3.1 Selection of the Design Software

Although SAP 2000 can be used for modeling analyses of SPSWS, the tentative calculation finds: As for the steel sheet with vertical slits, only the element division reaches certain precision can the elastic stiffness be simulated precisely. In order to obtain comparatively precise value of stiffness, the SPSWS with size shown in Figure 2 requires about 9000 division elements. If calculated with 20 pieces of such steel sheet wall in one structure, so only the part of steel sheet shear wall requires a total of near 110,000 division elements, which is undoubtedly an over-burden for the computer. Therefore, there exist some inconveniences for the SAP 2000 in the structural computation of SPSWS.

Figure 2: The Dimensional Drawing for the Sample Calculation of SPSWS

If the nonlinear FEA softwares, such as Ansys, Abquas and so on, are used in the structural computation of the project, on the one hand, similar to SAP 2000, the element quantity is too large for a ordinary computer to solve; on the other hand, because the analytical type software is very inconvenient for the structure design in the aspects such as lading condition combination, results post-treatment etc.

PKPM, which has closely combined to the national building design standard, is now one of the widely used design software in the engineering design. But because no success result has not been established for the system study of SPSWS, there is no corresponding computation module in this software.

However, if we use traditional lateral resistant member, such as brace, to replace SPSWS, so as to consider the steel sheet wall's contribution to the overall lateral resistant stiffness of a structure in the elastic stage. Then PKPM can solve the structural computation problems in such (type) project where the SPSWS is used, it is significant for the spread and exploitation of SPSWS.

To sum up, the final choice for the engineering structure calculation uses: PKPM +properly simplified model of SPSWS

3.2 The Problems of Elastic Simplified Model

According to the stiffness equivalence principle, we try to convert the SPSWS into X-brace; the Scheme of the Simplified Model is shown in Figure 3.

Figure 3: The Scheme of SPSWS Simplified Model

From Figure 3 above, according to the stiffness equivalence principle, we can obtain the sectional area of corresponding brace A, with the derivation process is mainly shown below:

If the elastic stiffness of SPSWS Kh is known, we can convert and obtain the corresponding brace section area from equation (4), and then carry out structural computation with the braces are arranged at corresponding position.

After simplifying as brace according to formulation (4), use PKPM to carry out the structural computation for the 11-story residential house of steel structure. The result is basically close to that of elastic calculation carried out with direct SPSWS model with SAP 2000.

3.3 The Problems in the Calculation of Elastic Stiffness

The formulation (4) indicates that the Kh of SPSWS stiffness is of crucial importance. At present, Kh can be obtained by theoretical calculation, finite element analogy and test method.

1) The formulation for theoretical calculation

The SPSWS is divided into 5 zones shown in Figure 4, in which the zone without slits Ksd, Ksm, Ksu, only the shear stiffness is taken into account; but as to the zone with column between slits, Kcu, Kcd, not only the flexural stiffness but also shearing rigidity is taken into account; and then superimpose in series the stiffness in each zone. The computing formula for the elastic stiffness is as follows (refer to literature [2] for the detailed process of derivation).

2) The Test Result and the Result from Theoretical Calculation

Recently, Tongji University has completed low-frequent cyclic loading test with two SPSWS (the size is the same as in Figure 2). The scheme of test apparatus is shown in Figure 5. The member stiffness values resulted from the test are shown in Table 2, the corresponding results of theoretical calculation are also given in the same table.

It can be seen from the Table 2: The theoretical calculation results are 20~30% higher than the test ones. The reasons by preliminary analysis are: In the theoretical formula, it is supposed the non-slit zones of the steel sheet have only pure shear deformation, and it is presumed no rotation occurs at the upper and lower border of the shear wall; but in the test, a little of flexion and rotation of steel beam is unavoidable in the test, and a little of flexural deformation may occur in the non-slit zones. In addition, after the steel sheet has slits, the highly concentrated stress at slit ends may cause entering plasticity at local zones comparatively early, and consequently cause the stiffness deterioration.

Figure 5: The Test Apparatus for SPSWS

Table 2: The Results from Japan Design Formula and Those from Test

Note: The size of specimen SPSWS1, SPSWS2 is the same as that in Figure 2, and their thickness is 14, 12 respectively, refer to literature [3] for detailed information.

3) The FEA Results, Its Comparison and Analyses

Table 3 analyzes the elastic stiffness values of SPSWS under four types of different constraint condition (refer to Figure 2 for the size), in which the latter 3 types have frames. It can be known from Table 3: Different boundary constraint has comparatively large affect on its stiffness, especially the rotation constraint in-plane of upper, lower boundary. Comparatively speaking, the stiffness values of shear wall under Class IV boundary restraint conditions coincide better with theoretical calculation results and test results.

