FLAT PLATES 



145 



253. Show that Thurston's rule for thickness of cylinder head, given in problem 

 252, makes thickness of head = ! times thickness of walls. 



254. Nichols's rule for the proper thickness of unbraced flat wrought-iron boiler 

 heads is 



, 



= 



Aw 



where 



h = thickness of head in inches, 

 A = area of head in square inches, 

 10 = pressure per square inch, 



p = working stress = ultimate 



in tension 



10 factor of safety 



Compare this empirical rule with Bach's formula, using the data of problem 249 

 and assuming the material to be wrought iron. 



255. Nichols's rule for the collapsing pressure of unbraced flat wrought-iron 



boiler heads is 



10 hu t 







where w = collapsing pressure in lb./in. 2 , h = thickness of head in inches, 



u t = ultimate tensile strength in lb./in. 2 , A = area of head in square inches. 

 Show that Nichols's two formulas are identical and that therefore they cannot be 

 rational . 



256. The following data are taken from Nichols's experiments on flat wrought- 

 iron circular plates. 



Using these data, compare Bach's and Grashof's rational formulas with Nichols's 

 and Thurston's empirical formulas, as given below : 



Circular plate, supported at edge and uniformly loaded. 



Bach, 



Grashof, 



6p 



Nichols, h = = 



Thurston, h = .00035 wD, 



where h = thickness of head in inches, 



p 



D = diameter of head in inches = 2 r, 

 p = working stress in lb./in. 2 , 



w = pressure in lb./in. 2 , 

 A = area of h< 

 Note that the Nichols and Thurston formulas apply only to wrought iron 



A = area of head in square inches = 



