Spring Constants for bimetallic bars

[Ksum006]

Hi all,

Im a third year mechanical engineering student, starting on the topics of vibration analysis.

Question:
A rectangular prism bar is made up of two parts. The top layer is Steel(E=207E9 Pa) and the bottom layer is Aluminum(E=83E9 Pa). The bar is in axial motion. The dimensions are 500mm by 20mm by 5mm.

Therefore the thickness of each part of the bar is 2.5mm. 2.5mm thickness of steel and 2.5mm thickness of aluminum. The two elements are in parallel because the bar is in axial motion.

so clearly,
k(eq) = k(1) + k(2) (1 is steel and 2 is Al)

I also know that,
W(force) = k(eq) * (deflection)

but now I am stuck .. how do i figure out k(1) and k(2) so that i can get k(eq)??

Any ideas ??

.Thanks

 

[Navin A S]

in advance.Answer:The spring constant for each layer can be calculated using the equation k = EA/L, where E is the Young's Modulus of the material, A is the cross-sectional area of the bar, and L is the length of the bar. For the steel layer, k1 = 207E9 Pa * (0.02m^2) / 0.5m = 6.8E10 Pa/m. For the aluminum layer, k2 = 83E9 Pa * (0.02m^2) / 0.5m = 2.76E10 Pa/m. The equivalent spring constant is then k(eq) = k1 + k2 = 9.56E10 Pa/m.