294 STRENGTH OF MATERIALS 



of safety. The modulus of rupture, also called the ultimate 

 strength of flexure, is the extreme fiber stress that a material 

 subjected to bending can withstand. Its value is intermediate 

 between the ultimate strength in compression and tension. 

 In the sixth column of the table on pages 276 and 277 are 

 given the average values of the modulus of rupture for several 

 kinds of metal. 



When a beam is to be designed to carry certain loads, the 

 maximum bending moment is determined and divided by /. 

 The latter is usually given or is found by dividing the modulus 

 of rupture of the material by a suitable factor of safety. The 

 problem then reduces itself to the finding of a section that has 



a value of , the section modulus, equal to . For rolled- 



steel sections, the value of can be taken from a manufactu- 

 c 



rers' handbook. For a rectangular section, 

 / bd* 



b being the breadth and d the depth of the section. Since the 

 expression contains two unknown quantities b and d, a value 

 for either one may be assumed and substituted, and the 

 formula solved for the other. If a built-up beam is used, 

 the section has to be found by trial; a suitable section is first 

 assumed and its section modulus is computed by the prin- 

 ciples given under the heading Moment of Inertia; if necessary, 



it is modified until it is equal to . 



EXAMPLE. Design both a rolled-steel I beam and a solid 

 wooden beam 10 ft. long, each to carry a uniform load of 250 Ib. 

 per ft. in addition to a central load of 2,000 Ib., assuming for wood 

 a working stress of 1,000 Ib. per sq. in. and for steel 15,000 Ib. 

 per sq. in. 



SOLUTION. The maximum bending moment occurs at the 

 middle oif the beam and is equal to the sum of the moments due 

 to the uniform load and the central load. Expressed in inch- 

 pounds, 





