These days, for structures ranging from the smaller roof systems to the bigger bridges, a truss is used as the main structural system, in order to carry loads and transfer to the supporting system. It is also an ideal solution for structures having large spans.
Let us define, what a Truss is.
A truss is an assemblage of interconnected straight members, jointed at their ends by ﬂexible connections to form a rigid conﬁguration. Because of their lightweight and high strength, trusses are widely used, and their applications range from supporting bridges and roofs of buildings. The only resulted in internal members’ forces are Axial forces.
The reason why it is mentioned as a ‘two-forces members’ is because of the individual member forming the system is only capable of restraining forces (no moments) acting on it in only two locations, particularly at the end of the members. Each member is connected by means of a hinge joint where no moment is restrained at every joint.
Stability of Trusses
Likewise, any other structures, a truss can be unstable both internally or externally. An internally unstable truss is a system that cannot maintain its shape or may undergo large displacement that can be considered unfunctional for operation when the supports are detached. Whereas externally unstable truss is a system that cannot offer enough means of external support to carry applied loads.
Internally stable/unstable truss systems
To find out the truss is stable or not internally, one has to first detach all the support and figure out that will not result in a change of the shape of the system just without any external load application.
- Internally stable truss systems
- Internally unstable truss systems
Externally stable/unstable structures
In order, to identifying trusses whether they are externally unstable or not, it is convenient to use the inequality equation provided below. This formulation is only specific to coplanar trusses, where all members are located in a given single plane. the inequality check was meant to verify that all the support reactions [forces/momets] have to be greater than or equal three in order for the system to be in equilibrium.
i.e. r < 3, the structure is considered as an unstable.
where r is the number of support reactions.
- An externally stable truss system
- An externally unstable truss system
Here one has to note that, externally unstable truss are classified according to the above inequality equation for a coplanar truss, only if all the loads are applied at any angle. For instance, the truss above can be externally stable eventhough the reaction are less than 3 as long as all the apllied loads are in the verical directions.
Types of truss
Truss can be classified as a plane or space truss depending on whether all the members and applied loads are on single or multi-plane. Plane trusses are those were all the members and forces are located on a single plane, and such trusses are mainly used in a roof a building and deck supporting bridges.
Whereas, Space trusses are structural systems with all members and applied loads are on a three-dimensional plane. The best examples for this truss types are transmission towers and lattice domes.
Further, plane trusses are also classified into different categories based on their geometrical configuration.
Analysis of statically determinate trusses
There are two methods for the analysis of statically determinate trusses.
- Joint Method
- Section Method
By statically determinate truss means if the forces in all its members, as well as all the external reactions, can be determined by using the equations of equilibrium. This can be verified using the following simple inequality of algebra.
i.e m= r + 2j
where m is the number of truss members,
r is the number of support reaction,
j is the number of joints.
The following assumption can be made;
- Members are connected by frictionless hinges.
- Loads are applied only at a joints
- Members centroidal axis coincides with a line connecting the centre of adjacent joints.
The joint method for analysis of trusses structures involves satisfying the equilibrium equations for each joint of the truss. These are the two equilibrium equations at a joint where the summation of forces in both orthogonal directions are zero.
i.e. ∑ Fx= 0 , and ∑ Fy= 0
the reason why the equilbrium equation is less three is because, hinge joints are not capable of restraining moment.
While using joint methods, it possible to assume all unknown member forces acting on the joint’s free body diagram to be in tension. Once the numerical solution of the equilibrium yields a positive member axial force, then our assumption is a correct that member is in tension, otherwise getting negative value will disprove the assumption and the member is in compression.
The section method which is also known as Ritter method after the German scientist August ritter who discovered the method. This method consists of passing an imaginary section through the truss, thus cutting it into two parts. This two parts should be in equilibrium as the whole truss is.
Right at the cut of a section, a third equilibrium equation of summation of a moment can be applied to compute the unknowns.
i.e. ∑ Fx= 0 , ∑ Fy= 0 ,and ∑ M= 0
In general, a section should pass through not more than three members in which the forces are unknown.
Tip: When applying the equilibrium equations, consider ways of writing the equations to yield a direct solution for each of the unknown, rather than to solve simultaneous equations.
Finally, Before ending my writing here, it is important to mention that a better understanding of how to analyze a truss structural system can be used as a tool for;
- Studying a diaphragm action of a floor slab for seismic/wind forces,
- Designing of D-regions in structural members like a pile-cap and corbel with a strut and tie method.