Page 351 - statbility for masters and mates

Bending of beams 339
applied to ®nd the longitudinal shearing forces and bending moments in ¯oating vessels. Suf®cient accuracy of prediction can be obtained.
However, beam theory such as this cannot be used for supertankers and ULCCs. For these very large vessels it is better to use what is known as the ®nite element theory. This is beyond the remit of this book.
EXERCISE 40
1 A beam AB of length 10 m is supported at each end and carries a load which increases uniformly from zero at A to 0.75 tonnes per metre run at B. Find the position and magnitude of the maximum bending moment.
2 A beam 15 m long is supported at its ends and carries two point loads. One of 5 tonnes mass is situated 6 m from one end and the other of 7 tonnes mass is 4 m from the other end. If the mass of the beam is neglected, sketch the curves of shearing force and bending moments. Also ®nd (a), The maximum bending moment and where it occurs, and (b), The bending moment and shearing force at 13 of the length of the beam from each end.