GIRDERS AND TRUSSES 103 



1200 Ibs. per square inch is used. A strip 1 in. x 4 ins. is spiked on 

 each side along the top. How much is the strength increased? 



rp, ,, fbh* 1200 x 3 x 14 2 



The original strength, M T =' - - - 117,600m. 



Ibs., the neutral plane being in the middle of the joist. To find the 

 position of the neutral plane in the T-section use the method of 

 moments, taking moments about the lower edge: 



The original piece, 3 X 14 x 7 = 294 



One added piece 1 x 4 x 12 = 48 



Second added piece 1 x 4 x 12 = 48 



390 - 7 ns in 

 Area = (3 x 14) + (2 x 4) = 50 ~~ 



First the area of the beam was multiplied by the distance of 

 the center of gravity above the bottom, the result being 294. 

 Then the area of each added piece was multiplied by the distance 

 of its center of gravity above the bottom of the beam. This was 

 12 ins., being half the depth of the piece added to the difference in 

 depth of the beam and the piece. The products were added to- 

 gether, the sum being 390. Dividing by the total area, 50 sq. ins., 

 the distance from the bottom to the center of gravity (center of 

 area in this case) was found to be 7.08 ins. 



The original moment arm = f x 14 = 9.333 ins., that is, 9.333 ins. 

 Before the pieces were added at the top the moment of resistance 

 was equal to the area on one side of the neutral axis multiplied by 

 the average fiber stress times the moment arm, that is: 



ionn 



- x 3 x 7 x 9.333 = 117,600 in. Ibs. 



2i 



The strength of the beam is fixed by the fiber stress and the 

 smaller stressed area. In this T-section the smaller area is the 

 portion in tension below the neutral axis and the resisting moment 



1200 



- X 3 X 7.08 X 9.333 - 118,944 in. Ibs. 

 A 



The increase in strength is very small, so the area added above 

 the neutral axis was excessive. Better results would have been 

 obtained by nailing one strip along the bottom and one along 

 the top, thus increasing the area equally in tension and compres- 

 sion, without altering the position of the neutral axis. The proper 

 method to follow is to increase the thickness by adding boards 

 on one or both sides for the full depth. An example will be worked 

 out: 



