142 QUESTIONS AND PROBLEMS. CHAPTER VII. 



1. Why is the curve formed by the axis of a beam called 

 the elastic line? 



2. Will a steel beam deflect more or less than a cast iron 

 beam of exactly the same size, if they are loaded in the same 

 way? 



3. .Name the five assumptions upon which the equation of 

 the elastic line is based. 



4. What are the difficulties attending the derivation of 

 the equation of the elastic line in certain particular cases? 



5. Derive the equation of the elastic line of a cantilever 

 beam carrying a uniformly distributed load. What is the end 

 deflection in this case? What is the end deflection if there is 

 also a load at the end? 



6. What is the end deflection of a cantilever beam for a 

 load PI at its end and a load P<^ at its middle? 



7. How do the deflections of ordinary beams and cantilever 

 beams vary with respect to their lengths? 



8. Show how to get ?/ m ax for the case of Art. 83 from the 

 formula derived in problem 5. 



9. If a beam supported at its ends is uniformly loaded, 

 how much must it be raised at the middle in order that each half 

 shall be in the condition of a beam fixed at one end and sup- 

 ported at the other? How many points of contra-flexure will 

 there be in it? 



10. How is the location of the point of maximum deflection 

 of a beam found? Why may this be a difficult problem? What 

 is the best method of solving it in complicated cases? 



11. What deflection does equation (40) give? How would 

 this equation be used in finding the maximum deflection when 

 the point at which it occurs is not known? 



12. Find the maximum deflection for the case of Art. 82, 

 by means of equation (40). 



13. What is the maximum deflection of a girder supported 

 at its ends and uniformly loaded, if the cross section varies in 



such a manner that -== is constant? Ans. ?/ max = lc 1? = -^. 

 til &liii 



14. Why is the representation of the elastic line analagous 



