A cantilever beam has a length L=50 mm. It has a rectangular cross-section width b=5 mm and a thickness t=1 mm. It is made of an aluminium alloy. By how much will the end deflect under an end-load of F=5 N (roughly that exerted by the weight of 5 apples)? Use data from Appendix A4 for the (mean) value of Young’s modulus of aluminum alloys, the equation for the elastic deflection of a cantilever from Appendix B3 and for the second moment of a beam from Appendix B2 to find out.

Data From Appendix B2

Data From Appendix B3

Data From Appendix A4 

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B.2 Moments of Sections A beam of uniform section, loaded in simple tension by a force F, carries a stress = F/A where A is the area of the section. Its response is calculated from the appropriate constitutive equation. Here the important characteristic of the section is its area, A. For other modes of loading, higher moments of the area are involved. Those for various common sections are given on the facing page. They are defined as follows. The second moment I measures the resistance of the section to bending about a horizontal axis (shown as a broken line). It is ction. y2b(y)dy where y is measured vertically and b(y) is the width of the section at y. The moment K measures the resistance of the section to twisting. It is equal to the polar moment J for circular sections, where 1= 2xr'dr section