Table 1. Comparison of hot rolled and cold rolled sections [Hankock, g.m.(2001)].
Cold formed steel structures are structural products that are made by forming plane sheets of steel at an ambient temperature into different shapes that can be used to satisfy structural and functional requirements. In recent years, the demand for high strength materials for wide range of structural applications has been instrumental for more developments in cold-formed steel sections as compared to the hot rolled steel sections. Therefore, the understanding of cold formed steel performance becomes an important issue to be studied. This paper holds three works. First, it reviews an introduction on cold formed steel structures. Second, it summarizes special design criteria and local buckling and post buckling strength of cold formed steel constructions. Finally, it offers a conclusion on the need for innovative sectional profiles over the conventional sections for cold formed steel.
In steel structures, two primary types of structural steel members are: Hot-Rolled steel members and Cold-formed steel members
The hot-rolled steel members are formed at elevated temperature, whereas the cold-formed steel members are formed at room temperature. Until recently, the hot-rolled steel members have been recognized as the most popularly and widely used steel group. But because of its several advantages over the hot-rolled steel sections, the use of cold-formed high strength steel structural members has rapidly increased lately. However, the structural behavior of this light gauge high strength steel members characterized by various buckling modes such as local buckling, distortional buckling, flexural torsional buckling is not yet fully understood [Chen J. and Young B, 2006], hence there is lot of scope for future research in this area. Open cold formed steel sections such as C,Z ,hat sections are commonly used because of their simple forming and easy connections, but they suffer from certain buckling modes due to their mono symmetric or point symmetric nature, high plate slenderness, eccentricity of shear center to centroid and low torsional rigidity [M. Meiyalagan et.al 2010]. It is therefore important that this buckling modes are either delayed or eliminated completely to increase the ultimate load carrying capacity of cold-formed steel members
The use of cold formed steel is increasing rapidly around the world. The main use of cold formed steel is found in the construction of residential buildings and other low rise buildings such as commercial, industrial and institutional buildings. Some of the commonly used cold formed section types in the above application include channel(C) section, Z-section, angel section , hat section, and tubular section such as rectangular hollow section and square hollow section [Hankock, g.m.(2001)].
These sections are commonly used, but they are more susceptible to structural unstability due to their geometrical shapes [Schafer et.al, (2006)]. The characteristics due to point symmetric nature of these sections are normally encountered in doubly symmetric sections such as I sections or tubular sections.
Therefore combining the advantages of Hot-rolled Isections( better stability) and conventional cold formed steel sections such as C and Z sections(high strength to weight ratio) can produce an improved cold formed steel section that can be made, using modern technologies available in the cold formed steel industries. Complex structural shapes may now be formed in two or more parts and then assembled to a single shape. This may have the advantage of combining the different material qualities and thickness into single component, however the use of higher strength steel is inevitably accompanied by reduction in thickness of the section and may result in more slender section which could be structurally unstable [Nayrayanan et.al, (2003)].
Structural behavior of the commonly used cold-formed steel sections has been well researched in the past However, only limited research has been carried out to investigate the structural performance of new shapes of cold formed steel sections. Therefore there is an urgent need in the cold formed steel industries to look beyond the conventional cold formed steel sections and generate new innovative cold formed steel beam sections which are structurally very efficient especially from buckling consideration and economical as well. Sarvade S.M., Sarvade M.M (2013).
The main drawback of the conventional hot-rolled steel sections is that they are available in certain standard predefined sectional shapes. When such sections are used in cases where only light loads are encountered, these sections are generally under-stressed (most of its sectional capacity is not mobilized). This not only leaves most of the section capacity un-utilized, but also adds to the selfweight of the structure which requires heavy foundations, which in turn increases the overall cost of the facility.
Hence there is an urgent need to come up with new innovative sections in which the sectional capacity is fully utilized.
This need can be catered by replacing the conventional hot rolled steel sections with light gauge cold formed steel sections McDonald, M., Heiyantuduwa, M.A., Rhodes, J. (2008).
