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Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
A column is an initially straight load-carrying member that is subjected to a compressive axial load. The failure of a column in compression is different from one loaded in tension. Under compression, a column can deform laterally or buckle, and this deflection can become excessive. The buckling of columns is a major cause of failure. To illustrate the fundamental aspects of the buckling of long, straight, prismatic bars, consider a thin meter stick. If a tensile axial load is applied to the meter stick, the stable equilibrium position is that of a straight line. If the stick is given a momentary side load to cause a lateral deflection, upon its release the stick immediately returns to the straight line configuration. If a compressive axial load is applied, a different result may occur. At small axial loads, the meter stick will again return to a straight line configuration after being displaced laterally. At larger loads the meter stick will remain in the displaced position. With an attempt to increase the axial load acting on the buckled column, the lateral deformations become excessive and failure occurs.
Elastic Rods Subjected to General Loading
Published in Abdel-Rahman Ragab, Salah Eldin Bayoumi, Engineering Solid Mechanics, 2018
Abdel-Rahman Ragab, Salah Eldin Bayoumi
A column is a bar subjected to an axial compressive force. Under such loading, a slender column may be unstable and buckle. Consider a long, slender rod (column) subjected to an axial force P, as shown in Figure 7.49a. If the rod is ideal in all respects, e.g., homogeneity of material, straightness, and so forth, and the force P is applied in an absolutely concentric manner, the rod will remain in equilibrium in a straight configuration under any value for the force P. In this case, the rod is subjected to the compressive stress σ = P/A and undergoes an axial deformation ε = P/AE, where A is the rod cross-sectional area and E is the material modulus of elasticity. However, a slight misalignment in load coaxiality or any small lateral disturbance (say, a small lateral force Q) will cause the rod to bend to the deflected shape shown in Figure 7.49a. As soon as the disturbing force Q is removed, the rod returns to its straight equilibrium position if the value of the applied force P is small. By increasing P to reach a certain critical value Pcr, the rod will not return to its straight position and will continue to remain in equilibrium in the slightly bent or buckled form resulting from Pcr only. Further increase of the compressive load will cause the lateral deflection to increase, producing collapse of the bar.
Structural Systems for Tall Buildings
Published in Kyoung Sun Moon, Cantilever Architecture, 2018
For both the gravity and lateral loads, progressively larger column sizes are required towards the base of the building. The size of the columns is mainly determined by the gravity loads that accumulate towards the base of the building. Column sizes determined for the gravity loads may need to be increased to provide the required lateral stiffness of the MRF. Examples of MRFs include the 26-story tall Lake Shore Drive Apartments in Chicago designed by Ludwig Mies van der Rohe, the 19-story tall One Park Place (formerly known as Business Men’s Assurance Tower) in Kansas City designed by Skidmore, Owings and Merrill, and the 27-story tall Tokyo Marine Building in Osaka designed by Kajima Design.
Experimental tests and numerical simulation of eccentrically loaded SRRC filled square steel tube columns
Published in Journal of Asian Architecture and Building Engineering, 2022
Hui Ma, Guoheng Zhang, Zhonghui Xie, Yanan Wu, Yanli Zhao
The final failure patterns of the eccentrically loaded SRRC-filled square steel tube columns are described in Figure 3. In general, the failure patterns of the eccentrically loaded columns can be summarized as a compression bending failure subjected to the eccentric compression loads. The main failure characteristics of eccentrically loaded columns can be described as the profile steel first yielded, then internal RAC was crushed, and finally the square steel tube yielded under eccentric compression loading. Moreover, the external square steel tube has a good restraining effect binding force on the internal RAC. In addition, square steel tube and profile steel also effectively delayed the cracking of RAC and improved the stiffness and bearing capacity of eccentrically loaded columns.
Optimisation of life-of-mine production scheduling for block-caving mines under mineral resource and material mixing uncertainty
Published in International Journal of Mining, Reclamation and Environment, 2022
Roberto Noriega, Yashar Pourrahimian, Eugene Ben-Awuah
Production scheduling is carried out over a 10 year horizon, in this particular case selected to be able to experiment extensively, however could be extended for longer periods to cover the life-of-mine. The production unit dimensions for aggregating resource blocks into columns are set at 20 m by 30 m to represent column extraction units in caving mines. The maximum column height is set at 300 m with a minimum column height of 60 m. These guarantee that if the optimisation model decides to open up a production unit at the undercut level, it will draw material from it until at least a height of 60 m and up to 300 m with the capability of stopping anywhere in between. The maximum adjacent relative height of draw, which represents the difference in the height of draw between a given PU and its adjacent ones, is set to 60 m. The selected PU dimensions provide a cave back slope of between 60° to 70°. The minimum draw rate per column is set to 70 kton/period, which is equivalent to a draw height of 30 m, with a maximum draw rate of 140 kton/period equivalent to a 60 m draw height. These parameters would be adjusted to reflect a given project’s geotechnical environment to guarantee good flow conditions for the broken ore. Based on these dimensions, the case study comprises 108 PU, representing drawpoints, and 864 MU representing slices to be extracted. The maximum undercutting rate is set at 9600 m2/period, which restricts the amount of PU and undercut area that can be developed in any given period.
Axial Load-Capacity of Bamboo-Steel Reinforced Cement Stabilised Rammed Earth Columns
Published in Structural Engineering International, 2019
Deb Dulal Tripura, Konjengbam Darunkumar Singh
Design of the column was as per NZS 4297.14 If the design axial load (N*) on the member cross section was less than 0.5 feAg, then the member shall be designed as a column. Minimum column dimensions shall be 250 mm square if reinforced, 580 mm square if unreinforced. The maximum slenderness ratio (Sr) of a column for earthquake zone factor: Z ≤ 0.6 and Z > 0.6 are (a) 4 and 3 for an unreinforced column; and (b) 8 and 6 for a reinforced column respectively. A column flue containing four bars shall have minimum clear flue dimensions of 150 mm x 150 mm. The diameter of longitudinal reinforcement used in a column shall not be greater than 16 mm and the minimum longitudinal reinforcement for a column shall be one bar of 12 mm diameter. It is to be noted that no guidelines have been provided on the use of lateral reinforcement/ties in the columns in this standard. Therefore, an attempt has been made to study the effect of lateral ties in the current research. It has been found to improve the axial load capacity of the columns as explained in earlier sections, and this kind of column can be used as shown in Fig. 1a.