Statics: Span and Deflection

Effect of spans

This demonstration shows the effects of span and second moment of area of a beam on its deflections.

(a)                                                                      (b)                                                                      (c)
Fig. 7-3: Deflections of a cantilever beam subjected to a concentrated load

A one-metre wooden ruler with cross section 5 mm by 30 mm is used and a metal block is attached to one of its two ends. One end of the ruler, with the long side of the cross section horizontal, is supported to create a cantilever with the concentrated load at its free end.

1. Observe the displacement at the free end of the cantilever with a span of say 350 mm. It can be seen from Fig. 7-3a that there is small deflection at the free end.

2. Double the span to 700 mm as shown in Fig. 7-3b and a much larger end displacement is observed. According to the results presented in Section 7.2, the end deflection for a span of 700 mm should be eight times that for a span of 350 mm when the effect of the self-weight of the ruler is negligible in comparison to the weight of the metal block.

3. Turn the ruler through 90 degrees about its longitudinal axis as shown in Fig 7-3c and repeat the tests when much reduced end displacement will be seen. The formula in Table 7.1 shows that deflection is proportional to the inverse of the second moment of area which for a rectangular section is given by . For the current test, the second moment of area of the section about the horizontal axis is 36 times that of the section used in the last test, resulting in maximum deflections of about one thirty-sixth of those in the second test (Fig. 7-3b).