578 THE DESIGN OF STEEL DETAILS. CHAP. XVII. 



If the controlling stress were 38,000 lb.' compression, the required area for 2%" X 2" angles 

 would be 



P 38,000 



A = 7- = = 5.20 sq. in. 



fc 7.320 



which could not be supplied by two 2^" X 2" angles, so that two 3^" X 3" angles will be used 



for which, r x = 0.90 and r y = 1.66 for % in. back to back, the values of l/r are - = 80 and 



0.90 



12 X 12 



-^- = 86.8, respectively, and the allowable unit stress is, /,. = 16,000 70 X 86.8 = 9,930 



lb. per sq. in., requiring an area of A = 30,000 -T- 9,930 = 3.83 sq. in., which will be furnished 

 by two angles 3^" X 3" X 5/i6". The spacing of the washers should not be greater than, 

 / = 86.8 X 0.63 = 54.6 in., 0.63 in. being the least radius of gyration of one angle 3^" X 3" 

 X 5/i6". These results may be obtained by the use of Tables 43, 44 and 45, from which it is seen 

 that the allowable stress in a member composed of two angles 3^" X 3" X 5/16" about axis 

 i-i ( Y-Y), the length being 12' o", is 38,000 lb., and about axis 2-2 (X-X), the length being 6' o", 

 is 40,000 lb., and the allowable load will be 38,000 lb. 



Two Angles Starred. Design a member consisting of two angles starred, as in Fig. 6, to 

 carry a compressive stress of 30,000 lb., the length to be 15' o". center to center of connections. 



References. 34, p. 57; 84, p. 60; 100, p. 61. 



Solution. Using 125 as the maximum value of l/r, and f e = 16,000 70 l/r lb. per sq. in. 

 as the allowable unit stress, the minimum allowable value of r is found to be 



,/ r , 125 , r = jL. 15.X" in . 



125 125 



Section m-m. 



FIG. 6. Two ANGLES STARRED. 



From Table 67 it is seen that 4" X 4" angles are the smallest equal leg angles that can be 

 used, and that r will be about 1.56 in., and the allowable unit stress is 



f c = 16,000 70 X ^ = 7,920 lb. per sq. in., 



which requires an area of 



P 30,000 



A = -J- = -- = 3.79 sq. m. 

 f> 7.920 



The area of two angles 4" X 4" X W is 3.88 sq. in., and r = 1.57 in., which will satisfy the condi- 

 tions. The batten plates must have a spacing of not more than 



= 75 in. = 6' 3"; 



the value of 0.79 in. being the least radius of gyration for one angle 4" X 4" X 1 A" (Table 23). 

 Convenience in detailing may make it advisable to make / much less than 6' 3". A spacing of 

 3' 9" was used as shown in Fig. 6. 



