CIVIL TUTOR

SFD &  BMD for a cantilever with a point Load at it's free end:  Consider a cantilever beam of span "L" fixed at end A and free at end B carrying a point load at end B.                    Consider a section X-X at a distance x from free end B & consider the right portion of the section.  The shear force at this section will be equal to the resultant of forces acting on right/left portion of the assumed section as per the definition of shear force. But the resultant force acting on right portion of X-X is "W" acting in downward direction. Since W lies in right portion of X-X,  it will be considered positive as per sign conventions of SFD. Hence shear force at X-X is positive. Let F x   = shear force at X-X.  F x   = +W _______________ (1) The shear force will be constant at all the sections between A and B since there is no other load present between A and B...

2.1 Shear force and Bending moment diagram for simply supported beam with a point Load at the centre of the span:                                               (fig. 2.1) Consider a simply supported beam  of span L carrying a point load w at a distance of L/2 from both the ends.  The reactions at both the supports will be equal to W/2 as the load is acting at mid-span.  Consider a section X-X between A & C at a distance of x from end A. The S.F at section X-X will be equal to the resultant forces acting on left portion of this section since we have considered the left portion of the section. But the resultant force acting on left portion of the section is W/2 acting upwards.  But the resultant force acting upwards in left portion is considered positive as per sign conventions.  Let F x  = S.F at X-X sect...