BUCKLING AND THEIR SECOND-ORDER EFFECT OF DUAL SYSTEMS CONSISTING OF TWO SHEAR-FLEXURAL STRUCTURES

A closed form of solution for the buckling of dual systems consisting of two shear-flexural structures is provided, and a simple formula for the total buckling load is obtained. It is found that the total buckling load is simply a summation of the buckling loads of two component structures when they work independently, and it is independent of the distribution of vertical loads among the two structures.
Linear and second-order analyses are carried out for dual systems loaded by uniform horizontal forces along height and vertical loads at the top. Amplification factors for the lateral displacements and bending moments are analyzed, a simple formula is suggested. The proposed formula is very accurate in predicting the total lateral displacement at the top of the system and slightly greater if used for displacements below the top. It has also acceptable accuracy for either bending moments of component structures as a whole or bending moments of columns when the component structure is a frame: it is slightly greater for bending moments below 2/3 of the total height, and slightly smaller for the top 1/3 height. From the derivation it is also found that the various amplification factors are also independent of the distribution of vertical loads among the two structures.