L 



60 PRACTICAL STRUCTURAL DESIGN 



load will have an eye ring at the top to receive the tie. The 

 eccentricity will not be large enough to make a great difference, 

 but even this small amount can be greatly reduced by running the 

 tie at a steeper angle. 



Assume that the lines of stress are contained within a beam, 

 Fig. 52, anchored in the wall in the usual way. The size of the 

 beam is proportioned to take care of the tensile, compressive, and 

 shearing stresses and the anchorage is the only item to be now con- 

 sidered. The wall reaction is 

 equal to the sum of all the 

 loads on the beam, so the 



weight of the wall resting on 



the beam must be equal to, or 



Fig. 52 Action of Moments in Anchor- exceed, the reaction. Weight 

 age of Cantilever Beam . ,. , n , , ,, . 



implies bulk and bulk implies 



bottom surface, and as the wall must be of a definite width to rest 

 on the beam a moment is created. 



In Fig. 52 the weight of the wall multiplied by the distance 

 from the face to the center of gravity must be equal to the moment 

 obtained by multiplying the loads on the beam by the respective 

 distances from their centers of gravity to the face of the wall. 



The illustration of how the stresses are obtained is true for 

 beams or frames resting on two or more supports, the stress being 

 equal to the moment at a point divided by the depth at that 

 point. When the lower member is a square piece of timber the 

 distance is measured from its center and when the upper member 

 is a rod the distance is measured to the center of the rod. That is, 

 all distances are measured between centers of gravity of the parts, 

 or members, of a frame, the total over-all height from the top to 

 the bottom being equal to the distance center to center plus half 

 the thickness of each piece. 



When a frame or truss is composed of angles or other rolled 

 shapes the distance is always measured between centers of gravity 

 of the top and bottom chords. Thus when depth is mentioned 

 it is not the over-all depth. The stress obtained is the stress on 

 the center line passing through the center of gravity, the stress 

 being slightly larger at the outer edge of the rolled section and 

 slightly smaller at the inner edge, when there is bending. In 

 pieces acting as plain ties or plain struts, so the stress is pure 

 tension or pure compression without bending stress, the stress is 



