## 2 Description of Test Campaigns and Properties of the Materials
### Summary of Tested Materials and Test Results  
TU Kaiserslautern's test campaign contained tests on two adhesives. The first adhesive was an epoxy resin (named mortar B in their report and referred to as Adhesive-1 henceforth), and the second adhesive was a cementitious mortar (called mortar C in their report and referred to as Adhesive-2 henceforth). CSTB's test campaign was on one epoxy resin (referred to as Adhesive-3 henceforth). Figure 1: TU Kaiserslautern’s furnace and loading system for fire tests on bonded anchors [20]. Figure 2: CSTB’s furnace and loading system for fire tests on bonded anchors [23]. Prediction of the Load-Bearing Capacity Using Pinoteau's Resistance Integration Method (RIM) and 3D Thermal Modelling of the Anchor  
The numerical model [22] is based on the following analytical procedures:  
* The bonded anchor adhesive is not modeled,
* Steel threads are not modeled (i.e., cylindrical geometry for the anchor rod),
* The concrete remains uncracked,
* Concrete spalling is ignored,
* The fire exposed surface of all elements is subjected to convective and radiative fluxes of ISO 834-1 fire temperatures [17] on all sides,
* The unexposed fire surface of concrete beams is subjected to convective and radiative fluxes of ambient air at 20 \({}^{\circ}\)C, and
* Slip of anchors is ignored. During a fire test, heat transfer from hot gas inside the furnace to the exposed elements occurs via convection and radiation. Inside the members, conduction transfers the heat from the fire exposed surface inside the elements towards the unexposed surface. This problem can be solved by finite element modelling using ANSYS with the governing differential equation for 3D transient heat conduction using the implicit scheme and iterative solver expressed in Equation (1):  
\[\rho c_{p}\frac{\partial T}{\partial t}=\lambda\left(\frac{\partial^{2}T}{ \partial x^{2}}+\frac{\partial^{2}T}{\partial y^{2}}+\frac{\partial^{2}T}{ \partial z^{2}}\right) \tag{1}\]  
The 3D model represents the anchor as a cylinder inside of a concrete bearing element with modelling of the extended and embedded length of the steel anchor element (Figure 3). Equation (2) describes the Neumann boundary condition satisfied at the fire-exposed surface:  
\[-\lambda\frac{\partial T}{\partial n}=h_{fire}\cdot\left(T_{s}-T_{fire}\right) +\varepsilon\cdot\sigma\cdot\left(T_{s}^{4}-T_{fire}{}^{4}\right) \tag{2}\]  
Equation (3) describes the Neumann boundary condition satisfied at the upper surface of the concrete bearing element exposed to ambient air at 20 \({}^{\circ}\)C:  
\[\dot{q}_{total}=h_{air}\cdot\left(T_{s}-T_{air}\right)+\varepsilon\cdot\sigma \cdot\left(T_{s}^{4}-T_{air}{}^{4}\right) \tag{3}\]  
Figure 3: Anchors directly exposed to fire using 3D modelling in ANSYS [22]. where:  
\(\dot{q}_{total}\) is the total heat flux applied to the exposed surface,  
\(\lambda\) is the thermal conductivity (W/m\(\cdot\)K),  
\(\rho\) is the mass density (kg/m\({}^{3}\)),  
\(c_{p}\) is the specific heat (J/kg\(\cdot\)K),  
\(h_{fire}\) is the convective heat transfer coefficient for the fire exposed surface (25 W/m\({}^{2}\cdot\)K),  
\(h_{air}\) is the convective heat transfer coefficient for the surface exposed to air at 20 \({}^{\circ}\)C (4 W/m\({}^{2}\cdot\)K),  
\(\sigma\) is the Boltzmann constant (5.667 \(\times\) 10\({}^{-8}\) W/m\({}^{2}\cdot\)K\({}^{4}\)),  
\(\varepsilon\) is surface emissivity (0.7),  
\(T_{\rm s}\) is the solid surface temperature (K),  
\(T_{fire}\) is gas temperature inside the furnace as a function of time (K),  
\(T_{air}\) is ambient air temperature (293 K), and  
\(t\) is time. Boundary conditions are represented in a profile view of the 3D model in Figure 4.  
The thermal properties of concrete and carbon steel (conductivity, specific heat and mass density) are a function of temperature. The properties according to the French national annex in Eurocode 2 [26] for both materials are adopted in this study (Figure 5).