Random Strength Parameters of Steel Corrugated Webs and Their Influence on the Resistance of Sin Plate Girders

K e y w o r d s : Corrugated web; Coefficients of variation; Normal distribution. 3/2018 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T 65 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T The Si les ian Univers i ty o f Technology No. 3/2018 d o i : 1 0 . 2 1 3 0 7 / A C E E 2 0 1 8 0 3 9 W . B a s i ń s k i , Z . K o w a l Based on the investigations, steel yield strength distributions were derived and factors of variation in yield strength VRe=D(Re)/E(Re) were computed, where D(Re) denotes standard deviation of yield strength Re, and E(Re) – the mean value of yield strength Re (notations in accordance with quantile algebra). On the basis of coefficients of variations VRe, partial factors of the yield strength γm were estimated. Because of the shape and thickness of the corrugated web in SIN girders, numerous phenomena occur that are related to web shear resistance. They are reported in studies [1, 2, 5, 6, 7]. In those phenomena, an important role is played by random variation in the material strength. Currently, for the resistance computations of already corrugated webs, according to recommendations [16] the yield strength of 215 MPa, guaranteed by the web manufacturer is assumed. The work hardening in corrugation that changes parameters of steel strength properties is not taken into account. Corrugated sheet bending along the wave is also disregarded (Fig. 1). The span of the SIN girder is limited by the shear resistance of the corrugated web. Shear resistance of the thin-walled web depends on corrugation geometry and yield strength of the steel web. Shear resistance of the web depends also on thickness and depth of the web. Consequently, investigations into steel strength and the scatter of sheet thicknesses were conducted. Yield strength of the corrugated web results from the individual stages of the manufacturing process: 1) in the casting process at the steel mill, the so-called slab, i.e. plate, 220 mm in thickness is produced; 2) the second stage involves rough hot rolling; 3) in the third stage, sheet metal is hot-rolled to the required thicknesses of 2; 2.5, and 3 mm; 4) the fourth stage consists in the cooling of flat sheet metal and winding it onto a coil, the internal diameter of which is 740–760 mm. The consecutive stages include: 5) decoiling 6) cold straightening 7) longitudinal slitting 8) the last stage involves by cold-formed corrugation (Fig. 1). Due to cold process of thin sheet folding, stress state along the wave occurs, which is shown in Fig.1. In European standards [17, 20], the assessment of random strength of the material is based on the method of load coefficients and load bearing capacity coefficients. Partial factor for a material property, also accounting model uncertainties and dimensional variations γM calculated from formula (1) were referred to the characteristic values Rk [20]: where: Rk – characteristic values (5% fractile at a given level of probability), Rd – design values, γm – partial factor of the material property acc. standard [20], γRd – partial factor associated with the uncertainty of the resistance model acc. standard [20]. This study presents the results of statistical investigations into random parameters of strength properties of steel from corrugated webs 2, 2.5 and 3 mm in thickness. Investigations were performed for samples randomly collected from twenty SIN girders that were earlier subjected to testing. Based on the investigations, variation coefficients of yield strength VRe and partial coefficients of yield strength γm were obtained. They were compared with the factors found in the investigations into thin flat sheets [6, 7]. It was proposed that the value of yield strength in the computations of strength of SIN girders should be applied in a uniform manner. 66 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T 3/2018 Figure 1. Concept of sheet metal folding Rd m Rd d k M R R γ γ γ γ = = . (1) ( )( ) Re e ek V , R E R 64 1 1− = , (2) ( ) ( ) e e ek m R D , R E R 04 3 − = γ , (3)