Design of Ribbed Sections

In any particular material, the flexural stiffness will be defined by the second moment of area, /, for the cross-section. As with a property such as area, the second moment of area is independent of the materid - it is purely a function of geometry. If we consider a variety of cross-sections as follows, we can easily see the benefits of choosing carefully the cross-sectional geometry of a moulded plastic component. 

All the sections have the same cross-sectional area (and hence the same weight). 

Example 2.11 An aluminium cantilever beam is SO mm wide, 80 mm long and 2 mm deep. The loading is 200 N spread uniformly over the cantilever. If the beam is to be replaced by one made from acetal and the design criteria is that the end deflections should be the same in each beam after one month, calculate the dimensions (a) of a solid acetal beam and (b) an acetal beam with unidirectional ribs. The modulus of the aluminium is 70 GN/m.  

In order to get the 1 month modulus for acetal, the strain in the beam must be known. 

Therefore, using (2.23) and ignoring Will) on each side 

Hence an acetal beam 7.6 mm deep and of the same width and length as the aluminium beam will perform in exactly the same way when the load of 200 N is applied. 

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