A hub is attached to a fastening with one shaft and one tube as shown below. The hub is exposed to torque Mv. The shaft is solid with the outer radius 2a and the length 2L.

The pipe has a length of 5L,the inner radius 3a and the outer radius 4a. The tube and shaft are made of a material with the shear part G and the stretch limit at shear τs, the hub and the fastening can be assumed to stiffen. Calculate the rotation of the shaft at the time of incipient plasticization. -Course is "strength of materials". Notations: Axel = Shaft, Infästning = attachening, rör = Pipe, nav = Hub

A freely supported beam with a T-cross section is subjected to a point load Q and a spread load with the total weight Q according to the figure below. The beam is a steel with the modulus of elasticity E 203 MPa, values of the load and dimensions are given in the figure. Calculate the maximum normal stress and shear stress that occur in the life of the beam (area marked in figure). Course name is "Strength of materials"