Task 5. Torsion computations

The shaft of a circular cross-section is loaded by torsion moments. Under condition of strength and torsion condition of rigidity of the shaft select the diameter of the shaft.

Draw diagrams of twisting moments, the greatest values of shear stresses and twisting angles along the shaft.

assume the allowable value of normal stress   = 160 MPа for shaft material.

Take the data necessary for computation from table 6 and shaft schime from fig.8.

Table 6

variant /group No./	201	202	203	204	205	206	207	208	209	210	211	212
Mt , kN m	11	12	13	14	15	16	17	18	19	20	21	22
a, m	1.1	1.2	1.3	1.4	1.5	1.6	0.7	0.8	0.9	1.5	1.2	0.6
 , o/m	0,21	0,22	0,23	0,24	0,25	0,06	0,07	0,08	0,09	0,16	0,11	0,12

Order of work

1. Draw the scheme of the shaft to scale.

2. From the condition of balance determine the moment at the fixed end or moment М₀.

3. Using the method of section determine value of the twisting moments on each section of the shaft and draw the diagram.

4. According to the properties of the shaft material determine allowable value of shear stress.

Fig. 8. (see also p.30)

Fig. 8. Continued (see also p.31)

Fig.8. Ending

4. According to the properties of the shaft material determine allowable value of shear stress.

5. determine diameter of the shaft by condition of strength in torsion.

6. determine diameter of the shaft by condition of rigidity in torsion. Finаlly choose the greatest value from two diameters which approximate to the nearest standard magnitude.

7. Determine the greatest value of shear stresses on the each chosen section of the shaft. Check the condition of strength in torsion.

8. Draw the diagram of maximum shear stresses in the section.

9. Determine the value of the angles of twisting for each section of the shaft and draw the diagram of the angles.

10. Determine the greatest value of the unit twisting angle.

11. check up rigidity of the shaft and make the conclusions.

Task 6. Torsion with bending

The shaft of belt transmission (see fig.9) is turned round with n frequency and passed K capacity. On the shaft are fixed two pulleys. Diameter of the first pulley D₁, diameter of the second pulley D₂ . Conducting branch of the belt transmission is stretched twice more than the force conducted. Using the third theory of strength determine the necessary diameter of the shaft.

The allowable stress =100 MPa.

Take the data which are necessary for computation from table 1 and table 2.

Order of work

1. Determine the torsional moments put to the shaft.

2. Construct the twisting moment diagram M_t.

3. Determine the environing forces t₁ and t₂ acting on pulleys.

4. Construct the bending moment diagrams M_b^hor due to the horizontal forces and M_b^vert due to the vertical ones.

5. Construct the total bending moment diagram as the geometric sum of the two previous diagrams M_b^tot = .

Fig.9

Table 7

Variant number	1	2	3	4	5	6	7	8	9	10
D1 , m	0.15	0.25	0.35	0.45	0.55	0.1	0.2	0.3	0.4	0.5
K , kVt	0.2	0.4	0.5	0.6	0.7	0.25	0.35	0.45	0.55	0.65

6. Find the dangerous cross - section of the shaft and determine themaximum conventional moment value M_con using the third theory of strength

M_con = .