12 Wilson and Weston, Torpedo- Boat Destroyers. 

 The twisting couple 



27r 



T= wMAco%—{x + vt) 



where 



2 



. /27r sin« ^\ „ /27r sine j5\ 

 \L cos-e 2/ \Z cos-e 2 / 



47r^ siiV'^e 27r sinO 



Z^ cos^e T cos^ 



= when y = o (11) 



The equation of motion is 



— -^'3^ - C^T-^ = wMAco%-f (x + vt) . . (12) 

 g dt^ dx' L^ ^ ' 



/^- = (radius gyration of weight about longitudinal 



axis)-. 

 /= geometrical moment of inertia of the section 



multiplied by the proper factor to allow for 



shape of section. 

 = angle of deviation of a line in section originally 



vertical. 

 C=- modulus of rigidity. 



Then 



WMA 27r, 



-COS-y(jf + vt) 



(cz-'4v) 



2-KVt . 2TcVt 



+ cos — j-{Ks\n7ix + ^cosnx) + sin— ^(Zsinwo: + Qcosnx) 

 where 



, 2t:V /wk"^ . 



End condition is the shearing force = when x= -\ — 



whence 6"= ^ = and R and P are determinate, and we 

 find shear force at centre 



Cdzv/l/cosOLA • I 



2' 



J7r(c/-^-^^v) 



