Effective buckling length of frames with tapered columns and partially tapered beams

2021 ◽  
Vol 187 ◽  
pp. 106993
Author(s):  
Sherif M. Ibrahim
Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 657
Author(s):  
Byoung Koo Lee ◽  
Joon Kyu Lee

This paper studies the buckling of standing columns under self-weight and tip load. An emphasis is placed on linearly tapered columns with regular polygons cross-section whose volume is constant. Five end conditions for columns are considered. The differential equation governing the buckling shapes of the column is derived based on the equilibrium equations of the buckled column elements. The governing equation is numerically integrated using the direct integration method, and the eigenvalue is obtained using the determinant search method. The accuracy of the method is verified against the existing solutions for particular cases. The effects of side number, taper ratio, self-weight, and end condition on the buckling load and mode shape are investigated. The contribution of self-weight acting alone to the buckling response is also explored. For a given column volume, especially, the buckling length and its stress distribution of the columns with different geometries and end conditions are estimated.


2003 ◽  
Vol 7 (3) ◽  
pp. 305-311 ◽  
Author(s):  
Byoung Koo Lee ◽  
Guangfan Li ◽  
Suk Ki Kim ◽  
Dae Soon Ahn

1989 ◽  
Vol 32 (6) ◽  
pp. 1217-1223
Author(s):  
Saeid Aboud AlGhamdi
Keyword(s):  

2000 ◽  
Vol 6 (2) ◽  
pp. 82-86 ◽  
Author(s):  
Vaidotas Šapalas

Two single-span frame tests were carried out. The width of frame is 6m, column's height 4.17m. Frame supports are pinned. Connection between column and beam is rigid. Beam of the frame was loaded with two vertical and one horizontal loads. The stability of tappered columns was analysed in frame plane and in perpendicular plane, according to [1] and [2] methods. All deflections were calculated taking into account support movements. During the first frame test R1-1 the tapered column collapsed at the load 2V=400kN and H=200 kN (vertical and horizontal loads). During the second test R1-2 the tapered column collapsed at the load 2V=390 kN and H=175 kN. In both tests columns collapsed in lateral-torsional buckling way. Because the column's web is very thin at the load 2V=300 kN and H=150 kN the column's web achieved local buckling. But the column was still carrying the load. During both tests at the load 2V=300 kN and H=150 kN the column began to twist in the middle of its height about the longitudinal axis and to bend about the weak axis. In test R1-1, the vertical experimental deflection (in point 6, see Fig 1 a) is about 17.5% smaller than the theoretical one. The horizontal experimental deflection (in point, see Fig 1 a) is about 11.6% smaller than the theoretical one. In test R1-2, vertical experimental deflection (in point 6, see Fig 1 a) is about 21.1% bigger than the theoretical one. The horizontal experimental deflection (in point, see Fig 1 a) is about 29.6% smaller than the theoretical one. In test R1-1, an experimental compression stresses in section A-A (see Fig 2) are about 11.2% smaller than the theoretical one. Experimental tension stresses in section A-A are about 8.65% smaller than the theoretical one. In test R1-2, an experimental compression stresses in section A-A is about 0.43% bigger than the theoretical one. An experimental tension strain in section A-A is about 1.73% smaller than the theoretical one.


2000 ◽  
Vol 6 (3) ◽  
pp. 158-161 ◽  
Author(s):  
Vaidotas Špalas ◽  
Audronis Kazimieras Kvedaras

In this paper, theoretical analysis of tapered column's bearing capacity is presented. A slender axially loaded column loses stability, when it achieves critical load (1). Critical load for uniform column can be calculated using L. Euler's formula (3). But this formula is only for uniform members. When we have non-uniform member, column's moment of inertia about strong axis (Fig 3) chances according to law (4). A. N. Dinik [4] suggested a differential equation (6) for non-uniform axially loaded member. So the critical load of tapered column can be calculated as for uniform member with additional factor K using (7) formula. Factor Kdepends only on the moments of inertia ratio (5) of column ends. In this paper, critical load of tapered column was calculated using FE program COSMOS/M. A lot of simulation were carried out with a wide range of moments of inertia ratio. From these simulations factor K was calculated (Fig 4 and Table 1) for axially loaded pin-end column. By computer simulation it was determined that factor K for pin-end column can also be used for other types of column support. After determining critical load, column slenderness (10) can be calculated using column's smallest cross-section A 1. Tapered column must satisfy (12) condition. A couple of examples (Table 2) with various moments of inertia ratio was solved. Three calculation methods were used: the author's suggested (Fig 5 curve 1): using [1, 2] method as for uniform member with the smallest column's cross-section geometrical characteristics (Fig 5 curve 2); and using [1, 2] method as for uniform member with average column's cross-section geometrical characteristics (Fig 5 curve 3). From Fig 5 we see that calculation of tapered column using methods for uniform members with average cross-section geometrical characteristics is not safe.


1976 ◽  
Vol 46 (3) ◽  
pp. 164-170 ◽  
Author(s):  
R. K. Singh ◽  
J. N. Vohra

A stuffer-box crimping unit was fabricated based upon the principle of heating, buckling, and cooling, and its process mechanics was evolved. Buckling theory was substantiated to negate the long-standing view of crumpling action inside the stuffing tube. Nylon 6 multifilament yarns of 70 den/17 fil and 105 den/17 fil were processed at 150, 170, and 190°C. The breaking load, buckling length, and crimp angle decreased with increase in temperature, while the denier, elongation, and work of extension at fifth cycle of loading showed an increase.


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