202 COMBINATIONS OF BUCKLING AND BENDING. Art. 115 



Substituting the value of 6 



P T 2 \ 



(71) 



This equation is similar to equation (64), the first term being 

 the deflection due to the transverse load acting alone. 



If the second term in the parenthesis be neglected and 

 yP t LM i =maximnm moment due to transverse load, be in- 

 troduced 



** ' ' (72) 



and 





approx. 



(73) 



If the ends are fixed, the deflection will be much smaller, and 

 values of :*/, nax corresponding to the approximate values given 

 above are sufficiently accurate. For this case equation (66) for 

 uniform load becomes, 



<W A 



16 



-** the middle 



(74) 

 (75) 



the ends 

 Equation (73) for a single load at the middle becomes 



lat the middle (76) 



the ends (77) 



If but one end is fi,xed and the other free to turn, the ap- 

 proximate formula corresponding with equation (66) for uniform 

 load is 



"D / r>F2 \ . 



(78) 



mx= r+8 WL-j- at the fixed end (79) 



Equation (73) for a single load at the middle becomes 

 p 



* I f 1"k ! I * -*- 1 v 1 



-> at 



at the fixed end 



(81) 



