Task 2. Determination of displacements in the beam

Determine the deflection at point A and the angle of rotation at point B for the beam shown in fig.10 using Mohr’s and Vereshchagin’s methods.

Assume P = q•a , m = q•a² . The allowable stress is [ ] = 160 Mpa, E =2•10⁵ MPa.

Take the data which are necessary for computation from table 9.

Table 9

Variant Number /group No./	201	202	203	204	205	206	207	208	209	210
a , m	1.8	1.6	1.5	1.4	0.8	1.2	1.1	1.0	1.2	0.8
q , kN/m	22	20	18	20	16	22	20	18	16	14

Order of work

1. Determine the values of the reactions of the beam supports.

2. Write down equations for bending moment produced by the external load on the each portion of the beam and draw M_p diagram.

3. In order to determine the vertical displacement choose a fictitious state of the beam with the unit load at point a.

4. Write down equations for bending moment produced by the unit force applied at point A. Draw M₁ diagram.

5. In order to determine the angle of rotation choose a fictitious state of the beam with the unit moment at point B.

6. Write down equations for bending moments produced by the unit moment applied at point B. Draw M₂ diagram.

7. Select the I-beam number from "I-beam guide" using the strength condition on normal stresses.

8. Determine the vertical displacement at point A using the Mohr’s method.

9. Determine the angle of rotation at point B using the Mohr’s method.

10.Determine the vertical displacement at point A using the Vereshchagin’s method.

11.Determine the angle of rotation at point B using the Vereshchagin’s method.

12. Compare the displacements calculated by both methods

Literature

1. Stepin P. Strength of materials. - Moscow, Foreign languages publishing house, 1962. -376 p.

2. Писаренко Г.С. Опiр матерiалiв / Г.С. Писаренко [та ін.]– К.: Вища шк., 1993. - 654 с.

3. Справочник по сопротивлению материалов / под ред. Г.С. Писаренко– К.: Наук. думка, 1988. - 374 с.

4. Сборник задач по сопротивлению материалов / под ред. В.К. Качурина - М. : Наука, 1972. - 429 с.

5. Strength of Materials. Tension and compression. Stress state theory. Geometrical characteristics of plane sections. Simple bending. Initial parameters method. Torsion: Training-book / Authors: S.Y. Bogdan, M.M. Borodachov.- K.: NAU, 2005.- 60 p.

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