38 STEENGTH OF MATERIALS 



For instance, consider an oak beam 8 in. deep and 4 in. wide. From Arti- 

 cle 22, the ultimate compressive strength for timber may be taken as 7000 lb./in.*, 

 and the ultimate tensile strength as 10,000 Ib./inA Therefore, using a factor of 

 safety of 8, the safe unit stress is p = 875 Ib./inA For the beam under consign- 

 ation I = 170.7 in. 4 and e = 4 in. Consequently, the maximum bending nuum-nt 

 which the beam can be expected to carry safely is 37,340 in. lb., or 3112 ft. Ib. 



Problem 39. J?ind the moment of resistance of a circular cast-iron beam (I in. 

 in diameter. 



Problem 40. Find the moment of resistance of a Carnegie steel I-beaui. N... p, i. 



weighing 80 Ib./ft 



Problem 41. Compare the moments of resistance of a rectangular beam 

 8 in. x 14 in. in cross section, when placed on edge and when placed on its si<l.-. 



45. Section modulus. In Article 43 the moment of inertia was 



defined as the integral 



1= CfdF. 



From this definition, it is apparent that the moment of inertia de- 

 pends for its value solely on the form of the cross section. Since it 

 is independent of all other considerations, it may therefore be called 

 the shape factor in the strength of materials. 



Since e denotes the distance of the extreme fiber of a beam from 



the neutral axis, the ratio - is also a function of the shape of tin- 

 cross section, and for this reason is called the section modulus. 



the section modulus be denoted by S. Then S=- t and the expres- 

 sion for the moment of resistance becomes 



M = p8. 



This expresses the fact that the strength of a beam depends jointly on 

 the form of cross section and the ultimate strength of the material. 



Problem 42. Find the section moduli for the sections givi-n in Problems 8.'.. 

 and 37 respectively. 



Problem 43. Compare the section moduli fora rectangle 10 in. high an<l 4 in. 



wide, and for one 4 in. high and 10 in. wi.l.-. 



46. Theorems on the moment of inertia. The following is a sum- 

 mary of the most useful theorems concerning the moment of inertia. 

 The proofs can be found in any standard text-book on mechanics. 



(A) Let I g denote the moment of inertia of any cross section with 

 respect to a gravity axis (see footnote, p. 37), / the moment of in 



