# Design Procedure of a Mono-Anchor Head for 2360 MPa High-Strength Steel Strand
## 3 Behavioral Mechanism of Mono-Anchor Head  
The anchorage device for single strands consists of a wedge and a mono-anchor head. When the strand is tensioned, the wedge is drawn into the anchor head together with the strand and transmits the tensioning force to the inclination inside the anchor head. As shown in Figure 2a, assuming that the inclination angles of the anchor head and wedge are the same, the normal stress is uniformly distributed over the entire inclined surface of the anchor head. The normal stress of the anchor head inclined surface is the load transmitted through the wedge (\(P_{normal}\)) divided by the inclined surface area of the anchor head (\(S_{Inclined}\)) as in Equation (2). The load acting perpendicular to the inclined surface is calculated by Equation (3). In this case, \(P\) is the load on the strand, \(\theta\) is the inclination angle  
Figure 1: Permanent deflection of the anchor head.  
of the anchor head, \(\alpha\) is the friction angle between the wedge and the anchor head, and the friction coefficient (\(\mu\)) is defined as \(\mu=\tan(\alpha)\)[14; 15; 16].  
\[\sigma_{normal}=P_{normal}/S_{Inclined} \tag{2}\]  
\[P_{normal}=P/\sin(\theta+\alpha) \tag{3}\]  
However, the wedge has a large inclination angle of 0.3\({}^{\circ}\) to 0.7\({}^{\circ}\) compared to the angle of the anchor head inclination, so the load is concentrated on the top of the wedge hole as shown in Figure 2b. The load applied to that location is several times higher than the load assumed to be uniform. In this context, the degree of external force concentration at the top of the wedge hole was defined as the concentration factor (\(k\)), and the unit force of that was expressed as \(k\times\sigma_{normal}\). When the unit load acting perpendicular to the anchor head inclination surface is converted into a cylindrical coordinate system in consideration of the anchor head shape, it is separated into a vertical load and a radial load. Each component force can be regarded as the principal stress acting on the element located at the top of the wedge hole, and the effective stress can be calculated as a combination of each principal stress applied to the element before yielding. The effective stress was calculated according to the von-Mises stress theory, and it can be arranged as in Equation (6) by combining Equations (4) and (5) [17].  
\[\sigma_{z,axis}=k\times\sigma_{normal}\times\cos\theta \tag{4}\]  
\[\sigma_{radial}=k\times\sigma_{normal}\times\sin\theta \tag{5}\]  
\[\sigma_{concentration}=\sqrt{\sigma_{z,axis}^{2}+\sigma_{z,axis}\sigma_{radial }+\sigma_{radial}^{2}}=k\times\sigma_{normal}\times\sqrt{1+(1/2)\sin\ 2\theta} \tag{6}\]  
The plastic hoop strain at the top of the wedge hole, which is a performance criterion of the mono-anchor head, can be quantified in relation to the stress at that location. Although the stress at the location can be calculated mechanically, it is difficult to derive a clear value numerically for the behavioral characteristics of the material. Therefore, the degree of concentration of external force is calculated based on finite element analysis.