Convert loading velocity rate to strain rate on 3-point bending tests
Convert loading velocity rate to strain rate on 3-point bending tests
(OP)
Hi,
I would like to ask if anyone knows how to convert 100 cm/sec (loading velocity) to strain rate which units are strain per second.
Thanks a lot.
I would like to ask if anyone knows how to convert 100 cm/sec (loading velocity) to strain rate which units are strain per second.
Thanks a lot.






RE: Convert loading velocity rate to strain rate on 3-point bending tests
For most flexure tests the load application is given in terms of the extreme fiber stress rate, usually less than about 200 psi/min.
RE: Convert loading velocity rate to strain rate on 3-point bending tests
They claim that the loading velocity of 100 cm/sec corresponds to 1.2 strain per second. I would like to know how they did work out the strain rate in an impact event.
Thanks a lot.
RE: Convert loading velocity rate to strain rate on 3-point bending tests
What is meant by loading velocity? The load falls on the beam with the stated velocity at impact, is that correct? As the beam absorbs the impact by deflecting, the velocity of load decreases to zero, then reverses as the beam recovers (assuming it remains in the elastic range).
BA
RE: Convert loading velocity rate to strain rate on 3-point bending tests
then as the beam deflection increases by 0.001m there'll be an increase in strain in the beam (max bending stress > strain) and this should be linear.
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RE: Convert loading velocity rate to strain rate on 3-point bending tests
BA
RE: Convert loading velocity rate to strain rate on 3-point bending tests
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RE: Convert loading velocity rate to strain rate on 3-point bending tests
It is not clear to me how 1.2 radians per second is derived from a loading rate of 100 cm/sec.
BA
RE: Convert loading velocity rate to strain rate on 3-point bending tests
The paper provides beam dimensions of 12.5 mm (thick), 75 mm (wide) and 300 mm (long).
The tests with the smaller velocities were used normally under flexural test. The other two higher velocities were performed using a drop-weight tower.
I don't know how did they work out the strain rates. What I have in mind is that they used strain gauges attached on the beams to record the strains during the impact event and work out the strain rate from the strain versus time plot.
What do you think?
RE: Convert loading velocity rate to strain rate on 3-point bending tests
strain rate is proportional to load point deflection rate.
for an assumed deflection, you can calculate the bending strain.
together with a known loading rate, you can calculate the strain rate.
note, very high loading rates (impacts) have different internal strains compared to slow loading rates, so that's the tricky bit to calc.
i had expected the slow rate loadings to have a proportional strain rate, but they seem to be out by a factor of 10 ?
4.23E-3 5E-6 ... 4.23/5E-3 = 846
0.846 0.01 ... 0.846/0.01 = 84.6 ?
70 0.8 ... 70/0.8 = 87.5 (round-off?, 70/0.827 = 84.6)
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RE: Convert loading velocity rate to strain rate on 3-point bending tests
The load point is moving down at a speed of 10 cm/sec under an instantaneous load P. P is not the actual load applied...it is the effective load at time t (the instantaneous load).
At time t, the bending moment is PL/4 if the load is applied at midspan. The instantaneous stress at any distance y from the neutral axis is PL.y/4I and the unit strain ey at the 'y' fiber is PL.y/4EI.
The instantaneous deflection of the beam is PL3/48EI.
But ey = PL.y/4EI = Δ.y/12L2
If dΔ/dt = 10 cm/sec
then dey/dt = 10y/12L2
L = beam span and remains constant.
For any given fiber, y is constant.
so if dΔ/dt = 10 cm/sec then dey/dt = 10/12 radians/sec = 1/1.2 rad/sec which is the inverse of what the OP stated.
Help!
BA
RE: Convert loading velocity rate to strain rate on 3-point bending tests
M = PL/4
fy = My/I (stress at fiber y from N.A.)
ey = My/EI = PL.y/4EI
Δ = PL3/48EI
ey = Δ*12y/L2
dΔ/dt = 100 cm/sec = 1000 mm/sec
y = 12.5/2 = 6.25 mm
L = 300 mm
de/dt = 1000*12*6.25/3002 = 0.8333 rad/sec
Still have a problem relating to the correct answer.
