HOMOGENEOUS BEAMS 169 



1 9 ono y 1 2 

 equals = 18,000 ft.-lb. To change this to inch- 



8 



pounds, multiply by 12. Thus, 12X18,000 = 216,000 in.-lb. 



The section modulus of the beam is - = = 326.67. 



6 6 



Substituting these values in the formula, 216,000 = 5 X 326.67, 

 and s = 216,000 -H 326.67 = 661. 22 Ib. per sq. in. Ans. 



MODULUS OF RUPTURE 



Assume that the load on a beam is increased until it 

 breaks. From the loading that causes failure, M can be 

 found, while S can be found from the shape of the beam sec- 

 tion. Substituting these values in the formula M = Ss, a 

 value for 5 will be obtained. This value of s, which corre- 

 sponds to the moment that causes the beam to break, is 

 called the modulus of rupture, or ultimate unit bending stress, 

 of the material. Since the formula M = Ss is strictly cor- 

 rect only for values of 5 below the elastic limit, the modulus 

 of rupture will not agree exactly with either the ultimate 

 unit tensile or the ultimate unit compressive strength of 

 the material. The modulus of rupture is a valuable constant, 

 however, because by substituting it in the formula M = Ss 

 the breaking moment of a beam can be ascertained. 



In designing a beam, of course the beam is not intended 

 to develop the ultimate unit bending stress, but only a 

 fraction of it, depending on the factor of safety used. For 

 timber, a factor of 6 is usually employed; for wrought iron, 

 one of 4 is sufficient; while for cast iron, from 6 to 10 is 

 employed. For structural steel, the factor of safety gen- 

 erally used is about 4. With structural steel, however, 

 instead of dividing the modulus of rupture by the factor of 

 safety it is customary to use certain approved unit working 

 bending stresses. For light roof construction, this value is 

 often taken as high as 18,000 to 20,000 Ib. per sq. in In 

 ordinary building construction, 16,000 Ib. is usually employed 

 and in bridge work, 12,500 Ib. per sq. in. is often used. 



EXAMPLE. Design a rectangular white-oak beam to carry 

 a safe load of 2,000 Ib. located at the center, the span being 

 11 ft. 5 in. 



