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Dimension

Wall thickness

Torsion constant (J equiv)

476000 mm4 724000 mm4 1080000 mm4.

(b) Having selected an appropriate mild steel tube, determine how much the entire mechanism will twist during operation at a constant torque of 3 kNm.

The shear modulus of stainless steel is 78 GN/m2 and of mild steel is 83 GN/m2. Neglect the effect of any stress concentration. [50 mm x 50 mm; 0.152 rad]

5.19 (B). Figure 5.21 shows the cross-section of a thin-walled fabricated service conduit used for the protection of long runs of electrical wiring in a production plant. The lower plate AB may be removed for inspection and re-cabling purposes.

Owing to the method by which the conduit is supported and the weight of pipes/wires that it carries, the section is subjected to a torque of 130 Nm. With plate AB assumed in position, determine the maximum shear stress set up in the walls of the conduit. What will be the angle of twist per unit length?

By consideration of maximum stress levels and angles of twist, establish whether the section design is appropriate for the removal of plate AB for maintenance purposes assuming that the same torque remains applied. If modifications are deemed to be necessary suggest suitable measures.

For the conduit material G = 80 GN/m2 and maximum allowable shear stress = 180 MN/m2.

[167 MN/m2; 397ml

5.20 (B). (a) Figure 5.22 shows the cross-section of a thin-walled duct which forms part of a fluid transfer system. The wire mesh, FC, through which sediment is allowed to pass, may be assumed to contribute no strength

Fig. 5.22. All dimensions (mm) may be taken as median dimensions.

to the section. Owing to the method of support, the weight of the fluid and duct introduces a torque to the section which may be assumed uniform.

If the maximum shear stress in the duct material is limited to 150 MN/m2; determine the maximum torque which can be tolerated and the angle of twist per metre length when this maximum torque is applied. For the duct material G = 85 GN/m2. [432.6 kNm; 0.5167m]

(b) In order to facilitate cleaning and inspection of the duct, plates AB and ED are removable. What would be the effect on the results of part (a) if plate AB were inadvertently left off over part of the duct length after inspection? [5.12 kNm; 12.67m]

5.21 (C). Figure 5.8 shows a polymer extrusion of wall thickness 4 mm. The section is to be stiffened by the insertion of an aluminium I section as shown, the centre web of the polymer extrusion having been removed. The I section wall thickness is also 4 mm.

If G = 3.3 GN/m2 for the polymer and 70 GN/m2 for the aluminium, what increase in stiffness is achieved? What increase in torque is allowable, if the design is governed by maximum allowable stresses of 5 MN/m- and 100 MN/m2 in the polymer and aluminium respectively? [258%, 7.4%]

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