12 BROOM ALL : 



It is seen in this case that the actual lateral stresses exceed 

 the values calculated by the ordinary methods, even causing 

 a reversal of stress in a direction perpendicular to the narrow 

 face. In the case of a bar under compression analogous 

 inverse results are met with. 



Again let us consider the question of shear in a bar under 

 tension. Under the assumption of no distortion, in the case 

 of the bar subjected to direct tension, the direction of the two 

 maximum shears will be at 45° with the axis of the bar and 

 at right angles with each other, the shearing unit stress being- 

 equal to one-half the longitudinal unit stress. This resolu- 

 tion may be made in any and all planes passing through the 

 longitudinal axis. Such is the common theory of diagonal 

 shear. 



In the actual bar, however, distortion takes place, and it 

 is necessary to know in what manner this affects the shears. 

 In the actual case with lateral contraction the effect is as if a 

 lateral compressive stress was acting upon the bar in all direc- 

 tions at right angles to the axis in addition to the applied longi- 

 tudinal stress. The forces to be resolved would therefore be 



in any chosen longitudinal plane. Without going into the 

 proof it may be shown that the direction of the maximum 

 shears in the actual case still remains 45°, but that the values 

 of the unit shears become one-half the algebraic difference 

 between the applied longitudinal unit stress and the lateral 

 unit compressive stress resulting from contraction. For 

 example, assume a steel bar 2" X i" in section subjected to a 

 pull of 20,000 lbs., and take the coefficient of lateral contrac- 



