Calculating stiffness from load and defletion

[Jackcheasley]

ok i loaded a composite laminate beam across the centre of a 1.44meter span with 415N load. This deflected the beam to a distance of 0.05m (5cm).
Im having trouble calculating the stiffness from this.
The composite laminate is 5mm of wood in a glass fiber sandwich with both the top and bottom layer measuring 1mm thick making a total depth of 7mm. The beam has a base of 27cm.


some of the equations i have are:
s=415*1.44^3/48EI
or
D=Eskin/12*(0.07^3-0.05^3)+Ec*0.05^3/12



If anyone had any idea even if its different equations as I am unsure on these, any help is great

Thanks

 

[pongo38]

What definition of stiffness would you be wanting to use? If it is force per unit displacement, then the experiment gives it you. If you want to compare that with a theoretical value, then maybe you should derive the formula for D from 1st principles, rather than trust it?

 

[PhanthomJay]

some of the equations i have are:
s=415*1.44^3/48EI

This equation is the theortical deflection of the beam at mid point if the beam is simply supported at each end. Since you may not know E or I for the composite material, your experiment gives you the deflection, as Pongo38 as noted. The stiffness of the beam under this loading and end condition is not the same as the deflection. The deflection has length units, and the stiffness has force/length units. Try using Hooke's law to calculate the equivalent stiffness of the beam loaded in this manner. you have the load and the deflection, what is the stiffness under this definition?

 

[Jackcheasley]

Awesome
Cheers guys Got it from hooks.
thanks

 

[DeeNos]

I would recommend using the equation s= FL^3/4bd^3, where s is the stiffness, F is the load, L is the span, b is the width, and d is the depth of the beam. In this case, the width (b) would be 27cm and the depth (d) would be 7mm. Plugging in the values, we get:

s = (415N * 1.44m^3) / (4 * 0.27m * 0.007m^3)

s = 48,000 N/m^2

This is the stiffness of the beam in N/m^2. If you want to convert it to a different unit, you can use the conversion factor 1 N/m^2 = 1 Pa. So in this case, the stiffness would be 48,000 Pa.

Another equation you can use is D = FL^3 / 48EI, where D is the deflection, F is the load, L is the span, E is the modulus of elasticity, and I is the moment of inertia. In this case, the moment of inertia (I) would be calculated using the composite laminate's properties. You can use the equation I = (bd^3)/12 for a rectangular cross-section. Plugging in the values, we get:

I = (0.27m * 0.007m^3)/12

I = 1.575x10^-6 m^4

Now, we can calculate the stiffness using the second equation:

D = (415N * 1.44m^3) / (48 * 1.575x10^-6m^4 * E)

0.05m = (415N * 1.44m^3) / (48 * 1.575x10^-6m^4 * E)

E = (415N * 1.44m^3) / (48 * 1.575x10^-6m^4 * 0.05m)

E = 2.105x10^11 N/m^2

Again, you can convert this to a different unit if needed.

Both of these equations should give you a good estimate of the stiffness of the beam. Keep in mind that these are simplified equations and may not take into account all factors that can affect stiffness, such as material