Experimental research on behavior of Q420 dual-angle steel with cruciform section under dynamic compression

2.1. Test specimens

Due to the field investigation results of latticed transmission towers and limited experimental conditions, cruciform sectioned dual-angle steel with specifications of 2L125×8 (two L125×8 angles combined with a cruciform cross-section), 2L140×12, and 2L160×10 were selected as tested specimens. The clearance between each component was 14 mm and the slenderness ratios of core members were set as 30, 40, 50, and 60. Test specimens were fabricated from Q420 high strength steel with a Young’s modulus of 200 GPa. The specimens were divided into 12 groups, with 3 members in each group, as summarized in Table 1.

The cruciform welded plate, with thickness of 14 mm, was used as interconnector between sub-members. For angle steel with limb width of 125 mm and 140 mm, the cruciform plate and each angle limb was connected with 3M20 bolts, and 4M20 bolts were adopted for that with limb width of 160 mm. The detail dimensions of different types of cruciform plates are shown in Fig. 3. Grade 8.8 high strength bolts were employed and tightened to a specified torques by dynamometric wrench, just as the way in practical engineering.

Fig. 3Two types of cruciform plates

a) Type 1 plate with 3 bolts in each face

b) Type 2 plate with 4 bolts in each face

Meanwhile, tensile coupon tests were carried out with standard specimens extracted from test members to obtain the material properties. As there is no obvious yield platform, the static 0.2 % proof stress was taken as yield stress. The results showed that the steel plates with thicknesses of 8 mm, 10 mm, and 12 mm had yield stresses of 517 MPa, 505 MPa, and 472 MPa, respectively.

2.2. Test set-up and procedure

As illustrated in Fig. 4(a), the dynamic compression was applied horizontally as the effect of self-weight was negligible. Test sections were connected to common sections and loading sections with encased angles, gusset plates, and a series of bolts. Two 6000 kN spherical hinges, with outer diameter of 450 mm and total height of 120 mm, were placed between loading sections and loading equipment to simulate pin-connections as designed. The common sections consisted of 2L160×14 with the corresponding slenderness ratios of the test sections, and loading sections were also composed of 2L160×14 with a length of 500 mm. The loading sections were welded to the 40 mm-thick end plates by partial penetration welds. The square end plates were 500 mm wide to confirm full contact with spherical hinges and enough local rigidity.

The lateral brace was designed with the bearing capacity no more than 2.5 % of that of core member, and single angle of L75×10 was selected. The lateral braces were connected to the splices of test section and common section horizontally and vertically, using 2M20 grade 8.8 bolts. To simulate boundary conditions in real latticed towers, the other ends of the lateral braces were connected to the flange plates of fixed H-shape beams with 2M20 bolts. A 3000 kN hydraulic jack was employed to apply dynamic loadings at one side, and the other side was set contact with the reaction wall.

Fig. 4Experimental set-up of test specimens

a) Diagram of experimental set-up

b) Field test set-up

c) Spherical hinge

The compression tests were conducted by applying multi-stage loading, and each load step was held for 1-2 minutes. Before the tests were conducted, a theodolite was used to ensure test specimens were loaded in the center, and electrical resistance strain gauges and displacement meters were placed at the typical positions of test specimens. The strain gauge dimension was 10.0 mm × 4.0 mm, with maximum ultimate strain value of 2-3 %.

As depicted in Fig. 5, twelve strain gauges were mounted at half the length of the compound members, with six in each angle, and four gauges were placed at a quarter length from each end. Four displacement meters, with measuring range of ±100 mm, were arranged at four corners of end plate in the loading side to measure the axial shortening during loading process. At the regular interval, a data acquisition system, named DH3816, was adopted to record the readings of strain gauges and displacement meters.

