Keywords: bracing patterns, simple frames, lateral stiffness, braced panels, bracing orientation.

Bracing systems have been widely used in tall buildings, temporary grandstands, scaffolding and similar structures for increasing their lateral stiffness. It has been conceptually identified and experimentally verified that a four-bay and four-storey frame using the X bracing arrangement is significantly stiffer than the same frame using conventional bracing arrangements [1]. However, it is not clear whether the frame using the X bracing is the stiffest of all possible braced frames. This paper conducts a thorough study of all possible bracing arrangements of the four-bay and four-storey frame for identifying the best bracing pattern and for developing design criteria that can make the frame stiffer. Considering the case that two bracing members are placed in each of the four storeys and each bracing member can be arranged in either forward or backward direction. This leads to 331,776 options. These cases are analysed using ANYSY and the twelve stiffest and twelve least stiff frames are examined. As bracing members are often arranged in a symmetrical manner, all possible 256 symmetrically braced frames of the 331,776 cases are then studied in more detail using both numerical and analytical methods. The lateral displacement of the frame is decomposed into those contributed by the horizontal, vertical and bracing members. This allows a close examination of the effect of the three types of member on the lateral stiffness. Then the relationships between the lateral stiffness, internal forces and bracing patterns of the frame are studied.

The study of the best and worst scenarios helps to identify what should be done and what should be avoided. It is found that bracing arrangements can be conducted in two steps:

1. The correct selection of braced panels can effectively avoid large internal forces in vertical members. The measures include: a) diagonal braced panels should be selected where possible, and b) independent vertical braced panels should be avoided.
2. The correct selection of the orientation of bracing members in the given panels can reduce the number of non-zero forced horizontal and vertical members. The measures are: a) straight linked bracing members should be used where possible; b) parallel arrangement of bracing members should be avoided.

The outcome from this study is limited to the simple braced frame but some of the findings have the potential to be extended to more complicated frame structures.

1

T. Ji, "Concepts for designing stiffer structures", The Structural Engineer, 81(21), 36-42, 2003.

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