murphy: maximum bending moments. 147 



k ' I M^ X J k ^ 



The first term in the second member of (lo) is the distance to the 

 point of zero moment on the right of P, hence, the second terra in the 

 second member of (lo) is the horizontal distance between the variable 

 points of zero moment. 



The maximum moment may occur under the load or on either side 

 of the center when the load is on the other side. The raoment under 

 the load may be found from Mx=(u — y)H, or from M| or Mj. by put- 

 ting z=x. From the latter we have 



M^=Px I I- -^ [- -.|. ^(xl-x2)k .....,(, I) 



<iM. PI. II _Pia,p (,,_,.!( _Ar,f^i' 



= ° (I2) 





Simplifying (12 we have 



30] ^\ -75|Xi +4o|-i-^- +^5\-Y-\ -MJ-i-j-+2=o 



(13) 



One root of (13), found by trial is — j-=.22-|-- This root makes 

 the second derivative of (13) negative and makes Mx a maximum. 

 Substituting this value of -j- in (11) we have 



(Mx)max=.o86Pl (14) 



Differentiating (5) with respect to x to find for what position of the 

 load the moment of the load is a maximum we have 



=0 (15) 



From (15) we find 



2I 



3 



X 



x] -nti +" 



Differentiating (5) with respect to z we have 

 f^lMr I 5k 



dz 1 2l3^ ^ 



^6) 



