Elongation of Tie Rods: LO or L?

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In summary, The formula for elongation of a tie rod is δ = FL/EA or δ = FL0/AE, depending on whether you use the tie rod length "L" or the original length "LO". This can be derived from the formula ε = σ/E, where σ = F/A. If there is an extension, the value of LO would need to be changed to get the new value for δ.
  • #1
Trenthan
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Hey guys, girls stupid question

Whats the actual formula for elongation of a tie rod
[tex]\delta = \frac{FL_{O}}{EA}[/tex]

or

[tex]\delta = \frac{FL}{EA}[/tex]

When searching the net, I've found some use the tie rod length "L"
Others use the original length of the tie rod LO (In my lecture notes the lecturer has used both interchangeably...)

I don't have a textbook on hand to check it against so I'm not 100% sure which one i can use.

Cheers Trent
 
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  • #2
Your formula is derived using

ε = σ/E

and σ = F/A so

ε = F/AE

ε = change in length/original length

so δ= FL0/AE

However, if there is an extension δ, and then it extends again, you'd need to change the value of L0 to get the new value for δ.
 

Related to Elongation of Tie Rods: LO or L?

1. What is the purpose of elongating tie rods?

The purpose of elongating tie rods is to provide stability and support to a structure, such as a building or bridge. This helps to prevent the structure from collapsing or becoming damaged due to external forces.

2. How does elongation of tie rods affect the overall strength of a structure?

Elongation of tie rods can increase the overall strength of a structure by evenly distributing tension and compression forces throughout the structure. This helps to prevent any weak points or areas of stress concentration, making the structure more stable and durable.

3. What factors can affect the elongation of tie rods?

The elongation of tie rods can be affected by a variety of factors, such as the material and thickness of the rods, the type of load being applied, and the length and angle of the rods. Additionally, environmental factors such as temperature and humidity can also play a role in the elongation of tie rods.

4. How can elongation of tie rods be calculated or measured?

Elongation of tie rods can be calculated by using the formula L = P * L0 / EA, where L is the elongation, P is the applied load, L0 is the original length of the rod, E is the modulus of elasticity of the material, and A is the cross-sectional area of the rod. This can also be measured using specialized equipment such as strain gauges.

5. What are the potential risks of not properly accounting for elongation of tie rods in a structure?

If the elongation of tie rods is not properly accounted for in a structure, it can lead to uneven distribution of forces and potential failure of the structure. This can result in safety hazards and costly repairs or replacements. It is important to consider the elongation of tie rods in the design and construction of any structure to ensure its stability and longevity.

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