Residual Stresses in HSS Section
Residual stresses play an important role in the behaviour of steel structures and are normally induced in the manufacturing process. They typically result in a reduction of the flexural rigidity of slender members, and consequently, a lower buckling load may result (Weng, 1984). Although residual stresses are self-equilibrating, the cross sectional effective moment of inertia will be changed when parts of the section reach their yielding strength prior to other parts. An extensive experimental investigation of the residual stresses of hollow structural cold formed steel shapes was performed (Davison and Birkemoe, 1983 and Weng and Pekoz, 1990). The magnitudes of the measured residual stresses were found to vary, approximately, from 25 to 70 percent of the yield strength, depending on the manufacturing process.
Short columns are typically used in lieu of coupon tests to provide the average compressive stress-strain curves (Bjorhovde and Birkemoe, 1979). This type of tests demonstrates the overall column performance at very low slenderness ratio, in the absence of overall instability. The capacity of these columns is achieved when all fibres reach the yield stress and the corresponding load is defined as the yield load. Because of residual stresses, the short columns do not typically show a distinct yield point, but rather a gradual transition from the linear elastic behaviour to the fully plastic plateau, as a result of the gradual yielding. The magnitude of residual stresses Frs can then be estimated by evaluating the difference between the proportional limit stress and the maximum stress levels. In this study, experimental short column tests have also been conducted by the authors on 175 mm long HSS columns of the same HSS sections used for the slender columns and the average load-strain curve is shown in Fig. 3. The behaviour shows a proportional limit load of 249 kN and a yield load of 410 kN. These two levels of load indicate that the magnitude of residual stress is in the order of 40 percent of the yield strength. In the proposed model, the through-thickness residual stress distribution will be idealized as shown in the schematic drawing in Fig. 3, as suggested by (Davison and Birkemoe, 1983) and by (Chan et al., 1991), where Frs equals to the minimum value specified in literature as 0.25 Fy.
In order to simulate the residual stress pattern, shown in Fig. 3, the wall thickness was first divided into three layers, as shown in Fig. 4(a). A pre-strain compressive value £rs of (-0.25 ey) was given to the inner third, while a tensile value of (+0.25 ey) was given to the outer third, where Ey is the strain at yield, based on Fig. 1(b). The middle third was divided into two equal halves. The inner half was given a uniform value of (-0.125 ey), while the outer half was given a uniform value of (+0.125 ey), as shown in Fig. 4(a).