5. CABLES

A cable is a slender flexible member with zero or negligible flexural stiffness, thus it can only transmit tensile forces.

Cables are specialized structures designed to handle forces that only pull or stretch them, rather than pushing or bending them. This characteristic makes them particularly useful in various engineering applications, especially in structures like bridges or tents.

Consider a piece of string. When you pull on it (applying a tensile force), it remains straight. However, if you try to push down on it, the string bends and collapses. This reflects how cables operate: they work best under tension.

The tensile force at any point acts in the direction of the tangent to the cable.

When a cable is under tension, the forces exerted on it can be visualized as arrows pointing in the direction that the cable is being pulled. This movement along the tangent ensures that the cable does not bend, which would cause it to fail since it cannot handle compressive forces.

Imagine holding a rubber band at both ends. As you stretch it, the tension pulls in a straight line along its length. If you were to push down on it, it would lose its shape and snap, similar to what happens if a cable is improperly loaded.

Its strength stems from its ability to undergo extensive changes in slope at the point of load application.

When a load is applied to a cable, it doesn't just hang straight down; instead, it sags, forming a curve that distributes the load along its length. This ability to change shape allows the cable to effectively manage the forces acting upon it without breaking.

Think of a hammock. When you sit in it, the fabric sags in the middle, allowing it to safely support your weight. The way the hammock changes shape demonstrates how cables also adapt under load.

Cables resist vertical forces by undergoing sag (h) and thus developing tensile forces. The horizontal component of this force (H) is called thrust.

When a cable sags due to vertical loads, it creates a tension that pulls upwards to counteract the load. This horizontal force, known as thrust, acts parallel to the supports of the cable. Understanding the relationship between sag and thrust is essential for designing stable structures.

Consider a tightrope walker. The tighter the rope (less sag), the more stable the walker's position. If the rope sags too much under their weight, it could become dangerous, similar to how cables function under load.

The distance between the cable supports is called the chord. The sag to span ratio is denoted by h/r = (h/l).

The chord of a cable is simply the straight line distance between two points of support. The sag-to-span ratio indicates how much the cable sags relative to the distance between supports. This ratio is crucial for ensuring that the cable can withstand expected loads without fully collapsing or losing its shape.

Imagine holding a taut rope between two poles. If the rope is perfectly horizontal with no sag, that's a span with a ratio of zero. Now, if you dip the center of the rope down into a 'U' shape, you've introduced sag—this change affects how the rope behaves under weight, just like in cable systems.

When a set of concentrated loads is applied to a cable of negligible weight, then the cable deflects into a series of linear segments and the resulting shape is called the funicular polygon.

In situations with specific concentrated loads, cables do not form a smooth curve but instead create a series of straight lines connecting the points of tension. This arrangement, known as the funicular polygon, is a useful geometric representation of how the cable behaves under these conditions.

Imagine a series of points connected by strings, like a puppet on strings where each string is taut. Each segment represents a portion of the cable between loads. The overall shape helps visualize how tension and loads interact within the system.

If a cable supports vertical forces only, then the horizontal component H of the cable tension T remains constant.

In the scenario where a cable is only subjected to vertical loads, whatever horizontal forces are present will stay unchanged. This principle is key to understanding how cables distribute forces, as it helps stabilize the structure by balancing these horizontal tensions.

Think about a tightrope walker again—while they may shift their weight (vertical load) while walking, the rope's tension stays consistent horizontally, providing the support needed for balance.

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