McRobie Allan, Millar Cameron, Baker William F
Cambridge University Engineering Department, Trumpington St, Cambridge CB2 1PZ, UK.
Skidmore Owings and Merrill, Chicago, IL, USA.
R Soc Open Sci. 2021 Jun 9;8(6):201970. doi: 10.1098/rsos.201970.
This paper presents a graphical method for determining the linearized stiffness and stability of prestressed trusses consisting of rigid bars connected at pinned joints and which possess kinematic freedoms. Key to the construction are the rectangular areas which combine the reciprocal form and force diagrams in the unified Maxwell-Minkowski diagram. The area of each such rectangle is the product of the bar tension and the bar length, and this corresponds to the rotational stiffness of the bar that arises due to the axial force that it carries. The prestress stability of any kinematic freedom may then be assessed using a weighted sum of these areas. The method is generalized to describe the out-of-plane stability of two-dimensional trusses, and to describe three-dimensional trusses in general. The paper also gives a graphical representation of the 'product forces' that were introduced by Pellegrino and Calladine to describe the prestress stability of trusses.
本文提出了一种图解方法，用于确定由在铰接点连接且具有运动自由度的刚性杆组成的预应力桁架的线性化刚度和稳定性。该构造的关键在于矩形区域，这些区域在统一的麦克斯韦 - 明科夫斯基图中结合了互易形式和力的图示。每个这样的矩形的面积是杆拉力与杆长度的乘积，这对应于由于杆所承受的轴向力而产生的杆的转动刚度。然后，可以使用这些面积的加权和来评估任何运动自由度的预应力稳定性。该方法被推广用于描述二维桁架的平面外稳定性，并一般地描述三维桁架。本文还给出了由佩莱格里诺和卡拉丹引入的用于描述桁架预应力稳定性的“乘积力”的图形表示。
