• International journal of steel structures
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• v.18 no.4
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• pp.1440-1463
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• 2018

The Wagner coefficient is a key parameter used to describe the inelastic lateral-torsional buckling (LTB) behaviour of the I-beam, since even for a doubly-symmetric I-section with residual stress, it becomes a monosymmetric I-section due to the characteristics of the non-symmetrical distribution of plastic regions. However, so far no theoretical derivation on the energy equation and Wagner's coefficient have been presented due to the limitation of Vlasov's buckling theory. In order to simplify the nonlinear analysis and calculation, this paper presents a simplified mechanical model and an analytical solution for doubly-symmetric I-beams under pure bending, in which residual stresses and yielding are taken into account. According to the plate-beam theory proposed by the lead author, the energy equation for the inelastic LTB of an I-beam is derived in detail, using only the Euler-Bernoulli beam model and the Kirchhoff-plate model. In this derivation, the concept of the instantaneous shear centre is used and its position can be determined naturally by the condition that the coefficient of the cross-term in the strain energy should be zero; formulae for both the critical moment and the corresponding critical beam length are proposed based upon the analytical buckling equation. An analytical formula of the Wagner coefficient is obtained and the validity of Wagner hypothesis is reconfirmed. Finally, the accuracy of the analytical solution is verified by a FEM solution based upon a bi-modulus model of I-beams. It is found that the critical moments given by the analytical solution almost is identical to those given by Trahair's formulae, and hence the analytical solution can be used as a benchmark to verify the results obtained by other numerical algorithms for inelastic LTB behaviour.

• Journal of Communications and Networks
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• v.6 no.3
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• pp.258-268
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• 2004

We demonstrate rotationally invariant space-time (ST) trellis codes with a 4-D rectangular signal constellation for data transmission over fading channels using two transmit antennas. The rotational invariance is a good property to have that may alleviate the task of the carrier phase tracking circuit in the receiver. The transmitted data stream is segmented into eight bit blocks and quadrature amplitude modulated using a 256 point 4-D signal constellation whose 2-D constituent constellation is a 16 point square constellation doubly partitioned. The 4-D signal constellation is simply the Cartesian product of the 2-D signal constellation with it-self and has 32 subsets. The partition is performed on one side into four subsets A, B, C, and D with increased minimum-squared Euclidian distance, and on the other side into four rings, where each ring includes four points of equal energy. We propose both linear and nonlinear ST trellis codes and perform simulations using an appropriate multiple-input multiple-output (MIMO) channel model. The 4-D ST codes constructed here demonstrate about the same frame error rate (FER) performance as their 2-D counterparts, having however the added value of rotational invariance.

• Structural Engineering and Mechanics
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• v.6 no.3
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• pp.305-325
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• 1998

A method that determines the minimum stiffness of baracing to achieve non-sway buckling conditions at a given story level of a multi-column elastic frame is proposed. Condensed equations that evaluate the required minimum stiffness of the lateral and torsional bracing are derived using the classical stability functions. The proposed method is applicable to elastic framed structures with rigid, semirigid, and simple connections. It is shown that the minimum stiffness of the bracing required by a multi-column system depends on: 1) the plan layout of the columns; 2) the variation in height and cross sectional properties among the columns; 3) the applied axial load pattern on the columns; 4) the lack of symmetry in the loading pattern, column layout, column sizes and heights that cause torsion-sway and its effects on the flexural bucking capacity; and 5) the flexural and torsional end restrains of the columns. The proposed method is limited to elastic framed structures with columns of doubly symmetrical cross section with their principal axes parallel to the global axes. However, it can be applied to inelastic structures when the nonlinear behavior is concentrated at the end connections. The effects of axial deformations in beams and columns are neglected. Three examples are presented in detail to show the effectiveness of the proposed method.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.37 no.2
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• pp.357-367
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• 2017

Bending and axial forces simultaneously occur at the cross-section of a shotcrete lining reinforced with steel supports due to the tunnel geometry. The shotcrete has changing flexural stiffness depending on the axial forces and, as a result, severely nonlinear behavior. The mechanical properties of a shotcrete-steel composite also depend on the type of steel support. This study presents a fiber section element model considering the effect of axial force to evaluate the nonlinear behavior of a shotcrete-steel composite. Additionally, the model was used to analyze the effects of different types of steel supports on the load capacity. Furthermore, a modified hyperbolic model for ground reaction, including strain-softening, is proposed to account for the ground-lining interaction. The model was validated by comparing the numerical results with results from previous load test performed on arched shotcrete specimens. The changes in mechanical responses of the lining were also investigated. Results show a lining with doubly reinforcement rebar has similar load capacity as a lining with H-shaped supports. The use of more materials for the steel support enhances the residual resistance. For all types of steel reinforcement, the contribution of steel supports during peak load decreases as the ground becomes stiffer.