Will a Compressive Force Bend a Bimetallic Rod Toward Brass or Copper?

[spl1017]

Question 1: A bimetallic rod is composed of brass and copper.
a. If the rod is subjected to a compressive force, will the rod bend toward the brass or the copper? Why?
b. Justify your answer mathematically if the compressive force is 5.00 X 104 N.

Here is my answer but I am having trouble with a formula for part (b).

a) The Rod Is Going To Bend Towards The Copper
b) Assuming Both The Rods Is Of The Same Crossectional Area. Copper Is Weaker In Compression Than Brass
Irrespective Of the Compressive Load with Reference from Data Hand Book

 

[Curious3141]

Question 1: A bimetallic rod is composed of brass and copper.
a. If the rod is subjected to a compressive force, will the rod bend toward the brass or the copper? Why?
b. Justify your answer mathematically if the compressive force is 5.00 X 104 N.

Here is my answer but I am having trouble with a formula for part (b).

a) The Rod Is Going To Bend Towards The Copper
b) Assuming Both The Rods Is Of The Same Crossectional Area. Copper Is Weaker In Compression Than Brass
Irrespective Of the Compressive Load with Reference from Data Hand Book

This is a question about the Young Modulus (YM), I believe. From some web references, the YM for copper is greater than that for brass (which is a copper/zinc alloy). This means that for a given load (stress value), the copper will deform less than the brass (copper will experience less strain than the brass).

Hence, when you place the two rods side by side, the copper part will end up longer than the brass part after the deformation. This means that the rod will bend such that the copper part is on the outside (convex part) of the curved rod, while the brass part is on the inside (concave part).

I don't get what sort of numerical justification they're looking for in the second part, since no dimensions, etc. were given for the rod. Moreover, once the rod starts to flex, it ceases to become elementary to work out the way the deformation will proceed since different parts of the rod will be oriented at different angles to the applied compressive force. Assuming ideal and uniform flexing, you can use calculus to work it out precisely, but I don't think the question wants you to go that far.

 

[kyle8921]

for Mechanical Engineers
The Modulus of Elasticity for Copper is 117 GPa and for Brass it is 103 GPa. Therefore, the copper will experience a greater strain under the same compressive force, causing the rod to bend towards the copper. This can also be explained by Hooke's law, which states that the strain in a material is directly proportional to the stress applied. Since the modulus of elasticity for copper is higher, it will experience a smaller strain compared to brass, causing the rod to bend towards it.

b) To calculate the strain in each material, we can use the formula:
ε = σ/E
where ε is strain, σ is stress, and E is the modulus of elasticity.
Assuming the cross-sectional area of the rod is 1 m^2, the stress can be calculated as:
σ = F/A
where F is the compressive force of 5.00 x 10^4 N and A is the cross-sectional area of 1 m^2.
Therefore, σ = 5.00 x 10^4 N / 1 m^2 = 5.00 x 10^4 Pa.
Substituting this into the formula for strain, we get:
ε(copper) = 5.00 x 10^4 Pa / 117 GPa = 4.27 x 10^-7
ε(brass) = 5.00 x 10^4 Pa / 103 GPa = 4.85 x 10^-7
Since the strain in copper is smaller, it will experience less deformation and the rod will bend towards it.