276 Prof. J. Perry on Struts and 



breaking. If Euler's value of F be called U, 



U=^ (21) 



Using this as a symbol, (20) becomes 



f=iWI~; .... (22) 



and we can at once apply (11) and (12) to find the greatest 

 compressive and tensile stresses in the strut. Then, writing 



U F 



-r as ft, and — as co, we see that if /is the compressive stress 

 A .A 



which the material will bear, 



HX'-S-S « 



From this, if we are given the dimensions of the strut and 

 / and W, it is easy to calculate co. The solution of the 

 quadratic is 



2 W =/+/3- V / (/+/3)' + (^-4/)/3, . . (24) 



the minus sign being taken because co is evidently less than/ 

 and less than /3. 



Coupling-Rods. — Starting from this result, my students 

 have for several years worked out the relative breadths and 

 thicknesses of the sections of coupling-rods and connecting- 

 rods of engines, which are struts whose lateral loads are due 

 mainly to centrifugal force. 



Every point in a coupling-rod describes a circle of radius r 

 inches. If the section is, say, rectangular (an elliptic section 

 is just as easy to deal with) of dimensions d in the plane of 

 motion and b at right angles to the plane of motion ; taking 

 the whole mass as 2 lb dx *28 divided by 32*2 ; the centri- 

 fugal force 



« r - Ibdrri 2 „ 

 W= 629M lbs - wt - 



if the rod makes n revolutions per minute. 



In one direction a coupling -rod is a strut hinged at the 

 ends, and the thrust per square inch that it can receive, as- 

 suming that it is properly made, is to be the same as the thrust 

 which it will stand in the other direction. In the first direc- 

 tion it has lateral loading due to centrifugal force. 



