By N. M. Belyayev (Auth.)
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Additional info for Problems in Strength of Materials
66 TENSION AND COMPRESSION 33 Solution. We assume that all the forces are tensile and that the beam, after the deformation of the rods, will take up the new position shown in the figure (b). We shall set up the two equations of equilibrium : Σ MA = -(S2 ΣΜΒ = x 1) - (S, x 2-25) + (P x 1-5) - 0, (Sx X 2-25) + (S2 x 1-25) - (P X 0-75) - 0. (1) (2) For the setting up of the necessary third equation we shall consider the deformations (figure (b)). From the trapezium in the figure it is possible to set up the following relationship : Al3 — Alx 2^25 = Al2 — Alx Ϊ * which we shall re-arrange as 1-25Alx - 2-25 Al2 + Al3 = 0.
Thus ax = a + Al = 4 + 6-25 = 10-25 mm. To determine the temperature at which the gap will disappear we shall equate the elongation of the rail with the length of the gap. oclAt = a. 6°C, and the stresses will begin to appear only at t > £4. TENSION AND COMPRESSION 55 They will be a = Eoe (f4 - y = 2 x 106 x 125 x 1(H (35-6 - 50) = = —360 kg/cm 2 . 109. Determine the required gap in rail joints, so that in summer there will be no compression of rails. The laying of the rails is carried out at a temperature of +10°C; the maximum summer temperature is +60°C; the length of the rails is 8 m.
A rigid rectangular slab is supported on four uprights of identical cross-section, length and material, placed under its corners as indicated in the figure. Determine the force in each upright. Answer: S± = 1-5 t; S2 = 4 5 t; S3 = 8-51; £ 4 = 5 5 t . 82. A steel bolt is put through a copper tube as shown in the figure. The pitch of the screw thread of the bolt is 3 mm. What 42 PROBLEMS I N S T R E N G T H O F MATERIALS stresses will occur in the bolt and tube if the nut is turned through one quater of a revolution?