# Safe and Sustainable Design of Composite Smart Poles for Wireless Technologies
## 2 Materials and Methods
### Experimental-Numerical CTE Determination  
The experimental setup for determining the CTEs of GFRP consisted of a coupon (projection 252 mm\(\times\) 60 mm) cut off from the tubular composite pole (\(D_{outer}=\) 168 mm, see Section 2.1). The coupon was clamped (clamping length 64 mm) to a robust holder from the other end and the free end was subjected to mechanical loading. The mechanical load was subjected by a wire and a free-hanging mass (1.230 kg) attached at a distance of 56 mm from the free end. A strain gauge (KFGS-5-120-C1, Kyowa, Japan) was glued according to the manufacturer's instructions at a 138 mm distance from the clamped end and middle in the transverse direction. The arrangements are illustrated in Figure 5. Finally, the entire setup was placed in a digitally controlled oven. The test included two steps: (1) loading the coupon mechanically; (2) heating the oven in steps (24 \({}^{\circ}\)C...60 \({}^{\circ}\)C). Each heating step was launched after the strain reading from the gauge had essentially settled.  
The finite element model assembly consisted of a coupon model and a gauge model. The composite was modelled using the material constants in Table 1. Because a solid element type (C3D8R) was used, a cylindrical material coordinate system was set so that the radial direction corresponded to the ABAQUS axis nomination '1', the perimeter direction to the nomination '2' and the axial direction to the nomination '3'. The gauge was modelled as a strip of isotropic polyimide (Kapton\({}^{\circledR}\)) with a [PERSON]'s modulus value of 4.0 GPa and [PERSON]'s ratio of 0.3 [32]. A CTE value of 1.17 \(\times\) 10\({}^{-5}\) 1/\({}^{\circ}\)C was used for the gauge based on the adoptable thermal expansion given by the manufacturer (i.e., the gauge follows corresponding expansion in terms of strain reading (zero)). The gauge was meshed by using parabolic (C3D20R) elements. The gauge model was attached to the coupon model by so-called tie-constraints. The model was run by a point load and thermal field (\(\Delta T=36\)  
Figure 5: Experimental arrangements and the finite element model of the test coupon to determine thermal expansion coefficients.  
The computed strain to match with the experimental strain gauge reading was calculated based on the residual axial stress in the gauge after the thermal load. By presuming that the composite is stiffer than the gauge, i.e., the gauge follows the expansion of the substrate (coupon), we have:  
\[\varepsilon_{g,residual}=\sigma_{g,residual}/E_{g}\,, \tag{1}\]  
where \(\varepsilon_{g,residual}\) is the residual strain of the gauge in the axial direction, \(\sigma_{g,residual}\) is the computed (FEA) residual stress in the axial direction, and \(E_{g}\) is the Young's modulus of the gauge. In Equation (1), it is presumed that the length-change of the gauge is simply due to the 'external' force by the expansion (contraction) of the composite coupon. In reality, the gauge has a finite stiffness and the force balance-given length-change is partly due to the thermal expansion of the gauge (which does not induce stresses). The gauge stresses were recorded from three elements and the average value was calculated.