Secant Stiffness Method for Inelastic Design of Strut-and-Tie Model

Headnote

A secant stiffness method was developed for the inelastic design of strut-and-tie models (STMs). According to the design strategy intended by the engineer, struts and ties are classified as elastic and inelastic elements. For the inelastic elements, secant stiffness is used to address the effect of inelastic deformations. By performing linear analysis for the STM, the forces and inelastic deformations of the struts and ties are directly determined. The safety of the struts and ties is evaluated by using deformation-dependent failure criteria. The proposed method was applied to existing test specimens including a deep beam, a coupling beam, and a shear wall. The design results were compared with the properties and deformation capacities of the test specimens.

Keywords: performance-based design; reinforced concrete; secant stiffness; strut-and-tie model.

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INTRODUCTION

The strut-and-tie model (STM) has been used for an efficient design method of reinforced concrete (RC) members with complicated force-transfer mechanisms, such as deep beams, shear walls, corbels, and beam-column joints.1-3 The conventional STM simplifies an RC member as a truss with concrete struts and reinforcement ties, depending on the internal force flow.4 The forces acting on the struts and ties are determined from the force-equilibrium equations. On the basis of the magnitude of the internal forces in the struts, the safety of the concrete struts and nodes was evaluated and reinforcements were provided for the ties. As such, the conventional STM emphasizes the forceequilibrium and force-based failure criteria of struts, ties, and nodes, but often does not directly address the effect of inelastic deformation. Although the conventional STM results in a satisfactory design in most cases, one must consider the effect of inelastic deformation for the following reasons:

1. For describing a complex force-transfer mechanism in a member, an indeterminate STM might be better than a determinate one. When an indeterminate STM is used for structural analysis, the forces in struts and ties vary depending on the inelastic deformation and stiffness of the members.

2. For performance-based earthquake design of RC members such as coupling beams and shear walls, each member should be designed to satisfy the inelastic deformation demand. Further, when cyclically loaded, such members often fail due to deformation-dependent failure mechanisms, including diagonal web crushing and reinforcement fracture.5-8

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