ANALYSIS OF STRESS IN BEAMS 



55 



being equal to or greater than the calculated value in order to insure 

 safety. 



If the section of the beam is to be of a shape not listed in the 

 handbooks, the dimensions of the section must be found by trial. 

 Thus a section of the required shape is assumed, and its section 

 modulus calculated from the relation 



If the value of S thus found is too great or too small, the dimensions 

 of the section are decreased or increased, and S again calculated. 

 Proceeding in this 

 way. the dimensions 

 of the section are 

 changed until a 

 value of S is found 

 \vhi-li is approxi- 



mately equal to ih- 

 ir 



calculated value 

 P 



Problem 62. Design 



a steel I-beam, 10 ft 



long, to bear a uniform 



Ioadofl6001b./ft,neg- 



ng its own weight. 



Problem 63. A built beam is to be composed of two steel channels placed on 

 edge and connected by latticing. What must be the size of the channels if the 

 beam is to be 18 ft long and bear a load of 10 tons at its center, the factor of 

 safety being given as 4 ? 



Problem 64. Compare the strength of a pile of 10 boards, each 14 ft. long, 1 ft 

 .md 1 in. thick, when the boards are piled horizontally, and when they are 

 placed close together on edge. 



Problem 65. Design a rectangular wooden cantilever to project 4 ft. from a 

 wall and bear a load of 600 Ib. at its end, the factor of safety being 8. 



Problem 66. A rectangular cantilever projects a distance I from a brick wall 

 and U-ars a single concentrated load P at its end. H.w far must the inner end of. 

 the cantilever be imbedded in the wall in order that the pressure between this end 

 and the wall shall not exceed the crushing strength of the brick ? 



Solution. Let 6 denote tin- width <.f the beam and x the distance it extends into 

 the wall. For equilibrium the reaction between the beam and the wall must con- 

 sist of a vertical force and a moment. If p a denotes the intensity of the vertical 



