Columns slender

Column slenderness factor, (AISC LRFD, Equation E2-4)... 

The governing differential Equation (64) is solved using the Galerkin numerical method for the buckling loads. Finite element method using ANSYS software are included in the curves of the normalized buckling loads versus column slenderness are plotted in Figure 6. 

When the buekling load is smaller than the load that will cause the column to fail under compression, it is called a thin or slender column. If compressive failure oecurs first, it is ealled a short column. 

M.A. Cook H.E. Farnam, Jr, USP 3341382(1967) CA 67, 118758q (1967) (Boosters which insure complete expln and propagation the full length of slender columns of expls, are described. Suitable boosters for Inducing reliable propagation of AN-fuel oil mixts, AN-TNT-water mixts, AN-A1-TNT-water mixts and AN-Al-water mixts were found to be cast or pressed 50/50-Pentolite, pressed Tettyl, pressed RDX and pressed RDX (wax)... 

General buckling in a slender column with a slenderness ratio, L/D, greater than 100, occurs when it is subjected to a critical compressive load. This load is much lower than the maximum load allowable for compressive yield. Although this problem can be easily solved using Euler s equation1, which predicts the critical load applied to the slender column, it lends itself very well to illustrate dimensional analysis. 

Occasionally, long slender fractionating columns undergo periodic sway from the action of winds of moderate velocity. Sometimes the sway significantly stresses the shell or skirt at the base of the column. Since most vessels are designed to resist static loads caused by winds of over 100 mph, large vibratory sways caused by winds of low or... 

Blick, R.G. How to Calculate Wind-Caused Swa> on Slender Columns. Petroleum Refiner, November 1958, p. 237. 

Structural parameters such as the slenderness ratio frequently govern what can and cannot be done. An engineer would be hard pressed to find a reputable contractor willing to build a 40-m-long column, half a meter in diameter. 

For short and intermediate cylinders the critical stress is independent of length. For long cylinders the length of the cylinder is a key factor. The range of cylinders whose slenderness ratios are less than Euler s critical value are called short or intermediate columns. 

Column formulas are found in most machine and tooling hand books as well as strength of materials textbooks. Euler first published this critical-load formula for columns in year 1759. For slender columns it is usually expressed in the following form ... 

Euler s formula is strictly applicable to long and slender columns, for which the buckling action predominates over the direct compression action and thus makes no allowance for compressive stress. The slenderness ratio is defined as the ratio of length i to the radius of gyration represented as t/k. 

When the slenderness ratio exceeds a value of 100 for a strong shm column, failure by buckling can be expected. Columns of stiffer and more britde materials will buckle at lower slenderness ratios. The constant factor m in Euler s critical-load formula clearly shows that the failure of a column depends on the configuration of the column ends. The basic four types with their respective m are ... 

Table 7.13 shows cross sections of the three common slender column configurations. Formulas for each respective moment of inertia I and radius of gyration k are given. With the above formulas buckling force F can be calculated for a column configuration. Table 7.14 lists values of slim ratios (I/k) for small-nominal-diameter column lengths. 

Most failures with the slender columns occur because the slenderness ratio exceeds 100. The prudent designer devises ways to reduce or limit the slenderness ratio. 

Temperature-dependant material property models were implemented into stmc-tural theory to establish a mechanical response model for FRP composites under elevated temperatures and fire in this chapter. On the basis of the finite difference method, the modeling mechanical responses were calculated and further vaUdated through experimental results obtained from the exposure of full-scale FRP beam and column elements to mechanical loading and fire for up to 2 h. Because of the revealed vulnerabihty of thermal exposed FRP components in compression, compact and slender specimens were further examined and their mechanical responses and time-to-failure were well predicted by the proposed models. 

On the basis of the identified parameters kj, k2, and k-j, the reduction factors were obtained from Eq. (8.8) (0.317 for specimen P-WCl and 0.281 for P-WC2) and the ultimate loads were estimated as shown in Table 8.5 [14]. The predicted values difiered by less than 5% from the experimental ones. The values for P-REF, given in Table 8.5, were directly taken from the column curves in [17] according to its nondimensional slenderness. 

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