Some of the main advantages of cold rolled sections, as compared with their hot-rolled counterparts are as follows:
It is possible to distribute the material away from the neutral axis in order to enhance the load carrying capacity (particularly in beams). There is almost no limit to the type of cross section that can be formed. In Table 1, hot rolled and cold formed channel section properties having the same area of cross section are shown. It is obvious that thinner the section walls, the larger will be the corresponding moment of inertia values (I xx and I yy ) and hence capable of resisting greater bending moments. The consequent reduction in the weight of steel in general applications produces economies both in steel costs as well as in the costs of handling transportation and erection. This, indeed, is one of the main reasons for the popularity and the consequent growth in the use of cold rolled steel. Also cold form steel is protected against corrosion by proper galvanizing or powder coating in the factory itself.
Table 1. Comparison of hot rolled and cold rolled sections [Hankock, g.m.(2001)].
Compared with other materials such as timber and concrete, the following qualities can be realized for coldformed steel structural members.
In general, two manufacturing methods are used to produce various shapes of cold formed steel sections (Figures 1 and 2), and they are cold roll-forming and press brake operations.
Figure 1. Cold Roll-Forming Processes [Hankock, g.m.(2001)].
Figure 2. Press Breaking [Hankock, g.m.(2001)].
The cold roll-forming process consists of feeding a continuous steel strip through a series of opposing rolls (Figure 1(a)) to deform the steel plastically to form the desired shapes. The process involved in cold-forming for a Zsection is illustrated in Figure 1(b). A simple section may be produced by as few as six pairs of rolls, but a complex section may require as many as 15 sets of rolls (Yu, 2000). This method is usually used to produce cold-formed steel sections where a large quantity of a given shape is required.
However, a significant limitation of this method is the time taken to change rolls for different size sections. Consequently, adjustable rolls are often used which allow a rapid change to a different section width or depth. From structural point of view, roll-forming may produce a different set of residual stresses in the section and hence the section strength may be different in the case where buckling and yielding interact.
The equipment used in the press brake operation essentially consists of a moving top beam and a stationary bottom bed that produce one complete fold at a time along the full length of the section (Figure 2). This method is normally used for low volume production where a variety of shapes are required and the roll-forming tooling costs cannot be justified. However, this method has a limitation that it is difficult to produce in continuous lengths exceeding approximately 5 meters.
The generally used connection types in the cold-formed steel construction include; welds, bolts, screws, rivets and other special devices such as clinching, nailing and structural adhesives (Figure 3).
Figure 3. Generally Used Cold-formed Steel Fasteners [Hankock, g.m.(2001)].
Due to the comparative low thickness of the material, connection technology plays an important role in the development of structures using cold-formed steel members. Although the above mentioned conventional methods of connections are available and used in coldformed steel constructions, they are practically less appropriate for thin-walled member connections in terms of cost, quality and construction efficiency The self-piercing riveting introduced commercially by HENROB is a recently discovered connection type with many advantages compared with other conventional methods used in coldformed steel connections (Hankock, G.M. (2001), Figure 4). Therefore, the choice of connection type is an important decision in cold-formed steel manufacturing, because it affects the combinations of cost, quality and construction efficiency of the whole project Bayan A, Sariffuddin S., Hanim O (2011).
Figure 4. Cross section of a Self-piercing Rivet (Voelkner, 2000)
Cold-formed steel shapes can broadly be classified into two groups: individual structural frame members, and panels and decks. The former includes sections shapes such as, I, L, C and Z, which are commonly used in engineering practices of cold formed steel construction. However with the improvement of industrial cold forming processes, more complex section types are possible (Figure 5) and offer competitive solutions to achieve structural weight reduction and having higher carrying capacity. There are wide range of applications for these section types: Typical Z or C sections are used as purlins and bracings in roof and wall systems in residential, commercial and industrial buildings and circular, square or rectangular hollow sections are used for structural members such as chords and webs in plane and space trusses. The panels and decks are used mostly for roof decks, floor decks, and wall panels.
Figure 5. Various Shapes of Cold-formed Steel Sections [Hankock, g.m.(2001)].
A set of unique problems pertaining to cold-formed steel design has evolved mainly due to the thinner materials and cold-forming process used in the production of cold formed sections. Hence, unlike the usually thicker conventional hot-rolled steel members, the design of coldformed steel members must be given special considerations during the design phase of such members.