BA
RE: Convert loading velocity rate to strain rate on 3-point bending tests
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RE: Convert loading velocity rate to strain rate on 3-point bending tests
I guess I could say that the strain rate dey/dt = 0.8333 sec-1 but I chose to use radians/sec which is the same thing.
BA
RE: Convert loading velocity rate to strain rate on 3-point bending tests
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RE: Convert loading velocity rate to strain rate on 3-point bending tests
BA
RE: Convert loading velocity rate to strain rate on 3-point bending tests
RE: Convert loading velocity rate to strain rate on 3-point bending tests
BA
RE: Convert loading velocity rate to strain rate on 3-point bending tests
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RE: Convert loading velocity rate to strain rate on 3-point bending tests
RE: Convert loading velocity rate to strain rate on 3-point bending tests
from peak load and E (and internal stress solution) you can easily get strain, and you need time to get strain rate (at least the way we're interpreting "rate"). could they have used "peak load rate" ?
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RE: Convert loading velocity rate to strain rate on 3-point bending tests
They used peak load rate from impact force versus time graph. Do you claim they used peak load rate to find the strain rate?
RE: Convert loading velocity rate to strain rate on 3-point bending tests
than the previous post (using peak load to determine strain rate)
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RE: Convert loading velocity rate to strain rate on 3-point bending tests
RE: Convert loading velocity rate to strain rate on 3-point bending tests
Why do you have to assume an E value to calculate strain rate? It seems to me you would need to assume an E value to get the moment rate or stress rate, but not for the strain rate because E is the same for load rate as it is for strain rate.
Δ = PL3/EI
M = PL/4
fmax = PL.y/4I
εmax = PL.y/4EI = 12Δ.y/L2
BA
RE: Convert loading velocity rate to strain rate on 3-point bending tests
BA
RE: Convert loading velocity rate to strain rate on 3-point bending tests
Ok. If I consider a 3 point bending test same with the paper written by Millard et al. 2013 with a deflection rate of 0.18 mm/min which is 0.003 mm/sec:
Span of beam = 300 mm
Width = 100 mm
Depth = 50 mm
s = My/I
M = PL/4
D = PL^3/48EI
stress = E x strain
strain = PLy / 4IE
Incorporating the deflection rate 0.003 mm/sec and rearranging the deflection:
strain = ( 48EIDLy / 4IE(L^3) )= 2 x 10^-5 s^-1.
According to the paper Millard et al 2013, the strain rate is 10^-5 s^-1 which does not agree with my calculations.
Stath
RE: Convert loading velocity rate to strain rate on 3-point bending tests
so strain rate = 12y/L^2*loading rate. it should be good for slow rates, there maybe impact effects for fast rates.
oh, I see your point (now) BA ... the relationship is only in terms of beam geometry.
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RE: Convert loading velocity rate to strain rate on 3-point bending tests
According to my calculation,
Unit Strain εmax = PL.y/4EI = 12Δ.y/L2
= 12*0.003*25/3002 = 0.0000100 which agrees with the paper you cited.
BA
RE: Convert loading velocity rate to strain rate on 3-point bending tests
You are completely right. I did use the full depth instead of diving it in 2. Thanks.
Stath
RE: Convert loading velocity rate to strain rate on 3-point bending tests
load rate (mm/sec) strain rate (strain/sec) strain/load
4.23E-6 5E-6 1.2
8.46E-2 1E-2 0.12
7E2 8E-1 0.0011
1E3 1E0 0.001
assuming load rate is reported, then to have a constant ratio (inferred by the geometry constants) you'd need ...
load rate (mm/sec) strain rate (strain/sec) strain/load
4.23E-6 5E-6 1.2
8.46E-2 1E-1 1.2
7E2 8.4E2 1.2
1E3 1.2E3 1.2
although it's reasonable that for high load rates (like 1m/sec) that the strain rate is lower, possibly a thousand times lower ...
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