×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Convert loading velocity rate to strain rate on 3-point bending tests

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.

RE: Convert loading velocity rate to strain rate on 3-point bending tests

The load rate you are noting is absurdly high. This would constitute shock loading.

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

(OP)
You are right. The loading rate is for impact loading actually. I am reading a paper based on impact properties of concrete.

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

I just noticed that this thread is included twice in this forum. You should remove the other one.

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

maybe the idea is that the pointing point is moving (in the direction of the load) at 0.1m/s

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.

Quando Omni Flunkus Moritati

RE: Convert loading velocity rate to strain rate on 3-point bending tests

The pointing point?

BA

RE: Convert loading velocity rate to strain rate on 3-point bending tests

where the impact is happening

Quando Omni Flunkus Moritati

RE: Convert loading velocity rate to strain rate on 3-point bending tests

I confess I don't understand the original question. Something is moving at a rate of 100 cm/sec. In so doing, it causes a change in the strain in the fibers of the beam. The unit strain is greater in the outer fibers than those closer to the neutral axis but the rate of change of unit strain is the same for all fibers.

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

(OP)
The loading velocities were: 4.23 x 10^-3, 0.846, 70 and 100 cm/sec. Corresponding strain rates were 0.5 x 10^-5, 0.01, 0.8 and 1.2 strain/sec.

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

bending strain is proportional to load point deflection;
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)

Quando Omni Flunkus Moritati

RE: Convert loading velocity rate to strain rate on 3-point bending tests

Well, I thought I found the answer but now I'm not so sure. Here is what I did:

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

Try again:
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

BA ... i wish you'd use "strain" as the dimensionless unit for, well, strain. i find your use of the dimensionless angle "radian" confusing.

Quando Omni Flunkus Moritati

RE: Convert loading velocity rate to strain rate on 3-point bending tests

rb...Sorry for the confusion. I could be wrong, but so far as I know the word "strain" is not a recognized unit. Unit strain has no units, that is it is dimensionless, i.e. mm/mm or inch per inch.

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

i think strain and microstrain are well understood engineering units. sec^-1 might be mathematically correct but it lacks something in meaning, no?

Quando Omni Flunkus Moritati

RE: Convert loading velocity rate to strain rate on 3-point bending tests

Now that you mention it rb, I have heard the term microstrain. Okay, I concede the point. Read strain/sec for my radians/sec in my earlier post.

BA

RE: Convert loading velocity rate to strain rate on 3-point bending tests

(OP)
You can record microstrains using strain gauges and convert them to strains. By plotting strain versus time you have the strain rate. But, can you work out the strain rate from deflection versus time data?

RE: Convert loading velocity rate to strain rate on 3-point bending tests

Deflection and strain are related as I have indicated above. If you know the deflection rate at time t under dynamic loading, then you should be able to calculate the strain rate at the same time (or vice versa).

BA

RE: Convert loading velocity rate to strain rate on 3-point bending tests

i agree, BA's calc was what i had in mind. strain and deflection are proportional to one another.

Quando Omni Flunkus Moritati

RE: Convert loading velocity rate to strain rate on 3-point bending tests

(OP)
There is also a paper that they worked out the strain rate by applying the Hooke's law. So they got the peak load and by applying an E value, they calculated the strain rate; you need time to calculate the strain rate.

RE: Convert loading velocity rate to strain rate on 3-point bending tests

yes? not sure if there was a question there or not ...

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" ?

Quando Omni Flunkus Moritati

RE: Convert loading velocity rate to strain rate on 3-point bending tests

(OP)
rb1957

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

that sounds much more reasonable (using the peak loading rate to determine the strain rate)
than the previous post (using peak load to determine strain rate)

Quando Omni Flunkus Moritati

RE: Convert loading velocity rate to strain rate on 3-point bending tests

(OP)
What I have done to much their results was to calculate the peak load rate, Moment rate, stress rate. By assuming an E value , we get the strain rate. But again, my solution does not much their results.

RE: Convert loading velocity rate to strain rate on 3-point bending tests

Stath,
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

Correction: Δ = PL3/48EI

BA

RE: Convert loading velocity rate to strain rate on 3-point bending tests

(OP)
BAretired

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

i guess to get strain from stress ... I'm guessing he doesn't have "delta" directly.

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.

Quando Omni Flunkus Moritati

RE: Convert loading velocity rate to strain rate on 3-point bending tests

Stath,
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

(OP)
BAretired,

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

but (from previous post) ...
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 ...

Quando Omni Flunkus Moritati

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources