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Recent research in engineering seismology demonstrated that in addition to three translational seismic excitations along x, y and z axes, one should also consider rotational components about these axes when calculating design seismic loads for structures. The objective of this paper is to present the results of a seismic response numerical analysis of a mine tower (also called in the literature a headframe or a pit frame). These structures are used in deep mining on the ground surface to hoist output (e.g. copper ore or coal). The mine towers belong to the tall, slender structures, for which rocking excitations may be important. In the numerical example, a typical steel headframe 64 m high is analysed under two records of simultaneous rocking and horizontal seismic action of an induced mine shock and a natural earthquake. As a result, a complicated interaction of rocking seismic effects with horizontal excitations is observed. The contribution of the rocking component may sometimes reduce the overall seismic response, but in most cases, it substantially increases the seismic response of the analysed headframe. It is concluded that in the analysed case of the 64 m mining tower, the seismic response, including the rocking ground motion effects, may increase up to 31% (for natural earthquake ground motion) or even up to 135% (for mining-induced, rockburst seismic effects). This means that not only in the case of the design of very tall buildings or industrial chimneys but also for specific yet very common structures like mine towers, including the rotational seismic effects may play an important role.

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A procedure for critical buckling moment of a tapered beam is proposed with the application of potential energy calculations using Ritz method. Respective solution allows to obtain critical moments initiating lateral buckling of the simply supported, modestly tapered steel I-beams. In particular, lateral-torsional buckling of beams with simultaneously tapered flanges and the web are considered. Detailed, numerical, parametric analyses are carried out. Typical engineering, uniformly distributed design loads are considered for three cases of the load, applied to the top flange, shear centre, as well as to the bottom flange. In addition simply supported beam under gradient moments is investigated. The parametric analysis of simultaneously tapered beam flanges and the web, demonstrates that tapering of flanges influences much more the critical moments than tapering of the web.