APPENDIX I. 



EXPLANATION OF FACTORS OF STRENGTH. 



Cross breaking. — From the cross-breaking test are obtained the mod- 

 ulus of strength at rupture (R), the modulus of elasticity (E), and the 

 elastic resilience per cubic inch (r). 



Th< modulus of strength at rapture is the intensity (in pounds per 

 square inch) of the stress upon the extreme fibers of a beam at the 

 point where, and at the time when rupture begins. 



For example, take a longleaf-pine beam of any length and height 

 and 10 inches wide, loaded to the point of failure. The value of the 

 modulus of rupture for this species is 5 by 1,550 (see Table IV) = 7,650 

 pounds per square inch. Now, if we conceive a layer of extreme fiber 

 a tenth of an inch in thickness and running the full width of the beam, 

 then the actual load on this square inch of material, tending to pull 

 the fibers apart or crush them together— depending upon whether this 

 layer was taken from the convex or concave side of the beam is 7,u5<> 

 pounds. 



The stress on the extreme fiber (/) is a function of the size of the 

 load, the method of loading, and shape of the piece. 



For rectangular beams of uniform cross section 



f= , 7 7 „ , for beam uniformly loaded, 

 ■ib/r 



and f= n 7 7 o , for concentrated load in middle; 



J 2 b li 



where 



W= total load on beam in pounds. 

 1= length of beam in inches, 

 5=breadth of beam in inches, 

 A=height of beam in inches, 

 the latter dimension being measured parallel to the direction of the 

 load. 



If W is the proof load on the beam, then/becomes equal to R, the 

 modulus of strength at rupture. 



The modulus of elasticity is the ratio of 



Unit stress (in pound s per square inch) , 

 Unit distortion (expressed as fractional part of length) 



Thus, if 30,000 pounds will stretch a bar of iron 1 inch square one 

 one- thousandth of its length, the modulus of elasticity for that iron is 



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