Individual elements forming cold-formed steel members are usually thin with respect to their width. Therefore, they are likely to buckle at a lower stress than yield point when they are subjected to compression, bending, shear or bearing forces. However, unlike one-dimensional structural elements such as columns, stiffened compression elements will not collapse when the buckling stress is reached, but they often continue to carry increasing loads by means of redistribution of stresses. The ability of these locally buckled elements to carry further load, known as post buckling strength, and this phenomenon in the design contributes in achieving the desired economical solution. Figure 6. Illustrates a case of local buckling of thin-walled box. The applied sagging bending moment induces longitudinal compressive stresses in the top flange plate, causing local buckling in the top flange.
Figure 6. Local Buckling of Compression Flanges
The individual plate components forming cold-formed steel sections are normally thin compared with their width. This may lead to local buckling of plate elements in coldformed sections before yield stress is reached. Local buckling in plate elements involves flexural displacements, with the line junctions between plate elements remaining straight (Figure 7). The local buckling failure in thin walled sections can occur under compression, bending or shear loading. Previous researchers C. Yu, B.W Schafer (2006) , C. Yu, B.W Schafer (2002) have extensively investigated and summarized the elastic critical stress for local buckling. The elastic critical stress for local buckling (f cr ) of a plate element is determined using Bryan's equation based on small deflection theory; Bryan's differential equation has been developed based on a rectangular plate of width w, length a and thickness t, with in plane stress fx acting on the plate as shown in Figure 7.
Figure 7. Rectangular Plate Subjected to Compression Stress (Hancock, 2001)
The elastic critical local buckling stress (fcr ) is a function of the elastic material properties (E,V), plate slenderness ratio w/t, and the restraint conditions along the longitudinal boundaries represented by the value k, where k, E are called as plate local buckling coefficient, elastic modulus and the Poisson's ratio, respectively. For example, a steel plate with simply supported edges on all four sides and subjected to uniform compression will buckle at a half wavelength equal to the plate width (w) with a plate buckling coefficient (k) of 4.0. C. Yu, B.W Schafer (2002). A slender section will buckle locally before the squash load (P y ) or the yield moment (My ) is reached. If the elastic critical buckling stress (fcr) exceeds the yield stress fy , the compression element will buckle in the inelastic range (Yu, 2000). Figure 8 shows local buckling in Z- section. A summary of local buckling coefficients, k with corresponding half wavelengths of the local buckles for a long rectangular plate subjected to different types of stress (compression, shear, or bending) and boundary conditions (simply supported, fixed, or free edge) are given in Table 2.
Table 2. Local Buckling Coefficient (Hancock, g.m 2001)
Although local buckling occurs at a stress level lower than the yield stress of steel, it does not necessarily represent the collapse of the members. In the case of considerably low (b/t) ratios, failure is governed by post-buckling strength which is generally much higher than local buckling strength. For example, a plate subjected to uniform compressive strain between rigid frictionless platens will deform after buckling, and will redistribute the longitudinal membrane stresses from uniform compression to those shown in Figure 8. Although the stiffness is reduced to 40.8% of the initial linear elastic value for a square stiffened element and to 44.4% for a square unstiffened element, the plate element will continue to carry load (Hancock, 2001). The theoretical analysis of post buckling and failure of plates is extremely difficult, and generally requires a sophisticated computer analysis to achieve an accurate solution (Hancock, 2001).
Figure 8. Local Buckling in Z-section [Hankock, g.m. (2001)
The structural use of cold formed steel in construction industry is continuously growing at a rapid pace across the world exceeding that for hot rolled steel structural members. The use of thinner sections and high strength steels leads to design problems for structural engineers, which may not normally be encountered in the routine structural steel design using hot rolled sections. This paper has concentrated on the importance of either delaying or completely eliminating the buckling modes so as to increase the ultimate load carrying capacity of coldformed steel members. Based on this review it was concluded that developing new innovative sections with appropriate stiffening arrangements and hollow compression flanges are new areas of study.
Following are some suggestions for future research.