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In the presence of axial force, clearly some material must be given over to carry the axial force and so is not available to carry moment, reducing the capacity of the section. Further, it should be apparent that the moment capacity of the section therefore depends on the amount of axial load being carried. Considering a compression load as positive, more of the section will be in compression and so the neutral axis will drop.

This is because the web carries the axial load whilst contributing little to the moment capacity of the section. Shear force can also reduce the plastic moment capacity of a section in some cases. In the presence of axial and shear, a three dimensional failure surface is required.

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This is a general result: the ratio of collapse load to first yield load is the shape factor of the member, for statically determinate prismatic structures. As can be seen from the diagram, the plastic material zones extend from the centre out to the point where the moment equals the yield moment. Methods of Plastic Analysis 3. This continues until sufficient hinges have formed to collapse the structure.

The Equilibrium or Statical Method In this method, free and reactant bending moment diagrams are drawn. These diagrams are overlaid to identify the likely locations of plastic hinges. This method therefore satisfies the equilibrium criterion first leaving the two remaining criterion to derived therefrom. The Kinematic or Mechanism Method In this method, a collapse mechanism is first postulated. Virtual work equations are then written for this collapse state, allowing the calculations of the collapse bending moment diagram.

This method satisfies the mechanism condition first, leaving the remaining two criteria to be derived therefrom. We will concentrate mainly on the Kinematic Method, but introduce now the Incremental Method to illustrate the main concepts. We will also look at the deflections for better understanding of the behaviour.

Also, the maximum moment occurs at A and so this point will first reach the yield moment. The load factor before yielding occurs, based on the maximum moment at A and the yield moment is 7. Thus a load of 1. The moment at A has now reached the yield moment and so the outer fibres at A are at yield stress. This applies because the beam is linearly elastic to this point. The rotation at A is still zero. The moment at A is now 9 kNm — the plastic moment capacity of the section — and so the cross section at A has fully yielded.

Plastic Analysis and Shape Factor - Design of Steel Structures

Thus a plastic hinge has formed at A and so no extra moment can be taken at A, but A can rotate freely with constant moment of 9 kNm. Also, the moment at C has reached the yield moment. Note that the structure does not collapse since there are not sufficient hinges for it to be a mechanism yet: it now acts like a simply-supported beam with a pin at A the plastic hinge and B the pin support.

Note that the assumption of an idealised bilinear moment-rotation curve means that the actual deflection will be greater as some rotation will occur — see Moment Rotation Curve of a Rectangular Section on page 16 for example. That is, a beam free to rotate at both ends. Therefore a plastic hinge forms at C and the structure is not capable of sustaining anymore load — becomes a mechanism — and so collapse ensues. The deflection is now comprised of two parts: the propped cantilever deflection of 1.

The load-deflection graph of the results shows the formation of the first hinge, as the slope of the line changes i. The actual load carried by the beam is 54 kN, greater than the load at which yield first occurs, 40 kN, the elastic limit. The height of the free bending moment diagram was PL 4 throughout, as required by equilibrium — only the height of the reactant bending moment diagram varied.