Temperature-Dependent Buckling Load

Figure 7.35 Comparison of measured temperature-dependent buckling loads and modeling results (normalized by 20°C-values) [22]. (With permission from Elsevier.)...

Typical load-lateral deformation responses at midheight are shown in Figure 7.33 for temperatures up to 180 °C [22], At 220 °C, deformations were less than 0.5 mm and therefore below the photographic measurement accuracy. The curves exhibit similar pre- and post-buckling shapes and temperature-dependence as shown in Figure 7.32 for the axial displacements. 

The compressive specimen stiffness was obtained from the slope of the linear part of the load-displacement curves shown in Figure 7.32 [22]. The temperature-dependent bending stiffness, EI(T), was back-calculated from the Euler buckling equation for temperatures between 20 and 180°C as foUows ... 

The temperature-dependent Euler buckling load Pg(T) depended on the temperature-dependent bending stiffness EI(T), as demonstrated by Eq. (7.12). Owing to a symmetric laminate architecture, the neutral axis was always located at mid-depth, and therefore, the moment of inertia, I, was temperature-independent and the specimen stiffness could be determined as ... 

The resulting temperature-dependent Euler buckling load is shown in Figure 7.35 (normalized by the values at 20 °C of 25.8 kN, and 7(20 °C) = 104.7 N m ). The normalized curve is identical to that of the -modulus it shows the same decrease and compares well to the experimentally determined values. A slight underestimation of less than 8% resulted at 140 and 180 °C [22]. 

The first reactor studied in the high temperature facility was an essentially uniform slab with low buckling in two directions and high buckling in the third direction, i.e., 30 in. hi by 30 in. wide by 8 in. thick. This reactor had hi leakage and hence its properties were very temperature dependent. A fuel load was chosen which made die core critical near room temperature. Then by increasing the fuel load in steps, the critical mass was determined as a function of temperature. Each step was obtained with control rods completely withdrawn from the core. At some of the critical steps measurements of the temperature coelBcient of reactivity were made and thermal flux traverses along the axes of the core were obtained. 

The behavior of plastic structures under compression plays a critical role in numerous applications. It has been recognized that the buckling of metals under elevated temperatures presents important distinctions from the classical Eulerian case, [11]. During an experimental study, [12], buckling times were registered for a range of compressive loads applied to the top of compression molded and annealed thermoplastic samples (see Fig. 2). A typical time - load dependence is shown in Fig. 3. 

Creep rupture from long term loading, creep-fatigue, and creep-buckling should also be addressed and procedures to do so within the Code have been around for some time now. In the past, at least some portions of the Code were limited to temperatures with the intent to avoid any time-dependent effects on the material, meaning that maximum permitted temperatures for materials were kept below the creep range. 

Since the compressive loads in Section II, Part D do not account for time dependent loads, the Welding Research Council (WRC) published Bulletin 443 for calculating design limits for elevated temperature buckling based on theory as well as factors from Section III, Division 1- Subsection NH. Bulletin 443 presents equations for cylinders under axial compression as well as external pressure, and spheres under external pressure. 

In a test of fire resistance, a load-bearing wall is exposed to fire by one side, and there is a heat transfer into gradually section which depends on the thermal dilfusiv-ity. Different temperatures on both sides of the wall cause the buckling of the element toward the area where the high temperatures are produced. [10]. 

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