## Problems

5.1 (A). A 40 mm x 20 mm rectangular steel shaft is subjected to a torque of 1 kNm. What will be the approximate position and magnitude of the maximum shear stress set up in the shaft? Determine also the corresponding angle of twist per metre length of the shaft.

For the bar material g = 80 GN/m2. [254 MN/m2; 9.787m.]

5.2 (B). An extruded light alloy angle section has dimensions 80 mm x 60 mm x 4 mm and is subjected to a torque of 20 Nm. If G = 30 GN/m" determine the maximum shear stress and the angle of twist per unit length. How would the former answer change if one considered the stress concentration effect at the fillet owing to a fillet radius of 10 mm? [27.6 MN/m2; 13.2°/m; 30.4 MN/m2.]

5 J (B). Compare the torsional rigidities of the following sections:

(a) a hollow tube 30 mm outside diameter and 1.5 mm thick; [2.7 x 10~8 G.]

(b) the same tube split along its length with a 1 mm gap; [0.0996 x 10-9 G.]

(c) an equal leg angle section having the same perimeter and thickness as (b); [0.0996 x 10-9 G.]

(d) a square box section with side length 30 mm and 1.5 mm wall thickness; [3.48 x 10-8 G.]

(e) a rectangular solid bar, side ratio 2.5 to 1, having the same metal cross-sectional area as the hollow tube.

Compare also the maximum stresses arising in each case.

[0.522 xl067; 15 x 106r; 15 x 106r; 0.41 x I067-; 4.05 x 1067\]

5.4 (B). The spring return of an interlocking device for a cold room door is to be made of a rectangular strip of spring steel loaded in torsion. The width of the strip cannot be greater than 10 mm and the effective length 100 mm. Calculate the thickness of the strip if the torque is to be 15 Nm at an angle of 10° and if the torsion yield stress of 420 MN/m2 is not to be exceeded at this angle. Take G as 83 GN/m2.

5.5 (B). A thin-walled member of 2 m long has the section shown in Fig. 5.11. Determine the torque that can be applied and the angle of twist achieved if the maximum shear stress is limited to 30 MN/m2. G = 250 GN/m2.

5.6 (B). A steel sheet, 400 mm wide by 2 mm thick, is to be formed into a hollow section by bending through 360° and butt-welding the long edges together. The shape may be (a) circular, (b) square, (c) a rectangle 140 mm x 60 mm. Assume a median length of 400 mm in each case (i.e. no stretching) and square corners for non-circular sections. The allowable shearing stress is 90 MN/m2. For each of the shapes listed determine the magnitude of the maximum permissible torque and the angles of twist per metre length if G = 80 GN/m'.

5.7 (B). Figure 5.12 represents the cross-section of an aircraft fuselage made of aluminium alloy. The sheet thicknesses are: 1 mm from a to b and C to D; 0.8 mm from b to C and 0.7 mm from d to ,4. For a maximum torque of 5000 Nm determine the magnitude of the maximum shear stress and the angle of twist/metre length.

10 mm rod.

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