21 



.*. taking the modulus of elasticity as 30,000,000 lbs. per 

 square inch, we have 



E I 30000000 x 3'57 



or = 



3570 



I 



2a 



P 30000 



.'. a = 59'805 



114 



= '953 = the circular measure of 54° 36' 



119'61 



* + / 



= cos 54° 36' 



'579 



Now putting / = 0'5", this gives us h = "364". 



It will be seen that in this example, as in most practical 



'864 



cases, the value of h in the exact equation = 



2a 



119-6 



is 



quite small, so that the approximate; method of solution used 

 gives no appreciable error. 



o 



U-> 



P 



Case 3. — Column with Fixed Ends 

 and Eccentric Loading. 



In this case the ends of the column 

 are supposed to be rigidly held parallel 

 to the direction of the compressive stress. 

 This requires the application of a 

 bending movement M. at each end (see 

 fig. 2). 



Taking the origin of co-ordinates at 

 the centre of the bent column, and using 

 the same notation as before, we have 



dp 

 EI p — 



dy 

 s =P(e-y)-M 



Ap 



(1+F 3 ) 2 ' ' 



= P(e-y) -Pc 

 writing M = P c 



EI 



Put 



= a 2 as before and integrate 



Fig. 2 



