## 4 Effects of Guardrails  
### Expansion Conditions  
Figure 8 illustrates the results of stock rail longitudinal force (SRLF) subjected to various installation torques of guardrail fasteners in the presence of expansion conditions, where 0 N\(\cdot\)m indicates that no guardrail has been used. Due to the existence of guardrail joints, the guardrails expand and contract with the variation of the rail temperature, which is equivalent to the breathing section of the CWR. Hence, the temperature variation of the stock rail, guardrail, and bridges should be considered at the same time. Based on the demonstrated results in Figure 8, the presence of guardrails does not have a substantial influence on the distribution rule of the SRLF, but it affects the amplitude of the SRLF. In the absence of the guardrails, the temperature span [22], which is the center distance between piers 6\(\#\) and 8\(\#\), is the largest, and the maximum SRLF appears at the 8\(\#\) pier position. The maximum value of SRLF is 1046.9 kN, also representing a crucial basis for both strength and stability designs of CWR on bridges. In the presence of guardrails, the SRLF at the 8\(\#\) pier position slightly reduces and then gradually rises with the growth of the installation torque of the guardrail fastener. When the installation torque ranges from 20 N\(\cdot\)m to 100 N\(\cdot\)m, the maximum value of SRLF at the 8\(\#\) pier position only increases by 24.2 kN, less than 3\(\%\). This reveals that the guardrails have little influence on the SRLF in the range of the CGB. As the span of the simply supported bridges is close to the length of a guardrail, the SRLF in the range of simply supported bridges is remarkably influenced by the guardrails. Taking the maximum SRLF at the 10\(\#\) pier position given in Figure 8a as an example, when the installation torque is placed in the range of 0-100 N\(\cdot\)m, the SRLF lessens by 115.4 kN, indicating a reduction of 12.2\(\%\). The variation rule of the SRLF along with the installation torque at the 13\(\#\) abutment position is contrary to that at the 10\(\#\) pier position. By growing the installation torque to 20 N\(\cdot\)m, the maximum SRLF at the 13\(\#\) abutment position reaches 1026.3 kN, which is nearly equal to that of the 8\(\#\) pier position under the same condition. For the CGB with small spans, the maximum SRLF at the abutment position is even greater than that at the end of the CGB and becomes the new basis for the design of strength and stability of CWR on bridges. However, the influence of guardrails is not considered in the design of CWR on bridges at present, and the unfavorable position of the abutment is ignored. This will increase the risk of rail fracture and lateral instability, hence reducing the safety of CWR on bridges. The existence of guardrails could also lead to variations in the longitudinal force of piers, as presented in Figure 9.  
Figure 8: SRLF under expansion conditions. (**a**) Distribution; (**b**) relation between \(M\) and SRLF. The demonstrated results in Figure 9 reveal that the piers' longitudinal force increases due to the existence of the guardrails, and the case of 0# abutment is the most significantly affected. As the installation torque rises from 0 N\(\cdot\)m to 20 N\(\cdot\)m, the longitudinal force of the 0# abutment magnifies by 112.8% and then lessens with the growth of the installation torque. For the case of the installation torque ranges from 20 N\(\cdot\)m to 100 N\(\cdot\)m, the longitudinal force of the 0# abutment decreases from 808.0 kN to 693.4 kN (i.e., a 14.1% decrease). The reason for the phenomenon is that the length of the breathing section near the 0# abutment decreases with the increase in the installation torque of the guardrail fastener, which can be seen from the distribution of the guardrail longitudinal force in Figure 10.  
JRGR is also an important factor affecting guardrail deformation. The installation torque of the guardrail fastener is 60 N\(\cdot\)m. JRGR ranges from 250 kN to 490 kN, and the interval is 60 kN.