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In a next phase the forces caused by wind must be considered. Wind will cause pressure on the upwind side of a roof (and truss) and suction on the downwind side. This will translate to asymmetrical loads but the Cremona method is the same. Wind force may introduce larger forces in the individual truss members than the static vertical loads.
Most trusses use gusset plates to connect intersecting elements. Gusset plates are relatively flexible and unable to transfer bending moments. The connection is usually arranged so that the lines of force in the members are coincident at the joint thus allowing the truss members to act in pure tension or compression.
The Unit dummy force method provides a convenient means for computing displacements in structural systems. It is applicable for both linear and non-linear material behaviours as well as for systems subject to environmental effects, and hence more general than Castigliano's second theorem.
Each element is then analyzed individually to develop member stiffness equations. The forces and displacements are related through the element stiffness matrix which depends on the geometry and properties of the element. A truss element can only transmit forces in compression or tension.
Michell structures are structures that are optimal based on the criteria defined by A.G.M. Michell in his frequently referenced 1904 paper. [1]Michell states that “a frame (today called truss) (is optimal) attains the limit of economy of material possible in any frame-structure under the same applied forces, if the space occupied by it can be subjected to an appropriate small deformation ...
(It may be necessary to calculate the stress to which it is subjected, for example.) On the right, the red cylinder has become the free body. In figure 2, the interest has shifted to just the left half of the red cylinder and so now it is the free body on the right. The example illustrates the context sensitivity of the term "free body".
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In other words, the summation of the work done on the system by the set of external forces is equal to the work stored as strain energy in the elements that make up the system. The virtual internal work in the right-hand-side of the above equation may be found by summing the virtual work done on the individual elements.