64 PRACTICAL STRUCTURAL DESIGN 



of the beam. Another is the tensile force in a beam balanced by 

 the compressive force. They are equal and opposite in amount, 

 acting at the end of an arm measuring the distance between the 

 centers of gravity of the two forces. 



It is customary to use in cast iron a tensile fiber stress of 3000 

 Ibs. per square inch and a compressive fiber stress of 10,000 Ibs. 

 per square inch. 



A cast iron beam, therefore, is made in the form of an inverted 

 T, the well-known cast iron window lintel being an example in 

 point. First the beam was proportioned and the center of gravity 

 of the cross section found. The tensile stress being the maximum 

 at the lower surface, the average stress multiplied by the area of 

 the section below the center of gravity gave the tensile force 

 (total tensile stress). The area above the center of gravity times 

 one-half the maximum compressive fiber stress gave the total 

 compressive force. If they were not equal a new section would 

 be chosen and after a few trials a section would be obtained in 

 which the area below the neutral axis times the average tensile 

 fiber stress equaled the area above the neutral axis times the 

 average compressive fiber stress. 



This particular example is interesting because it disproves a 

 statement frequently met with in books of a certain class, namely 

 that " the moments of the horizontal forces on the two sides of 

 the neutral axis must be equal." Assuming this statement to be 

 true, the distance from the center of gravity of the tensile area to 

 the neutral axis must equal the distance from the center of gravity 

 of the compressive area to the neutral axis. Having located the 

 position of the neutral axis as above described, take a moment 

 arm from the neutral axis to the center of area of each section and 

 multiply the area by the average stress times the moment arm. 

 One trial will show the falsity of the statement. The force (stress) 

 areas on each side must be equal, and the moments do not balance 

 about the neutral axis, except when the cross section is sym- 

 metrical and the tensile fiber stress is equal to the compressive 

 fiber stress. The moment arm is measured from the center of 

 gravity of the stress triangle on one side, not the center of area, 

 to the center of gravity of the stress triangle on the other side. 

 The moments of resistance will be equal, which is quite a different 

 statement from that which makes the moments equal on the 

 two sides of the neutral axis. 



