## 2 Description of Test Campaigns and Properties of the Materials
### Summary of Tested Materials and Test Results
The mass density of the steel (7850 kg/m\({}^{3}\)) [25] is considered constant with respect to temperature. Knowing the thermal distribution along the anchor at each moment of heating, it is possible to associate a resistance to each temperature using the resistance-temperature relationship. [PERSON] [16] illustrated schematically how the resistance at a depth \(x_{i}\) is determined at a time \(t_{i}\) based on the thermal distribution (Figure 6). Figure 4: Boundary conditions applied in the 3D heat transfer analysis for anchors directly exposed to fire [22]. Figure 5: _Cont_. This method allows the evolution of the load-bearing capacity of the bonded anchor during heating to be determined. Knowing the applied mechanical force on the anchor during heating, failure time under fire conditions can be determined. The bond capacity of the anchor at any given time is calculated according to Equation (4):  
\[N_{fire}=\pi\cdot d\cdot\int\limits_{0}^{h_{ref}}\tau_{uncr}\cdot k(\theta(x)) \cdot dx \tag{4}\]  
where:  
\(N_{fire}\) is the pull-out resistance of the anchor under fire conditions (N),  
\(d\) is the diameter of the anchor (mm),  
\(\tau_{uncr}\) is the mean bond resistance of the anchor at ambient temperature in uncracked concrete (N/mm\({}^{2}\)),  
\(k(\theta)\) is a reduction factor that depends on temperature,  
\(\theta(x)\) is the temperature distribution along the embedment depth of the anchor, and  
\(h_{ref}\) is the embedment depth of the anchor (mm). Figure 2:0 Variation of thermal properties of concrete and steel according to NF EN 1992-1-2 and EN 1993-1-2 [26]. By integrating the resistances, this method does not take into account the stress distribution along the anchor. When a tensile force is applied on the anchor, a distribution of bond stresses occurs in a phenomenon called \"shear-lag\". This stress profile is equal or lower than the resistance profile. When temperature increases under a constant mechanical load, the sum (integration) of the stress profile decreases until it reaches a maximum bond stress value at a certain depth. The saturation of bond stresses at certain depths leads to a redistribution of these stresses towards the deeper parts of the anchor where the stress is still less than the resistance. The area under the stress profile remains unchanged in a way to ensure the integrity of the anchor. Pull-out failure occurs when all the stresses along the anchor saturate, in this case the stress profile is equal to the resistance profile. Therefore, this justifies the determination of the load-bearing capacity by only considering the resistances (Equation (4)). Figure 7 illustrates the evolution of temperature and bond stress profiles at three different times during heating \(t_{1}\), \(t_{2}\) and \(t_{3}\). Stress profiles are represented for a constant load applied at \(x=0\) (head of the anchor), and temperature profiles are represented for a non-uniform heating applied near \(x=0\). At \(t_{1}\) (low temperatures), the stress profile is lower than the resistance profile because the temperature profile is still at low temperatures. At \(t_{2}\) (higher temperatures), heating at the head of the anchor decreases the resistance profile and leads to a saturation of stresses. At \(t_{3}\) (near failure point), all the stresses along the embedment depth have saturated and pull-out occurs if the temperature continues to increase.