Why does a rope have different stiffness than a rod of the same diameter?

In summary, a prismatic rod has a lower bending and compressive stiffness than a rod of the same diameter, but will have the same axial tensile stiffness.
  • #1
crazie25
1
0
Why would a rope have a lower bending and compressive stiffness that a rod of the same diameter, but would have the same axial tensile stiffness?
 
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  • #2
what do you mean by compressive and bending stiffness?

Do you mean the equivalent spring constant?
 
  • #3
Why would a rope have a lower bending and compressive stiffness that a rod of the same diameter, but would have the same axial tensile stiffness?

Well a prismatic rod stifness is defined by [itex] k = \frac{EA}{L} [/itex].

Now let's suppose you have a rod and a rope with the same diameter and length. First notice that for the rope the cross sectional area A is equal to the cross sectional area of the individual wires, which will be less than the cross sectional are of our rod.

Now, the modulus of elasticity of our rope will be less than the modulus of elasticity of the material from which is made, due to the inherent property of the wires squeezing themselves.

Will our rope and rod of the same diameter and length have the same axial stiffness?

Theoretically, it'll depend solely on the rope effective modulus and the rod elasticity's modulus.
 
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  • #4
It's actually really simple, a rope is made up of very small fibers. Imagine taking one fiber of the rope, and pulling on it, then pushing on it or bending it. It's really weak in bending, due to it's small second moment of area [a factor of the area and the geometry], and in compression it buckles easily because of the same factor. In tension however it is pretty strong for its thickness. A bigger rope is made up of many such stands and as such will share their properties.

A rod, made up of a material with the same properties as the rope, will have a similar resistance to tension. However it is MUCH harder to buckle because it has a very large second moment of area, and so it will have a much higher bending and compressive stiffness.

I know this is late for OP but it was the second google result of one of my searches so this might still help someone.
 

Related to Why does a rope have different stiffness than a rod of the same diameter?

What is axial tensile stiffness?

Axial tensile stiffness is a measure of a material's resistance to being stretched or pulled apart along its length. It is a property that describes the material's ability to maintain its shape and resist deformation under tension.

Why is axial tensile stiffness important?

Axial tensile stiffness is important because it affects the strength and stability of a material. Materials with higher axial tensile stiffness are able to withstand greater forces without breaking or deforming. This is important in many applications, such as building structures, bridges, and machinery.

How is axial tensile stiffness measured?

Axial tensile stiffness is typically measured using a tensile testing machine. A sample of the material is placed in the machine and pulled in opposite directions until it breaks. The amount of force applied and the resulting deformation are measured, and the axial tensile stiffness is calculated using these values.

What factors can affect axial tensile stiffness?

Several factors can affect the axial tensile stiffness of a material, including its chemical composition, structure, and processing methods. For example, materials with a higher percentage of strong, stiff fibers will have a higher axial tensile stiffness. Other factors such as temperature, humidity, and loading rate can also impact the stiffness of a material.

How can axial tensile stiffness be improved?

Axial tensile stiffness can be improved by using materials with high stiffness and strength, such as carbon fiber or steel. The design and manufacturing processes can also be optimized to enhance the material's stiffness. For example, using a specific weave pattern or increasing the number of layers in a composite material can increase its axial tensile stiffness.

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