Understanding Cable Profiles in Structural Engineering

The shape a flexible cable takes when supporting loads depends entirely on the type of load distribution along its span. Different load types result in distinct cable profiles.

• Catenary: A cable hanging freely under its own weight (a uniformly distributed load along the length of the cable itself) forms a catenary curve.
• Parabola: If a cable supports a load that is uniformly distributed horizontally (like the deck of a suspension bridge, simplified), it forms a parabolic shape.
• Polygon: When a cable supports concentrated loads (point loads) at specific points along its length, the cable forms a series of straight line segments between the points of load application and the support points. This shape is generally referred to as a polygonal shape.

Cable Supporting Concentrated Loads

In the case where a beam supports concentrated loads and is itself supported by a cable, the cable effectively carries these concentrated loads transferred from the beam. Since the loads are applied at discrete points, the cable profile will be composed of straight lines between the points where the loads are attached to the cable and the cable's support points.

Shape of Cable Profile with Two Concentrated Loads

If a beam supports two concentrated loads, and this beam is hung from a cable, the cable will support the beam at two specific points (or possibly more, depending on how the beam is attached). Assuming the cable supports the beam at points directly above or near where the concentrated loads are applied, the cable profile will consist of three straight segments:

1. A segment from the first support point of the cable to the point where the first concentrated load (via the beam) is attached.
2. A segment between the points where the two concentrated loads (via the beam) are attached.
3. A segment from the point where the second concentrated load (via the beam) is attached to the second support point of the cable.

These three straight segments form a polygonal shape. In the specific case of two concentrated loads, the resulting three-segment profile, especially if the supports are at the same height and the loads are symmetrically placed, often resembles a trapezoid when viewed in profile, where the middle segment is approximately horizontal (if the loads are symmetric and heavy) and the outer segments slope upwards to the supports. While technically a three-sided polygon, the term 'Trapezoidal' is used here to describe this specific multi-linear profile formed by straight segments under two concentrated loads, differentiating it from curved shapes like parabolic or catenary profiles.

Therefore, when a beam supporting two concentrated loads is supported by a cable, the cable follows a shape composed of straight line segments, which is best described among the given options as Trapezoidal.