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supports etc. These models allow the observer to recognise and understand the types of stresses occurring in many of the members. The deformation due to loading of the display model in Fig. C 1.15 shows tensile stresses on the bottom and compressive stresses at the top of the beam. The stress types of further members may also be derived from the way in which the model deforms. Members that remain unstressed by external loading are called zero-force members. Under no circumstances, however, can these members be omitted: first, this would break the formation rules, making the truss
Types of member forces In determining the forces in the members, it may be helpful to first gain a qualitative overview. In general, truss members can experience three different kinds of stresses. Depending on the external loading of the truss, some members will be subject to tensile stresses, some to compressive stresses and some perhaps to no stresses at all (Fig. C 1.14). To identify the tensile or compressive stresses in members, it is often useful to employ display models that have a basic similarity to the truss in question, e.g. in terms of external forces, arrangement of
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The two zero-force members in Fig. C 1.14 can be identified on the basis of the second rule.
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C = compression member, T = tension member, 0 = zero-force member C 1.14
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unstable; second, different loading conditions will produce different member stresses. Many zero-force members can be recognised through simple rules: • If a node with two members has no external forces such as loads or support reactions acting on it, then both members are zero-force members. • If a node with two members is acted upon by an external force in the direction of one of the members, then the other member is a zero-force member. • If a node with three members has no external forces such as loads or support reactions acting on it, and if two of the three members share a common axis, then the third member is a zero-force member.
C 1.15
Magnitudes of member forces To pre-dimension the individual elements of the truss structure, it is necessary to estimate the magnitudes of the forces in the members. Various methods are available for determining both the qualitative and the quantitative forces in the individual members of a truss due to acting loads. Graphical methods are very illustrative. In these, all loads and member forces are represented as vectors. The foundational principle is the knowledge that, in the static resting state, every node of a truss is in equilibrium. This means that all external forces, reaction forces and member forces at the node balance each other out. The sum of the forces 6 Fi is therefore equal to zero at every node and also for the entire system (Fig. C 1.17 a). The first step, whenever possible, is to use the three equilibrium conditions 6 M = 0, 6 V = 0 and 6 H = 0 to find the support reactions. Then the forces of the members at the nodes can be graphically constructed