Fig. 5Arrangement of strain gauges in core member

2.3. Test results

2.3.2. Load-bearing capacity

Fig. 7 describes the strain development in the midsection of a typical specimen (2L125×8 – $\lambda =$ 40)$.$ During the loading process, the strains in different angle tips showed great differences. The strain of the angle back in each sub-member developed consistently, but the internal forces of two components were unequal. It was assumed that additional moment was produced due to the relative movements between sub members, and the moment resulted in uneven forces in different sub-members.

As for dual-angle cruciform sections, the angle back of each component was relatively close to the neutral axis, so sectional stress caused by additional moment at this positions could be neglected. The internal force of each angle was estimated approximately due to the strain readings in angle backs, could be expressed by Eq. (1) and (2):

1

$N_1=\left(\frac{{\epsilon }_1+{\epsilon }_2}{2}\right)\cdot E\cdot A_1,$

2

$N_2=\left(\frac{{\epsilon }_1^{\text{'}}+{\epsilon }_2^{\text{'}}}{2}\right)\cdot E\cdot A_2.$

Fig. 6Failure modes of test specimens

a) Overall buckling

b) Local buckling

Fig. 7Strain development in the mid-section (2L125×8 – λ= 40)

a) Angle back

b) Angle tip

Table 2 listed the axial forces calculated due to the measuring strains recorded at design loads. It can be seen from the table that the value of $N_1/N_2$ ranged from 1.04 to 1.31, with the mean value of 1.157 and standard deviation (SD) value of 0.09. The similar results were also obtained from prototype tower tests, and it should be considered in later design procedure.

Table 2Internal forces of different angle limbs

Specification	$\lambda$	$({\epsilon }_1+{\epsilon }_2)/2$	$({\epsilon }_1^{\text{'}}+{\epsilon }_2^{\text{'}})/2$	$N_1/kN$	$N_2/kN$	$N_2/N_1$
2L125×8	30	1976	2598	780.5	1026.2	1.31
	40	1876	2338	740.9	923.7	1.25
	50	1780	2223	703.1	878.1	1.25
	60	1746	1975	689.6	780.0	1.13
2L140×12	30	2523	2651	1640.3	1723.4	1.05
	40	2212	2510	1437.9	1631.5	1.13
	50	1909	2366	1241.4	1538.3	1.24
	60	1727	2073	1122.9	1347.8	1.20
2L160×10	30	2415	2672	1521.5	1683.4	1.10
	40	2108	2195	1328.4	1382.9	1.04
	50	1770	1966	1115.1	1238.6	1.11
	60	1569	1672	988.2	1052.8	1.07
Mean value, $N_m$						1.157
SD value, $S_N$						0.09

4.1. Cruciform plate spacing

For the dual-angle cruciform section, Chinese standard [13] requires that under axial compression, the filled plate spacing of compound members does not exceed 40$i$, where $i$ is the gyration radius of sub-member, and the plate quantities between every two lateral bracing points should not be less than two. While for BS standard [14], the spacing is specified to be no more than 70$i$. ASCE [15] stipulates that the slenderness ratio between two filled plates does not exceed three quarters of that of the single angle. Table 3 lists the maximum filled-plate spacing of different member sizes, and comparisons with different standards. Compared with other design standards, the spacing requirements of filled plates in Chinese standard are more stringent, and the plate spacing of test members can satisfy the provisions. According to the investigation results of Temple et al. [6], we know that too many filled plates are uneconomical, and have no obvious effect on bearing capacities of compound members.

4.2. Local stability

An equilibrium equation based on the small deflection buckling theory of thin plate under unidirectional uniform compression is shown as Eq. (3). For the angle limb here, it can be assumed as a plate with one side simply supported and other three sides free, the buckling coefficient of it can be taken as $k=$ 0.425. The local buckling stress can be evaluated with Eq. (5), and it is determined by the width-to-thickness ratio ($b/t$):

For compression members, the local buckling cannot happen before overall instability. In order to meet this stipulation, a limited value of width-to-thickness ratio ($b/t$) is presented in GB standard [16], but the method to estimate the reduction of bearing capacity when $b/t$ exceeds its limited value is not given. While in many foreign standards, the estimations of local stability reduction factor $\beta$, are provided in terms of functional expressions of $b/t$ or $w/t$, where $b$ is the nominal width of steel angle, and $w$ is flat width. Table 4 summarizes $\beta$ values of various angle sizes as per different standards, the calculated results of $DL/T$ [13] agree with that of ASCE. For test specimens with dimensions of L125×8 and L160×10, the $w/t$ value exceeds the limited values, and the design strength should be modified by reduction factor.

