COLUMNS AND STRUCTURES 279 



tower diagram dotted lines are shown, transmitting the wind 

 from the tank to the frame. In the stress diagram the uplift is 

 measured from / to /. The tower loads are all positive (compres- 

 sion). In the tower diagram dotted counters are shown. These 

 are not stressed with the wind coming from the left, but are 

 stressed with the wind coming from the right. Each bay, there- 

 fore, is braced with cross braces designed both for tension and 

 compression. The stress diagram shown is only one method for 

 drawing such diagram. 



Wind acts against the side of a square or rectangular building 

 over the whole area. Against an octagonal structure the width 

 is measured on the longest possible diagonal, and the area of the 

 height multiplied by this diagonal is multiplied by 0.707, for 

 some of the force of the wind is lost against the sloping faces. 

 Against a cylindrical structure more of the force is lost on the 

 curved surface, so the diameter is multiplied by the height and 

 the product by 0.667. In old text books the statement is fre- 

 quently met with that the pressure of the wind against a cylindri- 

 cal surface is one-half that against a square having a side equal 

 to the diameter of the cylinder. Exact mathematical analysis 

 shows it to be two-thirds instead of one-half. 



The design of foundations under water towers is similar to 

 the design of foundations under the columns of buildings. The 

 weight of the water and tank carried down by each column, 

 added to the weight of the foundation, must be sufficient to oppose 

 the overturning effect of the wind, the uplift. It is necessary to 

 make a stress diagram, assuming the tank to be empty. It can 

 be assumed that the columns are rigidly braced so there will be 

 no bending to set up an eccentric load in the foundation blocks. 

 The bolts anchoring the column footings to the columns must be 

 strong enough to lift the weight of the blocks. 



The Design of Chimneys 



A chimney is subjected to direct stress and also to a bending 

 moment caused by wind. The resultant stress on the leeward 

 edge must not exceed the safe allowable stress. 



. , , W Me 

 The formula is/ - -r -j-t 



in which W - weight of stack above section considered, 

 A - area of ring in square inches, 



