70 



PRACTICAL STRUCTURAL DESIGN 



Construction," by the late Professor J. B. Johnson. His descrip- 

 tion of the apparent elastic limit is that when it is reached the 

 deformation for each increment of stress is about double the 

 deformation for the increment immediately preceding. The curve 

 becomes a parabola, or is very nearly parabolic. 



All the statements made about the moment of resistance of 

 beams are true only within the elastic limit of the material, for 



they are based on 

 "Hooke's Law" that 

 11 Stress is proportional 

 to strain." When the 

 elastic limit is reached 

 the law is no longer 

 true. A generation ago 

 when steel was stressed 

 to 16,000 Ibs. per square 

 inch it was said to have 

 a factor of safety of 4, 

 based on the ultimate 

 strength of the steel, 

 64,000 Ibs. per square 

 inch. To-day the fac- 

 tor of safety is based 

 on the elastic limit, and 

 as this varies between 

 29,000 and 36,000 Ibs. per square inch, averaging about 32,000 Ibs., 

 depending upon the hardness of the steel, the factor of safety is 

 said to be 2, based on the elastic limit. There is a permanent set 

 after the elastic limit is passed and a progressive weakening, even 

 though the material may not fail until it is stressed up to four 

 times the allowable working fiber stress. 



Modulus of Elasticity 



The modulus of elasticity is a number obtained by dividing the 

 stress by the deformation it causes. If it were a force it would 

 be defined as a force which will stretch a unit piece of material to 

 twice its length or compress it one-half. It is not a force, nor is 

 it a pure number, for it is expressed in pounds. 



A certain steel bar having an area of one square inch was stressed 

 in tension 16,000 Ibs. and the stretch carefully measured was 



Fig. 56 Stress-strain Diagram of Steel, Iron, 

 and Wood 



