Euler buckling

Manufacturing cost (cost/area) Installation and operating cost Compressive creep resistance Euler buckling resistance... 

Euler buckling theory predicts collapse at a constant force. However, finite element analysis (FEA) shows that the onset of buckling causes the load bearing capacity to decrease (Fig. 8.8). At high axial deflections, plastic hinges develop at mid-length and the ends of these slender struts. 

The lateral bending stifihess ofthe plate girder bridge is quite small in comparison to the axial stiffness (1 x EA = 3.255 GNm ) or the Euler buckling load of each span. So when the piers try to rotate about their cross-sectional axis, the superstructure i.e. bridge deck offers least resistance. 

Modeling of Time-Dependent Euler Buckling Load... 

Assuming the specimen as a hinged column, the time-dependent Euler buckling load, P (tf), can be expressed as... 

Figure 7.11 Modeling results for shift of neutral axis and decrease of Euler buckling load with time [17]. (With permission from ASCE.)...

The calculated lateral deformation caused by eccentricity rapidly increased for the NC specimen. A slightly slower decrease was obtained between 15 and 20 min when the stiffness of the inner face sheet was lost (see also slower decrease of Euler buckling load at this time step in Figure 7.11). The increase in deflection was much less pronounced in the case of the WC specimen. 

The noncooled specimen NC failed after 49min of ISO fire exposure. Owing to the fact that the nondimensional slenderness rapidly increased to a high value of 5.6, the ultimate load converged to the Euler buckling load. The time-to-failure prediction could therefore be based on the Euler buckling load prediction. 

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]. 

Figure 8.21 Recovery of Euler buckling loads as function of fire exposure duration for non-...

Sears and Batra [45] 2006 MM3 class n pair wise potential, FEM, equivalent continuum structures using Euler buckling theory Various zigzag CNTs 5 0 -350A — Buckling of axially compressed multiwaUed carbon nanotubes by using molecular mechanics simulations and developing continuum structures equivalent to the nanotubes... 

Barbero E and Tomblin J (1993), Euler buckling of thin-walled composite colunms, Thin-Walled Structures, Vol. 17, No. 4, pp. 237-258. 

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