186 PRACTICAL STRUCTURAL DESIGN 



increased, which will have the effect of reducing the unit stress in 

 bearing. 



To determine the flexure in pins the following formula is used 

 for the resisting moment: 



32 8 

 in which 



M = moment of forces for any section through the pin. 

 / = allowable unit fiber stress in bending. 

 TT = 3.1416. 

 d = diameter of pin. 

 A = cross-sectional area of pin. 



The load in every member must be reduced to the horizontal 

 and vertical component loads, and must be considered as acting 

 in each member along the center line, so that the point of applica- 

 tion of each horizontal and vertical component is at the center 

 of bearing of the corresponding member. This means that if 

 two |-in. bars are side by side the moment arm = ? + j = | in. 

 The horizontal forces are equal on both sides of the pin, other- 

 wise there would not be equilibrium. Similarly the vertical force 

 downward is equal to the upward acting vertical force. 



The bending moment (to which the resisting moment must be 

 equated) is as follows : 



M = V(Mh) 2 + (My) 2 . 



in which M = resulting bending moment in inch pounds. 

 (Mh) = maximum moment of all horizontal stresses. 

 (Mv) = maximum moment of all vertical stresses. 

 In designing pin joints no two adjacent bars should pull in the 

 same direction, unless they shall by so doing reduce the bending 

 moment. The joint must be symmetrically arranged to avoid 

 torsion. Diagonal ties should be placed close to the vertical 

 member and the horizontal ties should preferably be on the out- 

 side. Sometimes packing pieces are required between the mem- 

 bers that carry stress, but these packing pieces merely lengthen 

 the moment arm between adjacent members. The joint being 

 symmetrical the computation stops at the center piece. 



In determining the horizontal moments take one-half the sum 

 of the thickness of adjacent bars for the moment arm between 

 these two bars. The moment between the first two bars is equal 

 to the load on the outer bar times the moment arm. The moment 



