Comparing Aluminum & Copper Deflection Angles

[Loligo]

Homework Statement

The Shear modulus for aluminum and copper are 25GPa and 35GPa, respectively. An aluminum and copper pole, both the same length are subjected to the same shear force at the top of each pole, bending each pole a different angle y. Which pole has a higher angle of deflection and by how much?

Homework Equations

Formulas I am using are Shear Modulus = Shear Stress/Shear Strain
S = σ/ε = (F/A)/(Δx/L_o)
angle y = ε = Δx/L_o

The Attempt at a Solution

Since the forces are equal and area should be equal (under assumption the poles are the same dimensions the shear stress (σ) is equal for both poles.
Rearranging the formulas I get σ=S*y
σ_A=σ_C so 25GPa*y_A=38GPa*y_C
I get that the angle the deflection for the aluminum pole will be 1.52 times that of the copper pole.

 

[PhanthomJay]

is it 35 or 38 GPa? Insert correct value and round off to one decimal point, and your result will be OK. Shear stress is usually designated as $$\tau$$, and shear modulus is usually referred to as $$G$$. This distinguishes it from normal stress ($$\sigma$$) and elastic modulus ($$E$$) used for normal strains.

 

[Loligo]

The aluminum pole has a shear modulus of 25 GPa and the copper pole 35GPa.
Is it correct to say that the shear stress will stay the same with the poles are identical in proportions and are subjected to the same force

 

[PhanthomJay]

The aluminum pole has a shear modulus of 25 GPa and the copper pole 35GPa.
Is it correct to say that the shear stress will stay the same with the poles are identical in proportions and are subjected to the same force

Yes. The problem does not specifically state that both poles are similar in cross section, so it must be assumed that they are identically proportioned..