Table 3: The SPSWS Stiffness under Different Boundary Constraint

4) Actual Boundary Constraint

It can be known from the integration of 1), 2), 3) that different boundary constraint corresponds to the different initial stiffness of shear wall, but the actual boundary constraint is rather complex: Floor slabs constrain steel beams, and the steel beams constrain shear walls, and the shear walls in the upper story have constraint effect on those in the lower layer. To consider the floor slab in-plane as absolute stiffness, the out-of-plane translation Uz and out-of-plane rotation Rotx of the shear wall boundary should be constrained, but the rotation constraint of shear wall in-plane obviously belongs to elastic restraint, i.e. neither whole constraint nor all free. Its restraint degree is expected to be further analyzed and examined. Furthermore, the steel beams in the actual projects always have some bents; therefore the coupling of Ux, Uy at boundaries needs further analyses.

3.4 The Problems of Vertical Load

No vertical load has been applied to the shear wall, according to most of existing testing data, such as the data mentioned by the literatures, and recent test completed by Tongji University, as mentioned above. As for the affect analyses of vertical load, the author analyzed the load-shift curves of shear wall members with Class IV boundary constraints (refer to Figure 2 for size, t=12 mm), under different vertical load (evenly distributed vertical load), the results are shown in Figure 6.

Figure 6: The Effect of Vertical Load on Shear Wall Performance

It can be known from Figure 6: The vertical load has decrease effect on the initial stiffness of shear wall, but the decrease amplitude is not large (within 10%).

Considering that the actual projects can make the shear wall basically not receive the vertical load by the rational arrangement of construction sequence, furthermore, the floor slab may restrain the beam's rotation and decrease the vertical load effect, so the vertical load effect on the shear wall stiffness can be ignored.

3.5 The Design Issues of Single Slice Frame-shear Wall

1) The Buckling Resistant Problems:

It is the basic premise of assuring its good performance to avoid SPSWS from the premature buckling. The test and FEA shows there exist two major types of buckling form: Shearing buckling of overall sheet and torsion buckling of small walls between slits.

The buckling stress in overall shearing of non-slit sheet is shown in formulation (6):

Kcr is the buckling coefficient, and it relates to the sheet boundary constraint, sheet aspect ratio. The formulation above shows that, the most effective way of increasing overall buckling stress is to reduce the height-thickness-ratio H/t, and increase the boundary constraint. The increase of boundary constraint can be realized by the adding of stiffening at the vertically edge of shear wall. The test completed in Tongji University used the method of adding stiffening at square tube edge. In addition, the vertical slits provided at steel sheet may lead to the decrease of overall buckling stress. The less the breadth-thickness ratio b/t of the lath between vertical slits is, and the larger the height-thickness ratio h/t is, the higher the dropping down degree is.

Analyses indicate when the breadth-thickness ratio b/t of walls between slits is relatively large, and the torsion buckling will occur in walls between slits. The test data from Japan indicate the torsion buckling can be avoided by limiting the breadth-thickness ratio b/t of column between slits in SPSWS ≤15. However obviously, the buckling of column between slits shall also be related to height-to-breadth ratio h/b, but by now, no corresponding analyzing data has been seen.

2) The Problems of Stiffness, Bearing Capacity

The theoretical calculation of SPSWS stiffness is shown in formulation (5). The ultimate bearing resistance uses the plastic hinge forming at both ends of column between slits as limiting state, its formulation is shown in (7) (refer to literature [2] for detailed analyses).

It can be known from formulation (5) and formulation (7): The providing of the vertical slits enables the stiffness and bearing capacity to be flexibly adjusted in large range with h/b. It is an obvious advantage of SPSWS. It is more favorable for the commissioning of structural computation.

3) The Setting Up Problems of Slit Parameters

The principle of slit parameters setting is: Assure the yield before buckling of steel sheet wall; assure proper stiffness and load-bearing capacity. The suggested range is given out by Japan test data: The number of slit row m=1~3, the breadth-thickness ratio b/t of column between slits ≤15, the height to breadth ratio h/b of column between slits ≥3.

But after all, the test data are finite, moreover there must exist the optimization of slit parameter in the range above. The following research need to carry out a great deal of parametric analysis with FEA on the basis of test, and finally put forward some reasonable shear wall size and their slit parameters, and give the corresponding stiffness and load-bearing capacity, consequently make the design "tabulation".

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