172 QUESTIONS AND PROBLEMS. CHAPTER VIII. 



1. Are both the maximum shear and maximum moment 

 required in designing a simple beam? What is required for 

 a girder? 



2. Upon what assumptions are the formulas for deflection 

 accompanying Figs. 94 to 113 based? 



3. In Fig. 96, find the value of y at C from the equation of 

 the elastic line, for the segment CB, with origin at A. 



4. In Fig. -98, what must be the value of l^ in order that the 

 maximum negative moment shall be equal to the maximum pos- 

 itive moment? 



5. In the beams of Figs. 94 to 105, how do the maximum 

 moments vary with the total load? With the length? How do 

 the maximum deflections vary? 



6. In Fig. 107, how many points of contra-flexure are 

 there? How many maximum moments? 



7. What is the usual convention with regard to signs for 

 shears and moments? 



8. Construct a shear and a moment diagram for the case 

 of Fig. 114. 



9. A cantilever beam 9 ft. long carries a uniform load of 

 100 Ibs. per ft., and a concentrated load of 6000 Ibs. at 3 ft. from 

 the free end, what is the maximum shear? The maximum 

 moment? 



10. What size of I beam would you use for a floor joist 

 carrying a total uniform load of 12000 Ibs., the span being 20 ft. 

 and the greatest fiber stress allowed 16000 Ibs. per sq. in.? W T hat 

 is the greatest load this beam will carry if it is concentrated at 

 mid-span? 



11. In problem 10, the deflection is what proportion of the 

 span length? 



12. What is the maximum moment in the ties on a railway 

 bridge if the supports are 7 ft. center to center and the rails are 

 taken 5 ft. center to center, the total load on the tie being 

 18000 Ibs.? 



13. What is the maximum moment in a vertical beam 

 carrying a water pressure of 15 ft. depth if the beam is supported 

 at its ends, the distance between supports being equal to the 

 depth of water? What if the beam is fixed at the lower end? 





