# The 1970s

Cold-formed steel research started in the early 70s at the University of Waterloo with Prof. Lind as one of the leading Canadian researchers.

Lind and Schroff (1971, 1975) dealt with the utilization of cold work of forming in cold-formed steel. The mechanical properties of cold-formed sections can be substantially different from those of flat sheet steel before the cold forming operation. When a piece of flat sheet steel is bent about a radius, the yield strength and tensile strength will increase as a result of this forming operation, but at the same time decreasing the ductility. Lind and Schroff (1971, 1975) used a linear strain-hardening

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M. Pandey et al. (eds), Advances in Engineering Structures, Mechanics & Construction, 39-52.

© 2006 Springer. Printed in the Netherlands.

model and concluded that the increase in yield strength depends only on the inside bend radius ratio, г/t, and the hardening margin (Fu – Fy). Furthermore, to take the cold work strengthening into account, it is only necessary to replace the virgin yield strength by the virgin ultimate strength over a length of 5t in each 90° corner. The researchers concluded that the r/t ratio is not a significant parameter, which was established by examination of test data. Based on the work by Lind and Schroff (1971, 1975), the following simplified equation resulted:

where F’y is the calculated average tensile yield strength of the full cold-formed section of tension or compression members, or the full flange of flexural members. Fy and Fu are the tensile yield and tensile strengths of the virgin steel, respectively. D is the number of 90° corners – if other angles are used, D is the sum of the bend angles divided by 90°. W* is the ratio of the length of the centerline of the full flange of flexural members, or of the entire section of tension or compression members, to the steel thickness, t. Equation 1 was adopted by CSA Standard S136-74 – Cold Formed Steel Structural Members.

Another important work that was undertaken by Lind et al. (1971) and Lind et al. (1976) was investigating the effective width formula used at that time. Their study showed that, based on experimental evidence, the effective width formula for stiffened compression elements can be expressed independent of the flat width ratio, w/t, as follows.

(2)

One can conclude that this expression is simpler and offers greater computational advantages, often eliminating the usual time-consuming iteration process with the existing effective width formula that is a function of w/t.

Venkataramaiah (July 1971) carried out an extensive experimental investigation on different edge stiffeners that can be used with cold-formed sections instead of the typical simple lip stiffener. The objective of his work was to obtain optimum shape and optimum size edge stiffeners for thin-walled compression elements. Another extensive experimental study was carried out by Venkataramaiah (August 1971), Lind and Venkataramaiah (1972) into the behaviour of straight-lipped and L-lipped simply-supported channel sections, eccentrically loaded, thin-walled short columns. It was concluded that the ultimate strength of eccentrically loaded thin-walled short channel columns can be expressed by a simple but general formula involving critical stress.

Schuster (1972) started his research at the University Waterloo by investigating composite steel-deck reinforced concrete slabs, in short, “composite slabs”. In order for a steel deck to achieve the required composite action between the deck and concrete, the deck must be capable of resisting horizontal shear and prevent vertical separation between the concrete and deck. The most common of composite deck products in the marketplace today are decks that utilize a fixed pattern of embossments/indentations rolled into the deck, thus providing a mechanical interlocking device between concrete and deck so that the required composite action can be developed. These types of floor systems are typically used in high rise buildings because of their numerous inherent advantages, one of the major advantages being, the steel deck serves as a form for the concrete during the construction stage and it remains permanently in place as the positive reinforcement. Based on tests, “shear-bond” is the most common mode of failure with composite slab systems. Schuster (1972) developed the following shear-bond expression:

where Vuc is the ultimate calculated transverse shear; b is the unit slab width; d is the effective slab depth; fc is the concrete compressive strength; L is the shear span; p is the percent of steel; K5 and K6 are shear-bond coefficients that have to be obtained from a linear regression analysis of test data.

