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Difficulty: HardStructural Components

A vertical communications mast features a rigid horizontal steel cross-arm extending outward to support a heavy dish antenna at its far end. To support the load, a diagonal steel cable connects the outer tip of the cross-arm to an anchor point higher up on the main mast. Assuming the weight of the cross-arm itself is negligible compared to the antenna, which of the following best describes the primary internal forces experienced by these two structural components?

  1. The cross-arm experiences compression, and the diagonal cable experiences tension.Answer
  2. B
    The cross-arm experiences tension, and the diagonal cable experiences compression.
  3. C
    Both the cross-arm and the diagonal cable experience tension.
  4. D
    The cross-arm experiences bending, and the diagonal cable experiences shear.

Answer

The cross-arm experiences compression, and the diagonal cable experiences tension.
The correct answer accurately applies static equilibrium to the joint supporting the antenna. The heavy antenna pulls straight down. To counteract this, the diagonal cable must pull diagonally upward and inward toward its anchor point on the mast. Because the cable pulls on the joint, it is in tension. However, this inward pull from the cable would drag the antenna toward the mast if unopposed. The rigid horizontal cross-arm prevents this by pushing outward against the joint. Because the cross-arm is being squeezed between the mast and the inward-pulling cable, it is under compression.

Step-by-Step Solution

1
Analyze the forces acting on the joint at the outer tip of the cross-arm.
There is a downward force from the weight of the antenna.
Identifying the applied external load is the first step in finding internal forces.
2
Determine how the diagonal cable responds to the downward load.
The cable must pull upward to prevent the antenna from falling. Since it attaches higher up on the mast, its pull is directed upward and inward along its length.
Cables can only pull (tension); they cannot push.
3
Resolve the cable's tension force into vertical and horizontal components.
The upward vertical component supports the antenna's weight. The horizontal component pulls the joint inward toward the mast.
Vector resolution helps determine the effect of the cable on the horizontal cross-arm.
4
Analyze the horizontal cross-arm's response to the cable's inward pull.
To keep the joint stationary (in equilibrium), the cross-arm must push outward against the inward pull of the cable. A member that pushes outward at its ends is under compression.
Newton's laws of motion dictate that all forces at a stationary joint must sum to zero.

Key Concept

Vector resolution and equilibrium in truss-like structures determine whether a member is in tension or compression.
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Topics

Structural Components

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