4.3. Torsional buckling

Under axial compression, the member with biaxial symmetry section generally fails by flexural buckling. For the specimens with dual-angle cruciform section investigated in this paper, the torsional buckling around longitudinal axis may also happen. The equilibrium differential equation due to the tiny torsion deformation at critical state was then established as follows, based on the assumption that the member ends are simply supported:

The equivalent slenderness ratio of torsional buckling ${\lambda }_Z$ can be calculated as follows:

The parameters of steel angle, such as warping coefficient $I_w$, sectional area $A$, torsional inertia moment $I_t$, polar radius of gyration $i_0$, and shear modulus $G$ can be expressed:

Applying these variables above into Eq. (7) provides simple expression as follows:

Eq. (8) demonstrates that, the critical equivalent torsional slenderness ratio is only determined by $b/t$ value, and has no correlation with member length. The critical torsional stress can be evaluated by Eq. (9) and (10):

According to Eqs. (5) and (10), it is interesting to find that, the two failure modes of dual-angle compound members, local buckling and torsional buckling, have the same critical stress. In addition, no obvious torsional buckling was found in prototype test of latticed towers with compound leg members. Therefore, in design, since the effect of local buckling is considered, the torsional buckling can be ignored.

4.4. Modified design approach

Prevailing Chinese design standard stipulates that, if the filled plate spacing is less than 40$i$, the compound member can be calculated as a solid-web member. However, the experimental and finite element analysis results indicate that the failure mode of test members is a mixture of overall flexural buckling and local instability. The core members mainly bend around imaginary axis, and internal forces of different components are asymmetric. All these contradict with the provisions in the standards.

Under axial compression, the design procedure contains two steps, net section strength and overall stability. For the overall stability calculation of the compound member, the design method is provided in $DL/T$ specification, but the prototype tests indicate that it is was not accurate enough. To fit the test data, a modified design approach is established on the basis of current design method. Due to the failure modes of core members, the equivalent slenderness ratio ${\lambda }_e$, instead of effective slenderness ratio $\lambda$,is proposed to be used in the modified approach. The equivalent slenderness ${\lambda }_e$is defined by Eq. (11), where $S$ is the net spacing between adjacent filled plates, and modified method can be expressed by Eq. (12). Local stability reduction $\beta$ is applied to the design strength, and overall stability coefficient ${\mathrm{\Phi }}_e$ is calculated due to ${\lambda }_e$ and section classification. Table 5 shows the comparison of the test capacities and the design capacities for the specimens, and the design capacity is based on the material properties obtained from tensile coupon tests. In addition, the ratios of the test capacity to design capacity from Chinese specification ($P_{Exp}/P_{DL}$) and to the capacity of modified approach ($P_{Exp}/P_{MO}$) are plotted against slenderness ratios ($\lambda$), as shown in Fig. 9 and Fig. 10:

The mean value of $P_{Exp}/PDL$ is 0.93 with the $SD$ value of 0.058. It means that the design capacity predicted by Chinese specification is not conservative. Meanwhile, the ratio of $P_{Exp}/P_{Mo}$ is with mean value of 1.03, and $SD$ value of 0.076. It also can be seen in Fig. 10 that the proposed design values based on the equivalent slenderness ratio fit the test data well.

Fig. 9Ratio of test strength to design strength

Fig. 10Ratio of test strength to modified strength