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1316 x 103

In this case, therefore, the approximate method yields the same answer for maximum B.M. as the full solution. The maximum stress will then also be equal to that obtained above, i.e. 75.6 MN/m2.

Example 23

A hollow circular steel strut with its ends fixed in position has a length of 2 m, an outside diameter of 100 mm and an inside diameter of 80 mm. Assuming that, before loading, there is an initial sinusoidal curvature of the strut with a maximum deflection of 5 mm, determine the maximum stress set up due to a compressive end load of 200 kN. E = 208 GN/m2.

Solution

The assumed sinusoidal initial curvature may be expressed alternatively in the complementary cosine form

Now when P is applied, _yo increases to y and the central deflection increases from <$o = 5 mm to S.

Fig. 2.17.

For the above initial curvature it can be shown that

maximum B.M. = P8o 7T2EI

where Pe for ends fixed in direction only =

0 0

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