This document discusses the classification of cross-sectional shapes according to their ability to form plastic hinges and resist local buckling. It defines four classes of cross-sections: plastic, compact, semi-compact, and slender. Plastic sections can develop plastic hinges, compact sections can develop plastic moments but have inadequate rotation, semi-compact sections can reach yield stress but not plastic moments due to buckling, and slender sections buckle before yield. The document provides limiting width-to-thickness ratios for each class and works through numerical examples to classify I-beams, channels, and angles.

1. Sanjivani Rural Education Society's
Sanjivani College of Engineering, Kopargaon 423603.
-Department of Civil Engineering-
By
Mr. Sudhir B. Gayake (Assistant Professor)
Mail Id- gayakesudhircivil@sanjivani.org.in

2. Classification of Cross-Section ( Cl.No. 3.7 Pg.No.17 IS800:2007)-
§ Plate elements of a cross section may buckle locally due to compressive
stresses. The local buckling can be avoided before the limit state is achieved
by limiting the width to thickness ratio of each element of a cross-section
subjected to compression due to axial force, moment or shear.
§ In plastic analysis , the member shall be capable of forming plastic hinges
with sufficient rotation capacity (ductility) without local buckling to
redistribute bending moment before failure mechanism occurs.
§ In elastic analysis , the member shall be capable of developing yield stress.
Prof. Sudhir B. Gayake, SCOE Kopargaon

3. Prof. Sudhir B. Gayake, SCOE Kopargaon
Four Classes of Cross-Section ( Cl.No. 3.7. Pg.No.17 IS800:2007)-
§ Class 1-Plastic  Cross sections, which can develop plastic hinges and
have the rotation capacity required for failure of the structure by
formation of a plastic mechanism.
§ Class 2-Compact  Cross sections, which can develop plastic moment of
resistance, but have inadequate plastic hinge rotation capacity for
formation of a plastic mechanism.
§ Class 3-Semi-Compact  Cross sections, in which the extreme fiber in
compression can reach, yield stress, but cannot develop the plastic
moment of resistance, due to local buckling.
§ Class 4-Slender  Cross sections in which the elements buckle locally even
before reaching yield stress. When the width to thickness ratio greater
than Class 3 comes under this category.
(When different elements of a cross-section fall under different classes, the section
shall be classified as governed by the most critical element.)

4. Prof. Sudhir B. Gayake, SCOE Kopargaon
Dimensions of the Sections ( Fig No.2 Pg.No.19 IS800:2007)-
bi= internal element
be= external element

5. Prof. Sudhir B. Gayake, SCOE Kopargaon
Limiting Width to Thickness Ratio ( Table No.2 Pg.No.18 IS800:2007)-

6. Prof. Sudhir B. Gayake, SCOE Kopargaon
Neumerical Example-
§ Classify the following section using Fy=250MPa.
1) ISHB 400@77.4kg/m.
2) ISMC 300@35.8kg/m.
3) ISA 150X150X12@ 27.2kg/m.
Solution:
1) ISHB 400@77.4kg/m.
Using steel table writing properties of sections;
h= 400 , bf=250mm , tf=12.7 , tw=9.1mm , r1=14mm ;
h1=d= h-2(tf+r1)=400-2(12.7+14)= 346.40mm
ε= (√250/Fy)= 1
b=(bf /2)= (250/2)=125mm
Outstanding element of compression flange=(b/tf )=
= (125/12.7)
= 9.4ε<9.84ε<10.5ε (Flange is compact)
Web of I section(NA at mid depth)= (d/tw )= (346.40/9.1)
= 38.065ε<84ε( web is plastic)
Therefore the section is compact section

7. Prof. Sudhir B. Gayake, SCOE Kopargaon
2) ISMC 300@35.8kg/m.
Using steel table writing properties of sections;
h= 300 , bf=90mm , tf=13.6mm , tw=7.6mm , r1=13mm ;
h1=d= h-2(tf+r1)=300-2(13.6+13)= 246.8mm
ε= (√250/Fy)= 1
b=bf =90=90mm
Outstanding element of compression flange=(b/tf )=
= (90/13.6)
= 6.61ε<9.4ε (Flange is plastic)
Web of section(NA at mid depth)= (d/tw )= (246.8/7.6)
= 32.47ε<42ε( web is plastic)
Therefore the section is plastic.

8. Prof. Sudhir B. Gayake, SCOE Kopargaon
3) ISA 150X150X12@ 27.2kg/m.
Using steel table writing properties of sections;
d=150mm , b=150mm , t=12mm
ε= (√250/Fy)= 1
Leg of the angle
= (b/t)= (150/12)= 10.5ε<12.5ε<15.7ε
= (d/t)= (150/12)= 10.5ε<12.5ε<15.7ε
= (b+d)/(t)= (300/12)= 25ε=25ε
The angle section is semi-compact.