Strain Rate (Simple question) 3

[Logan82]

Hi,

I have this beam:

Would you say the strain rate (Δε/Δt) of the fiber in tension of this beam would be:

Δε/Δt = V / L0 = (0.00583 m/s / 7.11 m) = 0.000972 s^-1

Note: The beam will stay in the elastic realm.

 

[Lomarandil]

No, not at all.

Strain in the tension fiber is related to the bending moment generated by the applied loading. Assuming loading at the center of the span, δ=M*L₀²/(12*E*I), σ=M/S (using the US convention of S as the elastic section modulus), σ=E*ε.

Some algebraic substitution using the time-dependent displacement will give your strain rate. Δε=(12*I*V)/(S*L₀²)

----
just call me Lo.

 

[Tomfh]

Logan82,

Wrong formula. That formula would work if the beam is acting in tension, eg like a 7.11m long rope being stretched at that rate.

The answer for a beam depends on beam size. A smaller beam will have a higher strain rate than a larger beam.

 

[Logan82]

Thank you all! I felt something was off. I could not find some already built formulas of strain rates for different beam configuration. Do you have a website or book that shows the different strain rate formulas?

 

[Tomfh]

Just work it out.

Calculate the resultant flange stress at 5.83mm of beam deflection.

Convert that stress to strain. That’s your strain rate.

 

[rb1957]

to clarify tom's post ...
1) calculate the displacement, d, for a 1000 lb (or 1000 N) load,
2) calculate the stress, and strain, s, in the outer fiber,
3) scale so that for a displacement of 5.83mm, the outer fiber stress (or strain) is s*5.83/d

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[Logan82]

Thank you very much everyone! Your help was appreciated.