The 2-Mg concrete pipe has a center of mass at point G . If...

The 2-Mg concrete pipe has a center of mass at point $G .$ If it is suspended from cables $A B$ and $A C$ determine the diameter of cable $A B$ so that the average normal stress in this cable is the same as in the 10 -mm-diameter cable $A C$

Key Concepts

Static Equilibrium

Static equilibrium refers to the condition where the sum of forces and the sum of moments acting on a system are zero, ensuring that the system remains at rest or in a state of constant uniform motion. In the context of suspended structures, it is essential for determining how the total load is distributed among the supporting cables based on their geometric arrangement and the position of the center of mass.

Tensile Stress

Tensile stress is the measure of the internal force per unit area within a material when it is subjected to a tension force. It is calculated by dividing the applied force by the cross-sectional area of the material. In cable design, ensuring that all cables experience a similar tensile stress is important for maintaining structural integrity and preventing failure.

Cross-Sectional Area and Geometric Relationships

For circular cables, the cross-sectional area is computed using the area formula for a circle, which is proportional to the square of the diameter. This relationship is key in determining a cable’s capacity to bear load, as a specific tensile stress level dictates the necessary cross-sectional area—and therefore the required diameter—to safely support a given force.

Load Distribution in Suspended Systems

When an object is suspended by multiple cables, the load is not necessarily shared equally among the cables due to the layout and points of attachment. Analyzing the load distribution, taking into account the center of mass and orientation of each cable, is critical to ensure that each cable is designed to handle its share of the load, resulting in uniform stress conditions among the support elements.

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