Civil

Design of Steel Structures

Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar

2.5 Plastic analysis
In plastic analysis and design of a structure, the ultimate load of the structure as a wholeis regarded as the design 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. This method is rapid and provides arational approach for the analysis of the structure. It also provides striking economy as regards the weight of steel since the sections required by this method are smaller in size than those requiredby the method of elastic analysis. Plastic analysis and design has its main application in the analysis and design of statically indeterminate framed structures.

2.5.1 Basics of plastic analysisPlastic analysis is based on the idealization of the stress-strain curve as elastic-perfectly-plastic. It is further assumed that the width-thickness ratio of plate elements is small so that localbuckling does not occur- in other words the sections will classify as plastic. With these assumptions, it can be said that the section will reach its plastic moment capacity and then undergo considerablerotation at this moment. With these assumptions, we will now look at the behaviour of a beam up to collapse.

Consider a simply supported beam subjected to a point load W at midspan. as shown inFig. 2.14(a). The elastic bending moment at the ends is w 2/12 and at mid-span is w 2/24, where is the span. The stress distribution across any

cross section is linear [Fig. 2.15(a)]. As W isincreased gradually, the bending moment at every section increases and the stresses also increase. At a section

Indian Institute of Technology Madras

Design of Steel Structures

Prof. S.R.SatishKumar and Prof. A.R.Santha Kumar

close to the support where the bending moment is maximum, the stresses in the extreme fibers reach the yield stress. The moment corresponding to this state is called...