First loop: rad Second loop: rad Third loop: rad Fourth loop: rad Fifth loop: rad Sixth loop: rad Seventh loop: rad Eighth loop: rad Final loading:

The horizontal push and pull of static cyclic load as represent of earthquake loading was applied using the hydraulic actuator of 500 kN capacity and 500 mm strokes.

The top of shear wall specimen displacement was measured by using displacement-measuring device of 500 mm strokes. Small displacement and rotation of shear wall were measured by using displacement meter of 50 mm strokes. Figures 9 and 10 show the V and C brace and the shear wall specimen during testing.

3. Theory and Calculation

3.1. Analytical Methods for Predicting Envelop Curve

The following nonlinear calculation method was derived based on the article written by Murakami and Inayama [2] but modified so as to be applicable to such nailed-onsheathed shear walls whose nailing pattern are arbitrary arranged.

3.1.1. Derivation of Equations

1) Definition of Nail Position

Figure 11 shows nail positions and rotational center defined in the Cartesian coordinate system where the origin was determined arbitrary to be located at bottom left corner and a total of n nails are located arbitrary starting from I = 1 to n^th in a rectangular area of g × L as shown in Figure 11.

Let us assume that slip modulus of nail K_s is not orthotropic but having different values in each nail as this assumption will make it possible to execute step by step nonlinear calculation with considering material nonlinearity of each nail and movement of rotation center from the initial position to any ones which is ought to be determined by equilibrium of nail forces.

2) Derivation of Rotation Center

At first, let us assume a situation that a forced rotational deformation of angle q_x was given around the rotation center as shown in Figure 12. Due to this forced

deformation, i^th nail n_i will be displaced to x-direction by the amount of s_xi as shown in Equation (1).

(1)

Denoting slip modulus of i^th nail as K_si, the reaction force acting on i^th nail can be expressed as Equation (2).

(2)

Equilibrium of all p_xi along x-direction leads to Equation (3).

(3)

As q_x is constant, then Equation (3) leads to Equation (4).

(4)

From the same derivation process as shown in x-directional case, by assuming forced rotational deformation with angle as shown in Figure 13, x-directional rotation center can be derived as shown in Equation (5).

(5)

3) Derivation of Shear Deformation of Partial Shear Wall

Again let us consider x-directional displacement s_xi of i^th nail due to q_x;

(6)

Reaction force acting on the i^th nail is;

(7)

Individual small rotational moment due to reaction force p_xi is;

(8)

x-directional total moment M_x is;

(9)

In the same way, y-directional total moment M_y can be obtained as Equation (10).

(10)

As M_x and M_y must be equilibrium, then Equation (11) should be held good.

(11)

(12)

While, in Figure 14 shown thatpartial external shear force Q applied on the top of the corresponding shear wall of height “g” gives a rotational moment and this moment should be equilibrated with each internal moment M_x and M_y.

(13)

The shear deformation angle g_n of the shear wall caused

by nail slip will be defined as the summation of x-directional rotation q_x and y-directional rotation q_y just same as the definition of shear strain of solid materials, thus,

(14)

Substituting Equation (13) into (14), we can get the final relationship between applied shear forces Q and shear deformation angle g_n as in Equation (15).

(15)

where,

K_n = Shear rigidity component due to nail resistance.

If the shear deformation due to sheathing material itself should be taken into account, the relationship between shear force Q and shear deformation angle g_n will be expressed as Equation (16).

(16)

where, G is shear rigidity of sheathing materials.

L is length of shear wall.

t is thickness of sheathing materials.

Hence, the total shear deformation angle g of shear wall will be written as the summation of shear deformation angle as;

(17)

where,

is total shear stiffness of partial shear wall.

4) Derivation of Shear Deformation of Whole Shear Wall

In general, whole shear wall tends to be composed of plural partial shear walls due to unit size of sheathing material as shown in Figure 15.

From equilibrium condition of external and internal moment, Equation (18) should be held good.

(18)

The compatibility condition that all partial shear walls should share the same deformation angle will lead to Equation (19),

(19)

where, the suffix “j” indicates number of partial shear wall. Substituting Equation (17) into (18) and considering (19), finally we can get Equation (20) for the loadshear deformation relationship of whole shear wall.

