Strength of Materials (Stress n Torsion)

[DsG]

Homework Statement

1. Prove the equations.
2.Two solid circular shafts are connected by 5cm and 25cm-pitch-diameter gears as shown
in Figure 1.2 below. The shafts are assumed to be supported by bearing, as such bending
is negligible. Find the angular rotation at end D with respect to end A resulting from an
application of 280Nm torque. Given shaft AB is made of steel with G=80GPa, and shaft
CD is made of brass with G=35GPa.

Homework Equations

The Attempt at a Solution

i didn even know how to start this questions. any pro help pls..

 

[KataKoniK]

Thank you for your post. I am a scientist and I will be happy to assist you with this problem. First, let's review the given information. We have two solid circular shafts connected by gears, with different pitch diameters and made of different materials. The shafts are assumed to have negligible bending due to bearing support. We are given a torque of 280Nm and we need to find the angular rotation at end D with respect to end A.

To solve this problem, we will need to use the following equations:

1. Torque (T) = Force (F) x Distance (d)
2. Shear stress (τ) = Torque (T) / Polar moment of inertia (J)
3. Angular rotation (θ) = Shear stress (τ) x Shaft length (L) / Shear modulus (G)

We can start by finding the torque acting on each shaft. For shaft AB, the torque can be calculated as T = F x 5cm, where F is the force acting on the gear and 5cm is the pitch diameter. Similarly, for shaft CD, the torque can be calculated as T = F x 25cm.

Next, we can calculate the shear stress on each shaft using the formula τ = T / J, where J is the polar moment of inertia. For shaft AB, the polar moment of inertia can be calculated as J = π/32 x (5cm)^4, and for shaft CD, it can be calculated as J = π/32 x (25cm)^4.

Finally, we can use the formula θ = τ x L / G to calculate the angular rotation at end D with respect to end A for each shaft. For shaft AB, the angular rotation can be calculated as θ = τ x 5cm / 80GPa, and for shaft CD, it can be calculated as θ = τ x 25cm / 35GPa.

By plugging in the values for torque and polar moment of inertia for each shaft, we can calculate the angular rotation at end D with respect to end A. The total angular rotation can be found by adding the rotations from each shaft.

I hope this explanation helps you understand how to approach this problem. Please let me know if you have any further questions or need clarification on any of the steps. Good luck with your calculations!