156 COMBINED AND ECCENTRIC STRESSES 



Calculation of Stresses. The method of calculation will be il- 

 lustrated by calculating the stresses in the pin at U^ in (a) Fig. Sob. 

 In the complete investigation of the pin U lt it would be necessary 

 to calculate the stresses when the stress in U^ U 2 was a maximum, and 

 when the stress in U^ L 2 was a maximum. Only the case where the 

 stress in U 1 U 2 is a maximum will be considered. However, maximum 

 stresses in pins sometimes occur when the stress in U^ L 2 is a maximum, 

 and this case should be considered in practice. 



Bending Moment. The stresses in the members are shown in 

 (c), which gives the force polygon for the forces. The makeup of the 

 members is shown in (a), and the pin packing on one side is shown in 

 (b). The stresses shown in (c) are applied one-half on each side of the 

 member, the pin acting like a simple beam. The stresses are assumed 

 as applied at the centers of the members. 



Algebraic Method. The amounts of the forces and the distances 

 between their points of application as calculated from (b) are shown 

 in (d). The horizontal and vertical components of the forces are 

 considered separately, the maximum horizontal bending moment and 

 the maximum vertical bending moment are calculated for the same 

 point, and the resultant moment is then found by means of the force 

 triangle. 



In (d) the horizontal bending moments are calculated about the 

 points i, 2, 3, 4; the maximum horizontal moment is to the right of 3, 

 and is 208,600 Ib.-in. The vertical bending moments are calculated 

 about points 5, 6, 7, 8; the maximum vertical bending moment is to 

 the right of 8, and is 283,000 Ib.-in. The maximum bending moment is 



at and to the right of 4 and 8, and is V2o8,6oo 2 -{- 283,ooo 2 351,600 

 Ib.-in. 



Me 

 Substituting in the formula 5 = , the maximum bending stress 



is 5"= 16,600 Ibs. The allowable bending stress for which this bridge 

 was designed was 18,000 Ibs. 



Graphic Method. The amounts of the forces and the distances 

 between their points of application are shown in (e). The force poly- 

 gon for the horizontal components is given in (f), and the bending 

 moment polygon is given in (g). The maximum horizontal bending 



