4.1.1. Assumptions

Cables and trusses are 2D or 3D structures composed of an assemblage of simple one-dimensional components which transfer only axial forces along their axis. Cables can carry only tensile forces, trusses can carry tensile and compressive forces.

Cables and trusses are essential structures found in engineering. They can exist in two dimensions (2D) or three dimensions (3D). Both are made up of individual, straight components, referred to as members or elements. These members are designed to only handle axial forces, meaning the forces act along the length of the members.

Cables are particularly noted for their ability to carry tensile forces, which means they are pulled or stretched. In contrast, trusses can handle both tension (being pulled) and compression (being pushed). This distinction is crucial because it influences their design and applications in various structures.

Think of a suspension bridge. The cables act like strong strings that hold the bridge up, only stretching as they carry weight. Meanwhile, the trusses that make up the support structures can both hold weight (compression) and stretch (tension), allowing the bridge to remain stable under various loads.

Cables tend to be flexible, and hence, they tend to oscillate and therefore must be stiffened. Trusses are extensively used for bridges, long span roofs, electric towers, and space structures.

Cables, due to their flexible nature, can sway or oscillate when subjected to dynamic loads like wind or traffic. To counter this movement and enhance stability, cables often need to be made stiffer, which can involve the use of additional supporting structures or cross-bracing.

On the other hand, trusses are more rigid and are commonly used in a variety of important structures, including bridges, where they provide essential load support over long distances, large roofs that require structural integrity, electric towers that need to support heavy cables, and even in space structures like satellites due to their ability to distribute loads efficiently.

Imagine a tightrope walker using a pole; the pole acts like a truss, helping to keep balance and distribute weight. If the tightrope was made of rubber (like a cable), it would be hard to maintain balance due to its flexibility, just as cables must be stiffened to reduce swaying.

For trusses, it is assumed that:

1. Bars are pin-connected.
2. Joints are frictionless hinges.
3. Loads are applied at the joints only.

In analyzing and designing trusses, certain key assumptions are made:

1. Bars are pin-connected: This means each member of the truss connects to another member at a joint, allowing rotation but not movement. This simplifies calculations.
2. Joints are frictionless hinges: The assumption of no friction at the joints ensures that the forces can be easily transferred between members without energy loss.
3. Loads are applied at the joints only: This assumption helps in determining how forces are transmitted through the truss efficiently, focusing only on the points where loads are applied instead of along the members themselves.

Consider a tent supported by poles. If the poles are connected at the top like pins, they can pivot without losing structural integrity, much like the bars in a truss. Similarly, if people hang weights at the top of the poles (joints), the forces can be easily analyzed where they act.

A truss would typically be composed of triangular elements with the bars on the upper chord under compression and those along the lower chord under tension. Depending on the orientation of the diagonals, they can be under either tension or compression.

Trusses are commonly designed with triangular shapes because triangles provide inherent stability. In a standard truss, the upper members (or chord) generally experience compressive forces while the lower members handle tensile forces. The diagonal members can be under either tension or compression, depending on their angle and placement within the structure. This design allows for optimal load distribution across the entire truss.

Think of a children's toy made from triangle-shaped blocks. When they form a stable base, they support weight effectively. The top 'crossbars' pushing down illustrate how the upper chords are under compression, while the base pulls up, mimicking tension in the lower members. This way, the entire structure stays solid and balanced, just like real trusses.

It can be easily determined that in a Pratt truss, the diagonal members are under tension, while in a Howe truss, they are in compression. Thus, the Pratt design is an excellent choice for steel whose members are slender and long diagonal members being in tension are not prone to buckling. The vertical members are less likely to buckle because they are shorter. On the other hand, the Howe truss is often preferred for heavy timber trusses.

There are different designs of trusses, such as the Pratt and Howe trusses:

• Pratt Truss: In this configuration, the diagonals are positioned to handle tension. This design works well with steel, particularly for narrow or slender members that can efficiently carry loads without buckling under tension.
• Howe Truss: Conversely, in a Howe truss, the diagonals are under compression, making it suitable for sturdier materials like timber which are less vulnerable to buckling. This design takes advantage of the strength properties of the material used.

Imagine a bicycle wheel. The spokes can either pull (tension) or push (compression) depending on how the wheel is designed and used. A Pratt truss is like a wheel with tightly pulled spokes that support weight well but need to be strong against tension. A Howe truss is more like a solid wooden frame that can push back against weights, thus being useful in constructing things like large barns.

In a truss analysis or design, we seek to determine the internal force along each member.

The ultimate goal in analyzing trusses is to calculate the internal forces acting on each member. This information is essential for ensuring the structure can withstand the loads it will encounter. By understanding how forces are distributed among the members, engineers can optimize material use, ensure safety, and design effective trusses for various applications.

Consider a suspension bridge; engineers analyze the forces on each cable and truss member to ensure they can handle heavy traffic and environmental stresses. They track how each code translates into actual tension and compression, similar to how you’d check the health of each ingredient in a recipe to make sure your final dish turns out perfectly.

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