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.

本文提出了一种图形方法，用于确定预应力桁架的线性刚度和稳定性，该桁架由在销接头处连接的刚性杆组成，并且具有运动自由度。构造的关键是矩形区域，它结合了统一麦克斯韦-闵可夫斯基图中的倒数形式和力图。每个这样的矩形的面积是杆张力和杆长度的乘积，并且这对应于由于其承载的轴向力而产生的杆的旋转刚度。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。该方法被推广到描述二维桁架的面外稳定性，并一般描述三维桁架。该论文还给出了 Pellegrino 和 Calladine 引入的“积力”的图形表示，用于描述桁架的预应力稳定性。