Art. 78. WORKING STRESS FOR COMPOUND STRESS. 117 



The dotted lines are lines of tension, and the full lines, lines 

 of compression. The former are evidently lines of maximum 

 principal stress below the neutral plane, and of minimum prin- 

 cipal stress above it. The reverse is the case for the compression 

 lines. 



In accordance with the previous article, these lines cross 

 each other at angles of 90 and the neutral plane at angles of 

 45. The stresses along them gradually decrease from the cen- 

 tral plane to their ends, at the upper and lower edges. At a 

 the shearing stress is zero, the bending stress alone acts, and the 

 line is horizontal; toward the neutral axis, the influence of the 

 shearing stresses increases, and that of the bending stress de- 

 creases, bringing the line to an inclination of 45 at 6, where 

 the shearing stresses alone act; above the neutral plane the 

 compressive stresses gradually reduce the tension to zero at c, 

 and the line becomes vertical. At d, e, and /, the lines are in- 

 clined, owing to the influence of the shearing stress. 



In a beam carrying uniform load the lines would all be 

 horizontal at the middle section, because the shear is zero, and 

 the curves would be flatter, because the shear increases toward 

 the supports. 



If the lines of maximum and minimum shear were drawn 

 they would cross the lines of principal stress at angles of 45 



78. Working Stress for Cases of Compound Stress. It 



was pointed out in Art. 13 that transverse forces, acting upon 

 the sides of a bar in tension or compression, interfere with the 

 longitudinal deformation so that it is no longer proportional to 

 the longitudinal stress. There is a similar state of things in a 

 beam, the shearing and bending stresses resulting in tensile and 

 compressive stresses acting at right angles to each other. 



Working stresses are based upon experiments in simple, 

 tension, compression, and shear, for which cases equation (2), 

 ES==s, holds. W T hen stress and deformation are not directly 

 proportional to each other, the question arises, Shall the working 

 stress be based upon the intensity of the maximum stress or upon 

 the maximum deformation? Experiments alone can determine 

 this, and these are beset with such difficulties that authorities do 

 not agree, as yet, upon this matter. The weight of authority 

 seems to be in favor of considering the maximum deformation. 

 in the line of principal stress, as the best basis for a working 



