Tài liệu tham khảo giáo trình nhôm trong thiết kế xây dựng bằng tiếng anh - Chương 10 Calculation of section properties SUMMARY OF SECTION PROPERTIES USED The formulae in Chapters 8 and 9 involve the use of certain geometric properties of the cross-section. In steel design these are easy to find, since the sections used are normally in the form of standard rollings with quoted properties. In aluminium, the position is different because of the use of non-standard extruded profiles, often of complex shape | CHAPTER 10 Calculation of section properties SUMMARY OF SECTION PROPERTIES USED The formulae in Chapters 8 and 9 involve the use of certain geometric properties of the cross-section. In steel design these are easy to find since the sections used are normally in the form of standard rollings with quoted properties. In aluminium the position is different because of the use of non-standard extruded profiles often of complex shape. A further problem is the need to know torsional properties when considering lateral-torsional LT and torsional buckling. The following quantities arise a Flexural S Plastic section modulus I Second moment of area inertia Z Elastic section modulus r Radius of gyration. b Torsional 3 St Venant torsion factor Ip Polar second moment of area polar inertia H Warping factor px Special LT buckling factor. The phrase second moment of area gives a precise definition of I and Ip. However for the sake of brevity we refer to these as inertia and polar inertia . PLASTIC SECTION MODULUS Symmetrical bending The plastic modulus S relates to moment resistance based on a plastic pattern of stress with assumed rectangular stress blocks. It is relevant to fully compact sections equation . Firstly we consider sections on which the moment M acts about an axis of symmetry ss Figure a which will in this case also be the neutral Copyright 1999 by Taylor Francis Group. All Rights Reserved. Figure Symmetric plastic bending. axis. The half of the section above ss is divided into convenient elements and S then calculated from the expression S 2 AEyE where AE area of element and yE distance of element s centroid E above ss. The summation is made for the elements lying above ss only . just for the compression material C . Figure b shows another case of symmetrical bending in which M acts about an axis perpendicular to the axis of symmetry. The neutral axis xx will now be the equal-area axis not necessarily going through the .
