Relation Between Load, Shear And Moments: Moving Loads Assessment

The beam loaded as shown in Fig. P-438 consists of two segments joined by a frictionless hinge at which the bending moment is zero.

{Mh= 0
4R1= 200(6)(3)
R1-900 lb

To draw the Shear Diagram

1. Vx =0
2. V-V+ Area in load diagram
   200(2)--400 lb Vez Va+R-400+ 900 500 lb
3. V Vez+Area in load diagram
   VH500-200(4)--300 lb
4. VcVn + Area in load diagram
   Ve-300-200(2)=-700 lb
5. Location of zero shear:
   x/ 500-(4-x)/300
   300x2000 500x
   x=2.5 ft

To draw the Moment Diagram

1. Ma O (2) M M + Area in shear diagram
   Me 0-½ (400)
2. --400 lb-ft
3. M.-M. Area in load diagram
   M-400+ Vs (500X2.5) M.- 225 bit
4. McM+ Area in load diagram
   Mc-0-1 (300 700X2)
5. Mc--1000 lbft M.-M. + Area in load diagram
   Mh 225 1½ (300X4 2.5)-0 ok!
6. The location of zero moment in segment BH can easily be found by symmetry.