RELATIVE BENDING STRENGTH OF CROSS ARMS 37 



fiber stress factor used in computing the resisting moments for the arm of 

 minimum size with maximum slant grain and maximum knots was vS250 

 psi, which is simply vSOOO psi discounted 35% to allow for slant grain of \" 

 in 8", which is the maximum permitted by Specification AT-7075. A dis- 

 count is, of course, unnecessary for the presence of knots, since allowance 

 for their effect on strength was made in the section modulus values used. 



Since the 5000 psi value is an ultimate fiber stress and not a working 

 stress, and since the arms were assumed to be made of clear, straight grained 

 material, Graph 1 (Fig. 1) represents an idealized condition. The resisting 

 moments shown are probably the maximum that may be expected from 

 any commercial lots of southern pine or Douglas fir crossarms,* notwith- 

 standing the fact that the dimensions of some of the arms may exceed the 

 nominal specified. With respect to Graph 2 (Fig. 1), the objection may be 

 raised that 35% is not a sufiicient discount for a 1" to 8" slant of grain and 

 that the 3250 psi value makes no allowance for the effect of long continued 

 loading. On the other hand, the graph assumes the simultaneous occur- 

 rence of the maximum knot in a most damaging position in every section 

 of an arm of minimum dimensions and having the maximum slant of grain 

 allowed. Since the probability of such simultaneous occurrence of these 

 defects and conditions is extremely small, it is felt that the resisting moments 

 of Graph 2 represent the minimum strength of any arm of the two species 

 concerned that may be furnished under Specification AT-7075. 



Under the assumptions made. Graphs 1 and 2 (Fig. 1) may be regarded 

 as the upper and lower limits of the bending strength of specification cross- 

 arms. On the same diagram may be plotted the graph or graphs of the 

 moments resulting from any given load at each pin position, or any single 

 load concentrated at any point on the arm. As an illustration. Graph 3, 

 showing the bending moments from a load of 50 pounds per pin, is shown 

 in the diagram (Fig. 1). A load of 50 pounds per pin is calculated to be the 

 load of size 165 wire coated with ice having a radial thickness of \ inch in 

 span lengths of 235 feet, or of wire of the same size in 100 foot spans where 

 the radial thickness of the ice coating is | inch. Since Graph 3 is wholly 

 below Graph 2, even an arm of lowest specification quality would support 

 the assumed loads wdth some margin of strength to spare. This margin or 

 factor of safety, would, of course, be increased greatly if the quality of the 

 arm under consideration approached the quality assumed in Graph 1. As 

 previously indicated, the probabiUty is extremely remote that any single 

 arm will ever be furnished of a quality as low as assumed in Graph 2. It 



* Graphs 1 and 2 (Fig. 1 ) are for southern pine and Douglas fir crossarms. It is estimated 

 that the resisting moments of comparable graphs for the other woods included in Specifi- 

 cation AT-7075 should be about 20% lower. 



