The boom is supported by the winch cable that has a diameter...

The boom is supported by the winch cable that has a diameter of 0.25 in. and an allowable normal stress of $\sigma_{\text {allow }}=24$ ksi. Determine the greatest weight of the crate that can be supported without causing the cable to fail if $\phi=30^{\circ} .$ Neglect the size of the winch.

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Key Concepts

Normal Stress

Normal stress relates the applied force to the area over which it is distributed. In materials and structures, ensuring that the force per unit area does not exceed the material's allowable stress is crucial to prevent failure or yielding.

Cross-Sectional Area Calculation

For cylindrical members like cables, the cross-sectional area is derived from the diameter using the formula A = (?/4) * d². This calculation is essential in determining how much load the cable can safely bear without exceeding its allowable stress.

Force Decomposition

When forces are applied at an angle, it is necessary to resolve them into their components, typically using trigonometric relationships. This process ensures that the load is correctly analyzed in terms of its effect on the structural member, especially in determining the effective force contributing to the normal stress.

Allowable Load Determination

This concept involves using the material's allowable stress, along with the cross-sectional area and any geometric considerations such as the application angle, to calculate the maximum load that can be applied without causing failure. It is a key step in ensuring the design adheres to safety limits.

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