# Thermally Induced Displacements and Rotations of Pillars for Precise Geodetic Measurements
## 1 Introduction
[5; 6] investigated the impact of thermal effects on the positions of GNSS antennas and concluded that the temperature-induced bending of pillar monuments can lead to significant position shifts. Their research emphasizes the importance of continuous monitoring and environmental aspects in maintaining the accuracy of GNSS data. [PERSON] [7] and [PERSON] et al. [8] investigated how environmental factors, particularly temperature fluctuations and wind, affect the stability of GNSS monuments and emphasized the need for adequate construction and shielding of the pillars to ensure the reliability of measurements. [PERSON] and [PERSON] [9] assessed the stability of monuments within the SWEPOS GNSS network using terrestrial geodetic techniques. Their results indicate that thermal expansion and uneven heating can lead to deformations of the pillars that affect the positions of the GNSS antennas. The study recommends the insulation and temperature stabilization of pillars to minimize such effects. The importance of high-precision inclination measurements for monitoring in geodetic and structural applications was reported by several authors. [PERSON] [10] evaluates digital inclinometers for continuous deformation monitoring, showing their effectiveness in tracking structural tilts. [PERSON] and [PERSON] [11] highlight inclination monitoring as essential for assessing the stability of geodetic reference points in permafrost, where ground movements can affect measurement accuracy. [PERSON] and [PERSON] [12] and [PERSON] [13] demonstrate the role of inclination sensors in detecting landslide-induced angular changes, linking them to environmental factors. [PERSON] et al. [14] further confirm the long-term applicability of inclinometers by monitoring the headframe of a salt mine shaft, demonstrating their reliability in detecting slow structural deformations over extended periods. Together, these works stress the need for precise inclination control to ensure reliable geodetic and structural assessments. Despite the well-known thermal effects from solar radiation, it was only recently that more effort was dedicated to predicting these effects, focusing on bending deformations, thermal stresses, and structural integrity under moderate temperature changes and relatively large temperature gradients between heated and shaded surfaces. Several studies (e.g., [15; 16; 17; 18; 19; 20]) analyze temperature distributions in concrete elements, particularly in box girders and slabs. Extreme solar heating can increase internal stresses, which, when combined with mechanical loads, can accelerate fatigue and material degradation (see [21; 22]). To predict the varying thermal conditions in a concrete structure, numerical models were used by [PERSON] [23], [PERSON] et al. [24], and [PERSON] et al. [25]. We will here focus on the relationship between the horizontal displacements and the cross-sectional rotations measured as inclinations of a typical pillar used for stabilizing the reference points. The paper presents the experimental setting in controlled laboratory conditions where we simulated natural solar radiation by heating only one side of the column and leaving the other much colder. Through precise measurements, we captured the displacements near the top of the pillar, the inclination of the horizontal plate at the top, and the inclination of the angle bracket near the top, along with the time history of temperatures at several points of the observed structure. The aim of this study was to evaluate whether the horizontal displacement at the top of a pillar caused by uneven heating can be accurately estimated from inclinometer measurements and to assess the validity of an analytical model that relates the temperature gradients in the cross-section to the lateral displacement. Based on the presented setup,we established a novel experimental correlation between thermally induced inclinations and lateral displacements of geodetic reference pillars.