Lind (1973) investigated the buckling of multiple closely spaced intermediate longitudinal stiffened plate elements. When the stiffeners are spaced so closely that the compression sub-elements have no tendency to buckle individually, overall plate buckling of the entire element can occur. It was assumed in the 1963 edition of the CSA S136 Standard that the entire element was comprised of a rectangular plate having an equivalent steel thickness of ts. While this was a simple design method, Lind (1973) developed a more comprehensive expression by treating the entire stiffened plate element as an orthotropic plate, resulting in the following equation:

where t is the plate thickness; ws is the overall plate element width; Is is the moment the inertia of the full area of the multiple-stiffened element, including the intermediate stiffeners, about its own centroidal axis; p is the perimeter length of the multiple-stiffened element (between edge stiffeners). Equation 4 is valid up to the initial buckling stress, however, it was demonstrated by Sherbourne et al. (1971), Sherbourne et al. (1972) that some post-buckling strength is available. Based on this, Eq. 4 is meant to also apply in the post-buckling range as an approximation, and it was adopted in the 1974 Edition of CSA S136.

In 1974, the Solid Mechanics Division published a special publication, entitled “Design in Cold Formed Steel”, edited by Schuster. Contained in this document are a number of noteworthy papers dealing with the topic of cold-formed steel. Lind (Strength, Deformation and Design of Cold Formed Steel Structures), Lind (Design Procedures for Flexural Members), Lind (Recent Developments in

Cold Formed Steel Design Requirements), Lind (Additional Design Examples); Roorda (On the Buckling Behaviour and Design of Thin-Walled Beams and Columns); Schuster (Composite Steel – Deck Reinforced Concrete Floor Systems), Schuster (Current Design Criteria of Steel-Deck Reinforced Concrete Slabs), Schuster (Proposed Ultimate Strength Design Criteria for Steel-Deck Reinforced Concrete Slabs). Presented in this publication were important papers on cold-formed steel to date, providing structural engineers with the latest design information in cold-formed steel.

Schuster, in collaboration with Lind (1975) published the book, entitled, “Cold Formed Steel Design Manual”, which was the first document of its kind in Canada, containing the 1974 Edition of CSA Standard S136 and its respective Commentary. The purpose of this book was to assist engineers, designers, manufacturers and educators in the design of cold-formed steel structures. Including in the book were numerous design examples, helpful design aids, and many useful tables.

Lind et al. (1975) investigated the economic benefits of the connection safety factor used in the CSA S136-74 Standard and the AISI – 1968 Specification. Using an analysis based on economic principles of equal marginal returns, they concluded that the current safety factors in CSA S136-74 and AISI-1968 are not far from the economic optimum.

Knab and Lind (1975) developed a rational, reliability based design criteria for determining allowable stresses for temporary (2-5 years) cold-formed steel buildings. The method involves comparing differences in reliability levels between permanent and temporary building design criteria. It was shown that allowable stresses can be established that take into account the temporary nature of the buildings and, at the same time, maintain comparable permanent building reliability levels.

Parimi and Lind (1976) the objective of this paper was to explain the new limit states design option in the CSA S136-74 Standard for cold-formed steel design. It was concluded that in the case of cold-formed steel design, the limit states cases could be reconstructed rather easily from the working stress design format. As well, it was found that the stress format was also quite suitable for the limit states design format of cold-formed steel, which allows for ease of calibrating the respective resistance factors. Probabilistic and deterministic approaches were used in the resistance factor calibrations, resulting in identical results.

Schuster (1976) presented a comprehensive overview of the state of the art of composite steel – deck concrete floor systems in the US and Canada, outlining the important inherent attributes of such floor systems in the construction industry. Also presented in the paper is an overview of the latest research findings to-date.

Lind (1978) carried out a study relating to the buckling strength of steel plate assemblies. The analysis is reduced to an eigenvalue problem of an ordinary differential equation that is solved by a Vianello-Stodola procedure, using the tabular numerical approach presented by Newmark for buckling analysis of columns. Two example problems are presented, illustrating the simplistic approach.