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Forces in a Roof Truss with a Central and Wind Load

Forces in a Roof Truss with a Central and Wind Load

Theoretical Results

A truss that is assumed to comprise members that are connected by means of pin joints, and which is supported at both ends by means of hinged joints or rollers, is described as being statically determinate. Newton's Laws apply to the structure as a whole, as well as to each node or joint. In order for any node that may be subject to an external load or force to remain static in space, the following conditions must hold: the sums of all horizontal forces, all vertical forces, as well as all moments acting about the node equal zero (Ceulemans & Fowler, 1991: 52). Analysis of these conditions at each node yields the magnitude of the forces in each member of the truss. These may be compression or tension forces.

Trusses that are supported at more than two positions are said to be statically indeterminate, and the application of Newton's Laws alone is not sufficient to determine the member forces. In order for a truss with pin-connected members to be stable, it must be entirely composed of triangles. In mathematical terms, we have the following necessary condition for stability:

M +R = 2j

Where,

m =total number of truss members

j= total number of joints

r= number of reactions (equal to 3 generally)

When m = 2j - 3, the truss is said to be statically determinate, because the (m+3) internal member forces and support reactions can then be completely determined by 2j equilibrium equations, once we know the external loads and the geometry of the truss. Given a certain number of joints, this is the minimum number of members, in the sense that if any member is taken out (or fails), then the truss as a whole fails. While the relation (a) is necessary, it is not sufficient for stability, which also depends on the truss geometry, support conditions and the load carrying capacity of the members (Ceulemans & Chibotaru, 1999: 6916).

Some structures are built with more than this minimum number of truss members. Those structures may survive even when some of the members fail. They are called statically indeterminate structures, because their member forces depend on the relative stiffness of the members, in addition to the equilibrium condition described.

In a statically Indeterminate truss, static equilibrium alone cannot be used to calculated member force. If we were to try, we would find that there would be too many “unknowns” and we would not be able to complete the calculations (Calladine, 1978: 161). Instead we will use a method known as the flexibility method, which uses an idea know as strain energy.

Application of Truss

Trusses able to allows for the analysis of the structure uses a few assumptions and the application of Newton's laws of motion according to branch of physics known as static (Connelly & Fowler, 2009: 762). Trusses are assumed to be pin jointed where the straight components meet for purposes of ...

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