Study on the axial compressive ultimate load-carrying capacity of high strength steel tubes with lattice boom

1. Introduction

Due to the strong bearing capacity of high-strength steel tubes, Lattice boom are used on crawler cranes are welded by slender high strength steel tubes. When calculating the bearing capacity of the lattice boom chords, it is calibrated according to the calibration formula of axial compression members in the existing steel structure specification or crane design specification. The stability curves of axial compression members in the current steel structure specification are obtained based on the test and analysis of carbon steel members [1]. Representative steel structure specifications or crane design specifications mainly include: China’s GB 50017-2017 [2] or GB 3811-2008 “Crane Design Specification” [3], Europe’s Eurocode 3 [4], “Load and Resistance Factor Design Specification” of American Institute of Steel Structure [5], Australian steel structure standard AS4100:1998 [6] and Japan's JIS-B8821-2004 “Calculation Standard of Crane Steel Structure” [7], etc. For example, taking the hot-rolled 20Mn2 steel tubes (yield strength ${\sigma }_s=$ 590 MPa), who’s the stability coefficient curves calculated according to the steel structure or crane design specification of the above-mentioned countries are shown in Fig. 1. The stability curve of GB 50017-2003 in China is at a medium level according to the comparison results of various countries' standards, and the bearing capacity of high strength steel has some room for improvement.

More and more scholars pay attention to the ultimate load of high-strength steel members in recent years. Among them, Wang [1] found that the design curve specified in Eurocode 3 and GB 50017-2003 was 18.7 % and 23.2 % lower than the theoretical curve on average. Rasmussen [8] shows that the bearing curve in Eurocode 3 is too conservative. Hancock [9] compared all the test results with the Australian steel structure standard AS4100:1998, Eurocode 3 and the design specification of load and resistance coefficient of American Institute of Steel Structure. Yang’s [10, 11] results show that the more important where elastic local buckling and local buckling are for the more slender part, the effect of low strain hardening does not seem to be significant, and Yang improved the simple scheme of design capacity. Ye [12] put forward design suggestions specific to G550 steel. Ban Huiyong et al. [13-15] and Shi Gang et al. [16, 17] tested and analyzed the overall buckling behavior of a series of 460 MPa, 960 MPa high-strength steel I-shaped and square specimens. The results showed that the stability curve in the current design specification underestimated the buckling bearing capacity of high-strength steel.

At present, the rolling process and processing process of high-strength steel tubes have been greatly improved compared with the formulation of the stability curve. It is necessary to study the performance of high-strength steel tubes, and realize the further lightweight design of lattice boom.

Fig. 1Comparison of stability curves of hot rolled 20Mn2 steel tubes in various steel structure specifications

2. Specimens and test method

3. Test results

The damage forms of specimens made of 20Mn2 and S890 are permanent bending plastic deformation in the middle. The samples of this test are all hot-rolled hollow circular tubes. The bearing capacity of the steel tubes can be obtained based on the check formula of axial compression members in GB50017. The calculation formula is as follows:

where, $N$ is the pressure, $A$ is the cross-sectional area and ${\sigma }_s$ is the yield strength of the material. $\phi$ is the stability coefficient. The stability coefficient of hot-rolled hollow circular pipe should be determined according to the stability coefficient of type-a section axial compression member in GB50017. The calculation formula of stability coefficient $\phi$ is:

When ${\lambda }_n\le 0.215$:

when ${\lambda }_n\le 0.215$:

where ${\alpha }_1$, ${\alpha }_2$, ${\alpha }_3$ are coefficients, ${\alpha }_1$ = 0.41, ${\alpha }_2$ = 0.986, ${\alpha }_3$ = 0.152, and ${\lambda }_n$ are normalized slenderness ratio:

where $\lambda$ is the slenderness ratio and $E$ is the elastic modulus.

The test damage load of the 20Mn2 steel tubes and the bearing capacity calculated according to the specification are summarized and compared in Table 3. The test damage load of the S890 steel tubes and the bearing capacity calculated according to the specification are summarized and compared as shown in Table 4.

4. Coefficient fitting of stability coefficient calculation formula

The discrete test data cannot be directly used in engineering practice. Therefore, the calculation formula of stability coefficient in GB50017 is used for coefficient fitting, and finally, the stability performance calculation formula suitable for high strength steel tubes is obtained. Since the normalized slenderness ratio ${\lambda }_n$ of the test steel tubes are greater than 0.215, the form of the Eq. (3) is used for fitting.

In order to make the obtained corrected coefficient safe and reliable, all the lowest points are used as fitting data, and finally, the corrected coefficient ${\alpha }_2^{\text{'}}=$ 0.9718, ${\alpha }_3^{\text{'}}=$ 0.0912 is determined. The comparison between the fitted curve, Euler curve and the stability curve of type-a members in GB50017 is shown in Fig. 2. In Fig. 2, when the normalized slenderness ratio is ${\lambda }_n\in \left[\mathrm{0.75,1.75}\right]$, the fitting curve is obviously higher than the standard curve, that is, when the normalized slenderness ratio is ${\lambda }_n\in [\mathrm{0.75,1}.75]$, the stability coefficient $\varphi$ obtained from the test is larger than the standard stability coefficient. It can be concluded that the test data is effective for the normalized slenderness ratio ${\lambda }_n\in \left[\mathrm{0.75,1.75}\right]$, so the calculation formula of the standard stability coefficient is modified in this interval. Within the range of normalized slenderness ratio ${\lambda }_n\in \left[\mathrm{0.75,1.75}\right]$, the comparison of stability coefficient between type-a stability curve in GB50017 and test fitting curve is shown in Table 5.

Fig. 2Comparison between stability curve of test data fitting and stability curve in GB50017

According to Table 5, when the normalized slenderness ratio is ${\lambda }_n\in \left[\mathrm{0.75,1.25}\right]$, the test stability curve is nearly 9.5 % higher than the type-a stability curve in GB50017; When the normalized slenderness ratio is ${\lambda }_n\in [\text{1.25, 1.5]}$, the test stability curve is also more than 6.7 % higher than type-a stability curve in GB50017. It can be concluded that the modified stability coefficient calculation formula shows that there is at least 6 % improvement space in the lightweight design of the lattice boom, which is of great significance to improve the lifting performance determined by the chord of the crane lattice boom and realize the lightweight of the boom.

5. Conclusions

In this paper, through the axial loading test of high-strength steel tubes commonly used in crane lattice boom, the actual stable bearing capacity of high-strength steel tubes is obtained. The test damage load of the steel tubes is compared with the bearing capacity calculated according to GB50017 and Eurocode 3. The results show that the current steel structure specification underestimates the bearing capacity of high-strength steel tubes. Therefore, curve fitting is performed in the form of the stability coefficient calculation formula in GB50017, and the stability coefficient calculation formula suitable for high-strength steel tubes is obtained. When the normalized slenderness ratio of the lattice boom chord is in the range of 0.75-1.5, and the test stability curve is higher than GB50017 for 6.7 % at least.