Two-stage rod has been permanently fixed at end A and loaded with forces P and 2P as shown in the diagram. Calculate the diameter of both rods, knowing the allowable stresses in compression and tension. Draw diagrams of internal forces, normal stresses, and elongations and displacements of the rod. Data: 𝑃 =10⁢𝑘⁢𝑁,𝐸 =2.1 ⋅105⁢𝑀⁢𝑃⁢𝑎,𝑎 =1⁢𝑚,𝑘𝑟 =60⁢𝑀⁢𝑃⁢𝑎,𝑘𝑐 =80⁢𝑀⁢𝑃⁢𝑎

A two-stage rod has been permanently fixed at end D and loaded with forces P and 2P as shown in the figure. Calculate the value of force F so that Δ𝑙 =0

Data: 𝑑1 =20⁢𝑐⁢𝑚,𝑑2 =15⁢𝑐⁢𝑚,𝐸 =2.1 ⋅105⁢𝑀⁢𝑃⁢𝑎,𝑃 =15⁢𝑘⁢𝑁

Calculate the inner diameter of the hole that can be drilled axially to a depth of 3 meters.

Data: 𝐷 =20⁢𝑐⁢𝑚,𝐸 =85⁢𝐺⁡𝑃⁢𝑎,𝑃 =15⁢𝑘⁢𝑁,𝑢𝑚⁢𝑎⁢𝑥 =0.15⁢𝑚⁢𝑚

Calculate:

- normal forces on intervals N(x)

- stresses 𝜎⁡(𝑥)

Calculate the total elongation of the rod.

Given: P=20 kN, d=2 cm