Normal strain of cable through arc

In summary, the conversation discusses the concept of strain and rotation in a mechanics of materials class. The question is whether the height of a rod should be slightly less than 300mm after rotating at a 0.3 degree arc. The summary provides clarification that the 300mm length is not the height, but rather the length of the rod from B to C which remains unchanged. The solution involves using the law of cosines to solve for the remaining strained triangle.
  • #1
coasterguy
2
0

Homework Statement



See attachment

Homework Equations



eAB=(Lf-Lo)/(Lo)

The Attempt at a Solution



Ok, this is not for HW. I am preparing for a mechanics of materials class next semester. I don't understand when CB goes through the 0.3 degree arc, they say the height is still 300mm. Shouldn't it be slightly less than 300mm? If so, then I have only one angle and one non hypotenuse side, I can't figure out how to solve the rest of the new strained triangle.

Thank you!
 

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  • #2
300 mm is not the height, it is the length of the part of the rod from B to C, which is unchanged after rotation. Then use the law of cosines as shown.
 

Related to Normal strain of cable through arc

1. What is normal strain?

Normal strain is a measure of the deformation or elongation of a material due to an applied force. It is expressed as the change in length divided by the original length of the material.

2. How is normal strain calculated?

Normal strain is calculated by dividing the change in length of a material (ΔL) by its original length (L), and multiplying by 100 to express it as a percentage. The formula for normal strain is: ε = (ΔL/L) * 100%

3. What is the significance of "cable through arc" in normal strain?

The term "cable through arc" refers to the shape of the cable when it is under tension. It is commonly used to describe the behavior of cables that are bent or curved, such as those used in bridges or suspension systems. When a cable is under tension and curved, the normal strain will vary along the length of the cable due to the varying curvature.

4. How does normal strain affect the strength of a cable?

Normal strain can have a significant impact on the strength of a cable. When a cable is under tension, it experiences tensile stress, which can cause it to elongate and potentially fail. The higher the normal strain, the greater the risk of failure. Therefore, it is important to carefully consider the normal strain when designing and constructing cable structures.

5. Can normal strain be reduced in a cable?

Yes, normal strain can be reduced in a cable by adjusting the shape or curvature of the cable, as well as the amount of tension applied to it. For example, increasing the diameter of the cable or reducing the angle of curvature can help to reduce the normal strain. Additionally, using materials with higher tensile strength can also help to reduce normal strain and improve the overall strength of the cable.

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