2.2. 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. 7 using Mohr’s and Vereshchagin’s methods. Assume P = qa, m = qa².

The allowable stress is [] = 160 Mpa, E =2·10⁵ MPa.

Take the data which are necessary for computation from Table 10.

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.

Table 10

Variant /group No./	201	202	203	204	205	206	207	208	209	210	211	212
a, m	1,8	1,6	1,5	1,4	0,8	1,2	1,1	1,0	1,2	0,8	1,0	1,2
q, kN/m	22	20	18	20	16	22	20	18	16	14	20	18

Fig. 7. (see also p. 28)

Fig. 7. Continued (see also p. 29)

Fig. 7. Continued (see also p. 30)

Fig. 7. Continued (see also p. 31)

Fig. 7. Ending