RELATIVE BENDING STRENGTH OE CROSS ARMS 



33 



below the top segment would extend beyond the hole; and its effect would 

 be the same as in Calculation 3 (Table 1), where the section modulus of a 

 section containing a 2" knot similarly located was found to be 2.50. On 

 the other hand, since a 2" knot is within the limits 1.78" and 2.16", the 

 section modulus of a section containing such a knot located at its top 

 would be 1.99. 



1.7S" Knot: 



A knot of this size immediately below the top segment would enter the 

 bolt hole since it is within the 1.45" and 1.83" limits, and the section 

 modulus value associated with it would be the same as shown in the 

 Calculation 6 results (Table 3) for a section containing a H" knot, or S = 

 2.62. But, as evident from previous discussion, the section modulus 

 associated with this knot, if located at the top of the section, would be 

 1.99. 



1.5" Knot: 



It can be shown that the section modulus of a section containing a knot 



of this size located at the top of the section would be 2.55; and that the 



section modulus associated w'ith a similarly located 1" knot would be 4.55. 



The foregoing analysis for minimum sections may be summarized as 



follows : 



A study of this summary shows that knots 1^" and over are more dam- 

 aging when located at the section top; and that knots under 1§" are more 

 damaging when located immediately below the top segment. The section 

 modulus values associated with 2|" and 3" knots would be the same as 

 shown in the Calculation 1 results (Table 1). 



By a similar analysis for arms of nominal size it can be shown: 



(1) That the more damaging position for knots 1|" and under is imme- 

 diately below- the top segment; 



(2) That the more damaging position for any knot within the diameter 

 range from 1.875" to 2.25" and all the larger knots is at the top of the 

 section; 



