# Strength of materials

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Problem 1_1
Construct a diagram of longitudinal stresses and displacements in tension, compression of a bar of variable cross-section. The stepped bar is subject to axial forces. Plot longitudinal forces, normal stresses and displacements. Determine the displacement of the section I-I. The rod is made of steel (E = 2.1 ∙ 105 MPa).
Given: A = 10cm2; a = 2m; b = 2m; s = 1m; F = 100 kN; E = 2.1 ∙ 105 MPa.
Problem 2
Compressed bar stability.
Determination of critical and permissible load.
For a bar loaded with axial compressive force, determine
critical load Fcr and allowable Fadm. Bar length is given in m,
section dimensions in cm.
L = 3.5m, I-beam N70, K = 1.6
Four moments are applied to a steel stepped shaft having a solid cross section. The left end of the shaft is rigidly fixed in the support, and the right end is free and its end has angular displacements relative to the left end.
Required:
1. Plot the torques along the length of the shaft.
2. At a given value of the permissible torsional stress, determine the diameters d1 and d2 of the shaft based on strength. Round off the obtained values.
3. Plot the actual torsional stresses along the length of the shaft.
4. Plot the angles of rotation of the sections. Elasticity characteristics are adopted for steel.
5. Carry out a hardness test (shear modulus G = 0.8 x 1011 Pa).
The lengths of each of the 4 sections should be taken equal to 1 m.