(20)

3.1.2. Nonlinear Calculation Method

1) Load-Slip Data of Nail for Non-Linear Calculation Method

Figure 16 shows load-slip data of N75 nail taken from single shear test on Akasia wood with FCB sheathing. For this data, a three-parameters exp-equation shown in Equation (21) was fitted up to maximum load for nonlinear calculation. And beyond maximum load level, simple linear equation showed on (22),

(21)

(22)

where, p_u = 550 N, K_u = –10 N/mm, K_s = 1200 N/mm, K_u2 = –10 N/mm.

2) Non-Linear Calculation Procedure

Figure 17 shows flow chart of non-linear calculation procedure in this study.

3.2. Modeling of Hysteresis Loop

In order to analyze dynamic property of shear walls it is necessary to established any appropriate hysteresis loop model. In this study we adopted so-called Normalized Characteristic Loop (NCL) Model that was proposed by Tani and Nomura [3,4] for reinforced concrete structures and recently modified by Matsunaga, Miyazu and Soda [5-7] for timber shear structures.

Figures 18 and 19 show the NCL Model for Akasia frame and FCB sheathing shear wall system were expressed by following Equation (23) in accordance with the studies of Matsunaga, Miyazu and Soda [5-7],

(23)

where, L(x) and x are normalized load and deformation angle respectively divided by maximum value in each loop and A, B, n1 and n2 are parameters governing shape of hysteretic loop. In the second term of Equation (23), the minus mark should be used in the case of upper curve while plus mark should be used in the case of lower curve. Four parameters are shown in Table 4.

4. Results and Discussions

4.1. Envelope Curve

Figures 20 and 21 show comparisons between predicted envelope curve and experimental ones. As can be seen from SWC specimens, prediction coincident with experimental ones well, while in the case of SWB specimen, prediction over-estimated performances of shear walls after yielding a little bit. The reason why only one specimen was used for the comparison in SWB specimen is that in experimental procedure, tests were carried out for two specimens without sufficient restriction from up-lift of test specimens. Therefore, the load-deformation curves of those specimens without restriction became abnormal. The rest of one specimen was tested with sufficient restriction for up-lift thus normal load-deformation curve that was usable for the comparison between experiment and prediction was obtained. Therefore, the discrepancy for SWB specimen might be fallen down into the experimental variance.

Figure 22 shows initial failure at edge nail, which occurs at 1/75 radian deformation angle due to insufficient edge distance. This kind of initial failure could not be predicted by the theory derived in this study therefore in order to predict this kind of initial failure precisely, nail shear data having effect of insufficient edge distance should be used in the analysis. Figure 23 shown failure of FCB at 1/15 radian.

4.2. Whole Load Deformation Curve

Figures 24 and 25 show comparisons between experimental

curve and theoretical prediction, which was obtained by combining, envelop curve with hysteresis NCL Model.

Although there are some sorts of discrepancy between prediction and experimental results, comparisons shown in this study seemed to be fairy good at least for predicting whole nonlinear behaviors of wooden shear walls whose nailing pattern are arbitrary arranged. These comparisons might suggest that better prediction will be obtained by paying careful attention to nail shear data so as to be reflected by in sufficient edge distance effect.

5. Conclusion

In this study we derived a non-linear calculation method for predicting whole load-deformation curve of FCB sheathed nail-on shear wall made by Akasia wood frame.

NCL Model formulated hysteresis loops. By combining these two theoretical methods we could predict whole nonlinear cyclic load-deformation behavior of specimens. Although there were some discrepancies between prediction and experimental observations, further better prediction might be obtain by paying careful attentions to nail shear data so as to be reflected in sufficient edge distance effect.

6. Acknowledgements

We would like to express our sincere thanks to JSPS for Ronpaku program, Structural Function Laboratory, RISH, Kyoto University, Japan, Dr. Akihisa Kitamori, Structural Function Laboratory, RISH, Kyoto University, Japanand RIHS, Ministry of Public Works of Indonesia for all research activity.

REFERENCES