What is STM? - 2. Elements of Strut-Tie Model

Strut-tie models are statically equivalent discrete representation of stress fields in a member at failure. Strut-tie model consists of three basic elements namely, concrete compression struts, concrete or steel tension ties, and nodes. Whereas the tension steel ties are one-dimensional elements between two nodes, the concrete struts and concrete ties represent indeed two- and three-dimensional stress fields tending to spread between two adjacent nodes. Nodes which correspond to the pinned joints of a truss represent the regions where internal forces are redirected.
2.1 TiesTies are the tension elements of a strut-tie model. Usually, tie forces are resisted by reinforcement placed symmetrically about the line of action of the force. The reinforcement must extend the entire length of the tie and should be properly anchored at the nodes. The amount of reinforcement to be provided is determined from the tie force. Ideally, the tie should be proportioned so that at the ultimate design load it will just yield. In order to ensure a ductile failure mode, sufficient yielding must occur to allow the formation of a failure mechanism prior to crushing of the concrete. Tie reinforcement may consist of single or multiple bars or prestressing strand. Reinforcement considered to be part of a given tie should undergo similar strains in order to act as a unit or a single tie. 2.2 StrutsCompression elements of a strut-tie model are known as struts. Struts are usually considered to be comprised of concrete. Struts represent stress fields in the concrete. Various types of struts have been developed to characterize different stress fields. There are mainly three different configurations for concrete compression stress fields which can be used to visualize the flow of the internal forces. These are the fan-shaped, bottle-shaped and prism struts as illustrated in Fig. 2.1. The fan-shaped stress fields are developed at points of concentrated loading or at supports. Fig. 2.2 illustrates a fan region such as that which develops at the support in a simple beam. This fan region incorporates a series of trapezoidal struts which act to distribute force from the node at the point of reaction to several stirrups. The stress field which narrows near points of concentrated loads or at supports is modeled using a bottle-shaped strut as shown in Fig. 2.3. The inclined struts produce tensile stresses normal to the line of action of the applied forces which must be resisted by transverse reinforcement or by tension in the concrete. Fig. 2.3 shows the bottle or bulb strut represented using a simple strut-tie model for analysis. The prismatic strut is the simplest idealization of a compressive stress field. Prisms are generally used to model stress fields having uniform parallel stress trajectories.



2.3 NodesNodes of a strut-tie model are simple idealization of the more complex state of stress in the regions where there is a change in direction of the load path. Nodal regions connect the elements of a strut-tie model. In strut-tie models, nodes represent the pinned joints of a truss. Physically, nodes represent regions in which internal forces are redirected. The shape of nodal zone is determined by the intersection points of three or more struts or ties framing into it. Since several one-dimensional stress fields meet in the nodal area, a two-dimensional stress field is developed for plane structures. The concurrent force system within the nodal zone prevents bending of the truss member due to any eccentricities. The importance of nodes in design process is twofold. First, concrete stress levels in nodes must be controlled to allow for the safe transfer of forces. Secondly, dimensioning of nodes is the key to satisfying anchorage requirements for reinforcement and designing bearing plates. Based on the sizes of the struts and ties framing into a node, two types of nodes are defined. If one of the struts or ties represents a concentrated stress field, the node is called singular node. On the other hand, wide concrete stress fields joining each other with tension ties form a large node which is called smeared node. Of the two types of nodes, the singular node is generally more critical since the force transfer is more abrupt and creates higher stress concentrations. Fig. 2.4 illustrates singular and smeared nodes.



 

What is STM? - 1. Introduction

In the past several decades, there has been a major movement in the design methods for reinforced and prestressed concrete towards methods based on equilibrium solutions from the theory of plasticity and related conceptual models (such as strut-tie models). Strut-tie models represent a generation of the truss analogy method for beams. They are powerful and promising tools for designing structural concrete which includes both reinforced and prestressed concrete structures.
In a strut-tie model, the stress distribution is idealized as a static force system consisting of three basic elements: struts, ties, and nodes. A strut-tie model provides truss-like load path. Compressive forces are directed along struts representing compressive stress fields within the concrete. Tensile forces are directed along ties which represent reinforcement. Intersections of struts and ties occur at nodes which are idealizations of areas where internal forces change directions.
Design procedures for reinforced and prestressed concrete members in general consist of three major steps. The designer first chooses the initial concrete dimensions. In the second step, concrete dimensions and amount and detailing of reinforcement are determined using equilibrium and ultimate strength considerations. An estimate of the deformations under service condition can be considered as the last step. Strut-tie models are conceptual tools employed in the second stage to investigate the equilibrium between loads, reactions and internal forces in the concrete and reinforcement. By replacing a complex structural system with a strut-tie model, the estimates of internal forces due to shear, flexure, torsion and axial loads in the system can be obtained by analyzing the strut-tie model with the external forces applied to the system. The estimates of internal forces may then be used to determine reinforcement requirements, check concrete stresses and determine anchorage requirements.