218 FRAMEWORK 



Direct stress in A-ij = 14,900 Ibs. ; and bending moment = 

 924,000 inch-lbs. "A 4-angle laced column will be used. 



Try four 4" x 3" x 5-16" angles, long legs out, and a depth of 

 18" out to out of angles ; y%" lacing and connection plates will be used. 

 The radius of gyration of two 4" x 3" x 5-16" angles with the long 

 legs out, is found on page 189 Cambria to be 1.93 inches. 



The moment of inertia of a section of the post about the shorter 

 axis is 



/ = 4 /' + 4 Ad 2 



= 4x1. 65 + 4x2. 09 (9.00 o. 76) 2 

 = 574.24 

 and the radius of gyration is 



574.24 



-V 



8. 3 inches. 



8.36 



The maximum fibre stress will occur on the windward side of the 

 post and will be found by substituting in formula (300) to be 



, f 14,900 924,000 X 9 



7-A+/1 - g>36 -h 14,900X240* 



574 - Z4 " 280,000,000 



= 1780 + * 456o = 16,340 Ibs. per square inch. 

 The allowable stress per square inch for direct loads is 16,000 

 70 / -j- r = 16,000 70 x 29 = 14,000 Ibs. ; and since the wind mo- 

 ment comes only occasionally we will increase the allowable stress for 

 direct loads by 25 per cent when wind loads are considered, making an 

 allowable stress of 14,000 x 1.25 = 17,500 Ibs. per square inch. The 

 section chosen is therefore sufficiently large. 



The direct load will have to be carried by the column, and it will 

 be necessary to investigate the column about its longer axis. For this 

 case / -T- r = 240 -j- i .93 == 125, which is allowable under the specifica- 

 tions, and the section is ample. 



The lacing will be designed to take the shear, which is 5,500 Ibs. 

 below and 12,800 Ibs. above the foot of the knee brace. The maximum 

 stress in the lacing will be 12,800 x sec 30 = 14,700 Ibs. The al- 

 lowable tensile stress per square inch will be 16,000 x 1 . 25 = 20,000 



