Shear Area Calculation

For rolled I and H sections the shear area is calculated as follows:

• Load Parallel to Web: A_v,z = max(A - 2*b*t_f + (t_w + 2 r)*t_f, η*t_w*h_w) (as it is defined in EC3-Part 1.1 §6.2.6(3))

NOTE: The η factor in the above equation is defined in National Annex. However, the value of 1.2 is recommended for steel grades up to and including S460 according to EC3-Part 1.5 §5.1(2) Note 2.

• Load Parallel to Flanges: A_v,y = 2*b*t_f (conservative assumption)

Section Classification

Four classes of cross-sections are defined, as follows (EC3-Part 1.1 §5.5.2(1)):

• Class 1: cross-sections are those which can form a plastic hinge with the rotation capacity required from plastic analysis without reduction of the resistance.
• Class 2: cross-sections arc those which can develop their plastic moment resistance, but have limited rotation capacity because of local buckling.
• Class 3: cross-sections are those in which the stress in the extreme compression fibre of the steel member assuming an elastic distribution of stresses can reach the yield strength, but local buckling is liable to prevent deve lopment of the plastic moment resistance.
• Class 4: cross-sections are those in which local buckling will occur before the attainment of yield stress in one or more parts of the cross-section.

The classification of a cross-section depends on the width to thickness ratio of the parts subject to compression. Compression parts include every part of a cross-section which is either totally or partially in compression under the load combination considered. The various compression parts in a cross-section (such as a web or flange) can, in general, be in different classes. A cross-section is classified according to the highest (least favourable) class of its compression parts. Exceptions are specified in §6.2.1(10) and §6.2.2.4(1).

The following table defines the maximum width-to-thickness ration for both internal parts and outstand flanges in compression.

Maximum width-to-thickness ratios for compression parts
Class	Internal compression parts (Web)		Outstand flanges
	Subject to Compression	Subject to Bending	Subject to Compression
1	cw / tw ≤ 33ε	cw / tw ≤ 72ε	cf / tf ≤ 9ε
2	cw / tw ≤ 38ε	cw / tw ≤ 83ε	cf / tf ≤ 10ε
3	cw / tw ≤ 42ε	cw / tw ≤ 124ε	cf / tf ≤ 14ε
	cw = h - 2*(tf + r)		cf = 0.5*(b - tw) - r

ε = (235 / fy)0.5, where fy in MPa	fy	235	275	355	420	460
	ε	1.0000	0.9244	0.8136	0.7480	0.7148

References

1. EN 1993-1-1 (2005). Eurocode 3: Design of steel structures. Part 1.1: General Rules and Rules for Buildings. CEN, European Committee for Standardization, Brussels, Belgium.
2. EN 1993-1-1 (2005). Eurocode 3: Design of steel structures. Part 1.5: General rules - Plated structural elements. CEN, European Committee for Standardization, Brussels, Belgium.
3. Anwar N. and Najam F.A. (2017). Structural Cross Sections (Analysis and Design), Butterworth-Heinemann, ISBN 978-0-12-804443-8.