T

100 mm

6 mm

5.14 (B/C). An I-section has the dimensions shown in Fig. 5.18(a), and is subjected to an axial torque. Find the maximum value of the torque if the shear stress in the material is limited to 56 MN/m2 and the twist per metre length is limited to 9°. Assume the modulus of rigidity G for the material is 82 GN/m2.

If the I-section is replaced by a T-section made of the same material and transmits the same torque, what will be the limb length, D, of the T-section and the angle of twist per metre length? Assume the T-section is subjected to the same limiting conditioning as the I-section and that it has the dimensions shown in Fig. 5.18(b). For narrow rectangular sections assume k values of ^ in the formulae for torque and angle of twist.

5.15 (B/C). (a) An aluminium sheet, 600 mm wide and 4 mm thick, is to be formed into a hollow section tube by bending through 360° and butt-welding the long edges together. The cross-section shape may be either circular or square.

Assuming a median length of 600 mm in each case, i.e. assuming no stretching occurs, determine the maximum torque that can be carried and the resulting angle of twist per metre length in each case.

Maximum allowable shearing stress = 65 MN/m2, shear modulus G = 40 GN/m2.

(b) What would be the effect on the stiffness per metre length of each type of section of a narrow saw-cut through the tube wall along the length of the tube? In the case of the square section assume that the cut is taken along the centre of one face.

[B.P.] [14.9 kNm, 0.975°; 11.7k Nm, 1.24°; reduction 1690 times, reduction 1050 times.]

5.16 (B). The two sections shown in Fig. 5.19 are under consideration for an engineering application which includes both bending and applied torque. Make a critical comparison of the strengths of the two sections under the two modes of loading and make a recommendation as to the section which should be adopted. The material to be used is to be the same for both sections.

The rectangular section torsion constants k\ and kj may be found in terms of the section djb ratio from Table 3.1.

[Tubular]

5.17 (B). Compare the angles of twist of the following sections when each is subjected to the same torque of 3 kNm;

(a) circular tube, 80 mm outside diameter, 6 mm thick;

(b) square tube, 52 mm side length (median dimension), 6 mm thick;

40 mm

40 mm

3 mm

10 mm

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