Keywords: non-linear, stress, strain, high performance steel, power function, yield, steel, girder.

Cold bending is commonly used for fabricating curved steel plate girders. In this process, mechanical loads are applied separately to the top and bottom flanges of the steel girder at different intervals along their length and the required curved shape of the girder develops as a series of short straight segments based on the permanently deflected shape of each segment.

The efficiency of the cold bending operation relies on accurate prediction of the bending loads, induced deformations and segment length as a function of the structural steel girder shape, geometry and properties in the post-yield range. This paper derives closed form solutions that relate bending loads to induced residual deformations and curvatures based on non-linear analyses of symmetric steel plate girders bent about their weak axis using concentrated forces. The non-linear solution is intended for HPS 485W, a new grade of high performance steel with mechanical properties that surpass ASTM A709 requirements.

Closed form expressions for bending loads and induced deformations are calculated based on engineering mechanics principles. Loads are calculated from elasto-plastic stress distributions and equilibrium between moments due to externally applied loads and internal moments developed by flexural stresses. Induced residual deformations are determined from integration of curvatures approximated by the flexural moment to stiffness ratio in the elastic range and strain variation in the inelastic range.

As the analysis is non-linear, it relies on the post-yield characteristics and mechanical properties of high performance steel. In conventional steel, strain curves are idealized as elastic-perfectly plastic. In high performance steel, the non-zero hardening stiffness in the yield plateau region needs to be incorporated in the idealization of the stress-strain curve. For this purpose, a power function was used to replicate the stress-strain properties of HPS 485W obtained from comprehensive tests conducted by the Federal Highway Administration (FHWA). Closed form expressions defining the relationship between loads and residual deformation were developed using these constitutive relations. A geometric procedure that identifies the idealized qualitative response of the horizontal curve that develops based on the deflected shape of each segment due to plastic hinging is also presented.

A simple procedure that allows prediction of the bending load and segment length as a function of the induced curvature and strain is provided and illustrated by a numerical example. This paper facilitates standardization of the cold bending process for HPS 485W steel. The analysis can be readily extended to other high performance steels with similar stress-strain characteristics but different yield stress values.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £145 +P&P)