io6 



AN ANAI.YSIS 01^ TfiSTS 01^ WATER-TIGHT BULKHEADS. 



sensible error use the above formulas for Tq and Ti not only for uniform 

 load but also for increasing load and for combined uniform plus increasing 

 load. 



riG. 8. 



OEFUECTtONS. 

 1» » UNIFORM LOAD. 

 /> • TRIANSULXR LOAD. 



ENDS FREE. ENDS FIXCO. 



'-^- 



(b) Formulas for Defi.e;ction, Bending Moments and Supporting 



Forces. 



Having thus determined T independently, we may without undue 

 complications use more perfect or complete expressions for y, M and P than 

 were given in last year's paper: — 



I. STIFPENER A A FIXED VERTICALLY AT BOTH ENDS AND LOADED BY A 



UNIFORM LOAD wh = p. 



Referring to last year's paper, Appendix II, page 427, we may now 



i~T 

 avoid the expansion of the exponential functions, since «=v-— can be 



\ EI 



determined at once. 



Let 

 we then obtain: — 



«J —nl nl ~nl 



e2+e 2=a and e^—e 2=^ 



^'Trb'^U'"'-'-^--^] 



(13) 



