ELASTO-PLASTIC ANALYSIS OF JOINTS IN TRADITIONAL TIMBER FRAMES SUBJECTED TO CYCLIC LOADING

Appropriate evaluation of the structural characteristics of joints is necessary in order to understand their horizontal resistance characteristics of traditional timber frames. For this purpose, it is important to create a simple joint model that takes into account hysteresis when the joint is subjected to cyclic loading, and to establish a suitable analysis method. We have developed a spring model that considers compressive strain inclined to the grain in addition to the friction characteristics of the wood in a joint, and we have proposed an incremental displacement analysis method based on that model. The model considers resistive components at contact surfaces inside the joint by decomposing them into directions perpendicular and parallel to the contact surface. We represented the resistance perpendicular to the contact surface using compression springs and assumed a slip-bilinear constitutive law. We represented the resistance parallel to the contact surface using shear elastic springs and Coulomb's sliders. When the joint deforms, the spring force due to compressive strain inclined to the grain changes, and so the maximum friction force also changes. The shear springs must also satisfy the constitutive law with respect to the changing spring force due to compressive strain inclined to the grain. In the past, we introduced the concept of an apparent shear stiffness with regard to the shear springs. Using this method, we found that the apparent shear stiffness does not depend on the shear elastic spring stiffness. This method required an iterative calculation in order to derive the apparent shear stiffness. Consequently, there is a problem when dealing with complicated joint shapes in that there is an increase in the number of contact surfaces and spring models, so that the number of iterations required for the calculation to converge also increases. In the present article, to solve this problem, we introduce a method of incorporating the constitutive law of Coulomb's friction for the shear spring directly into the stiffness equation. Fundamentally, the spring force rate for the shear spring depends on the elastic spring stiffness. If the shear spring continues to satisfy the constitutive law of Coulomb's friction as the joint deforms, the spring force rate for the shear spring must continue to satisfy the maximum friction force. Incorporating these relationships directly into the stiffness equation and solving the equation makes it possible to obtain