Statics: Shear and Torsion

Opening a drinks bottle

(a) Connectors in the cap of a drinks bottle                                   (b) Shear failure of the connectors
Fig. 5-13: Opening of a drinks bottle

When opening the lid of a common plastic drinks bottle, a torque T applied to the cap is gradually increased until the plastic connectors between the cap and the bottle experience shear failure.

Fig. 5-13a shows the connectors which keep the bottle sealed. If there are n connectors, each with an area A, uniformly distributed along the circumference of the cap which has a radius of r and the failure shear stress of the plastic connectors is , the equation of torsional equilibrium for the cap before being opened is . To open the bottle, the failure shear stress has to be reached and the design of the cap and its connection to the bottle, in terms of the size of the cap and the number and size of the connectors, needs to be such that this can be achieved with a modest effort. Fig. 5-13b shows the shear failure of the connectors.