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Zorluk: KolayStructural Shapes and Profiles

A structural engineer is choosing between a solid steel rod and a hollow steel tube to act as a horizontal support beam. Both items are made of the exact same steel, have the same length, and weigh exactly the same. Which of the following is true regarding their ability to resist bending?

  1. The hollow tube provides greater resistance to bending.Cevap
  2. B
    The solid rod provides greater resistance because solid objects are inherently stiffer than hollow ones.
  3. C
    Both provide the exact same resistance to bending because they have the exact same weight.
  4. D
    The hollow tube is less effective because hollow shapes are always more brittle than solid shapes.

Cevap

The hollow tube provides greater resistance to bending.
The hollow tube is more resistant to bending because its mass is distributed further away from its central axis. When a beam bends, the maximum stress occurs at the outermost edges (top and bottom). By moving the material away from the center to form a tube, the shape achieves a higher moment of inertia, maximizing its strength-to-weight ratio.

Adım Adım Çözüm

1
Identify the constraints and conditions of the problem.
We are comparing a solid rod and a hollow tube that share the exact same material, length, and weight.
Understanding that the total amount of material is identical is crucial for comparing structural efficiency.
2
Analyze how material distribution affects bending strength.
Resistance to bending (stiffness) is determined by the area moment of inertia, which increases when material is placed further from the central, neutral axis.
The forces of tension and compression are greatest at the outer edges of a bending beam, so placing material there provides the most support.
3
Compare the cross-sections of the solid rod and the hollow tube.
Because they weigh the same, the solid rod must be narrower, while the hollow tube has a larger overall diameter with its material pushed to the outer edge.
This geometry means the hollow tube has a greater moment of inertia, making it more resistant to bending.

Anahtar Kavram

Cross-sectional shape and the area moment of inertia dictate that hollow tubes are stiffer in bending than solid rods of equivalent weight.
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Structural Shapes and Profiles

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