Someone me understand the Stiffness of Materials

[Mason98]

Summary:: I would appreciate it someone could help me as my mind is completely gone on this and I am struggling to get the correct answer.

Hello,

I am trying to use this formula to fill in the rest of the table and I expect to get an answer between 0-5 x10-11. However i am getting nowhere near this however many times i attempt.

[Thread moved from the technical forums, so no schoolwork Template is shown]

Load (m) (g)	Load (W) (N)	Deflection (mm)	Deflection (δ) (m)	48δI/L³ = (in x10^-11)
0​	0​	0​	0​	0​
100​	0.981​	5​	0.005​
200​	1.962​	10​	0.01​
300​	2.943​	15​	0.015​
400​	3.924​	20​	0.02​
500​	4.905​	25​	0.025​
Material: Aluminium	L^3 =0.36^3 = 0.046656
Beam Size: 9.5mm x 3mm
b = 9.25mm	Length =360mm
d = 3mm		I = bd^3/12

 

[berkeman]

I am trying to use this formula to fill in the rest of the table and I expect to get an answer between 0-5 x10-11. However i am getting nowhere near this however many times i attempt.

When you say "this formula", are you referring to the one at the top of that last column?

48δI/L³ = (in x10^-11)

If so, what value do you calculate for I (including units)?

What values are you calculating so far? Can you show your work so we can check it? Thanks.

 

[Mason98]

Hello,

I have calculated I to be = 1.78 x 10^-15 m^4
Yes the top of the last column, when i calculate it (48δI/L^3) I am getting answers that aren't in that range:
9.1537 x 10^-15.
I am not sure if i am typing it wrong into the calculator or my calculation for I is wrong.

The plan is to then put those answers onto this graph which has the values set from 0-7 x 10^-11 and my answers aren't near that.
Thank you for replying I appreciate any help,

Mason.

 

[berkeman]

I'll try to do the calc in a bit, but for now, can you show the whole calculation you did for one of the values? I wonder if there is a missing units conversion or similar issue.

 

[Chestermiller]

You seem to be doing a 3-point bending test for which the stiffness formula is $$\frac{F}{\delta}=\frac{48 EI}{L^3}$$How did you get $\delta$ in your stiffness formula. The stiffness should be the slope of the graph of F vs $\delta$. When you calculate the right side of the equation for comparison, make sure it is in consistent units.

 

[Mason98]

You seem to be doing a 3-point bending test for which the stiffness formula is $$\frac{F}{\delta}=\frac{48 EI}{L^3}$$How did you get $\delta$ in your stiffness formula. The stiffness should be the slope of the graph of F vs $\delta$. When you calculate the right side of the equation for comparison, make sure it is in consistent units.

Hello thanks for your time and the reply and apparently this is why: Rearranging the equation in the form y = mx+c means that the gradient of a chart of W against 48 δI /𝐿 3 will give the value of E.

 

[Mason98]

I'll try to do the calc in a bit, but for now, can you show the whole calculation you did for one of the values? I wonder if there is a missing units conversion or similar issue.

Okay so i did: 48 x 0.005 x 1.78 x 10^-15 / 0.36^3
However i think the issue may be the deflection values, do you think 5mm is a lot of deflection of that beam with 100grams applied to it? maybe the indicator showed 5 but it really meant something like 0.05? or 0.5?
I am so confused but thank you for your time i really do appreciate it.
Mason.

 

[Mason98]

I'll try to do the calc in a bit, but for now, can you show the whole calculation you did for one of the values? I wonder if there is a missing units conversion or similar issue.

I think I have solved it! I was using the unit conversion for metres for δ, which was 0.005. However, when typing in just 5mm i am getting answers between 0-7 x 10^-11.

 

[Chestermiller]

Hello thanks for your time and the reply and apparently this is why: Rearranging the equation in the form y = mx+c means that the gradient of a chart of W against 48 δI /𝐿 3 will give the value of E.

I think this is a silly way to do it. I would plot F vs $\delta$ and fit my best straight line through the origin to this. I would then calculate E from the slope m: $E=\frac{L^3}{48 I}m$

 

[Mason98]

I think this is a silly way to do it. I would plot F vs $\delta$ and fit my best straight line through the origin to this. I would then calculate E from the slope m: $E=\frac{L^3}{48 I}m$

This is how my University says how to do it. Just shows that I'm paying for people who probably don't know what they're doing haha. Thanks for your help Chester.