168 PRACTICAL STRUCTURAL DESIGN 



forces are as shown by the heavy lines. Below the end piece the 

 uncut area of the chord carries all the tension, and this acts in 

 the center, as shown by the heavy arrow. 



The two forces form a couple with a moment arm of 4 ins. 

 The moment = 4 x 25,000 = 100,000 in. Ibs. 



If the center line of the support is placed under the vertical 

 line dropped from the center of the end face the bending moment 

 just found will exert a tendency to open the joint, because of the 

 pull around the lower edge. The reaction therefore should come 

 under the intersection of the center line drawn through the face 

 of the end piece and the line through the center of area of ten- 

 sion, as illustrated in Fig. 98. The exact position may be computed 



by dividing the moment just found, by the reaction, ' = 4 ins. 



^5,000 



which is the distance required to the left. It is merely a coincidence 

 that in this particular example the reaction equaled the tension 

 in the end panel of the lower chord. 



It remains to find the chord projection for shear, the length a. 

 The width of the chord is 8 ins. and the allowable shearing stress 

 is 120 Ibs. per sq. in., with a total compression load of 25,000 Ibs. 



a = ~ - 26 ins. = 2 ft. 2 ins. 



We have discovered that the center line of the reaction should 

 be 4 his. to the left of the center of the bearing area on the end 

 brace. This is 5.42 ins. to the left of the lowest point of the end 

 brace, where it is set into the chord, and there is consequently a 

 projection, 26 5.42 = 20.58 ins. beyond the center of the sup- 

 porting wall or column. This may be concealed by corbelling out 

 the brickwork of the wall, but very often such a projection is 

 objectionable. Designers who do not think clearly will often place 

 the support under the very end of the projecting piece, and this 

 sets up bending moments which will cause the chord to break. 



Assume, for example, in the present instance that the center 

 line of the support is 6 ins. from the end of the projecting chord. 

 This leaves 20 ins. to the deepest cut and 18.58 ins. to the vertical 

 line from the center of the face of the brace. The bending moment 

 = 18.58 X 25,000 = 464,500 in. Ibs. The vertical moment arm 

 between the compression and tension area is 4 ins. and the area of 

 the tension side below the cut = 8 X 5.17 = 41.36 sq. ins. 



