CIVIL TUTOR

6.1 Centre of gravity: The point at which whole weight of the body is assumed to be concentrated, is known as the centre of gravity of that body. 6.2 Centroid: The point at which whole area of a plane(circle, rectangle, triangle, quadrilateral etc) is assumed to be concentrated is known as the centroid of that area. It is represented by C.G or simply G. •  The centroid and centre of gravity lie at the same point. 6.3  C.G of simple plane figures: C.G of a uniform rod lies at it's middle point C.G of a rectangle or a parallelogram lies at a point where it's both the diagonals meet.  C.G of a triangle lies at a point at which the three medians of the triangle meet. C.G of a circle lies at the centre of the circle. 6.4 Centroid of plane areas by Method of Moments: Consider a plane area with a total area "A" whose C.G is to be determined.  Let's divide this area into a nu...

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...

1.1 Shear force and Bending moment: When a beam is subjected to a set of loads and reactions, as a result of which the internal forces and moments tend to setup within the beam This internal force is the shear force  and the internal moments are the bending moments.  For illustration,  consider a beam with a given set of loading supported at two points A &  B giving rise to reactions at the two supports.                        (fig.  1.1) Let's cut the beam into two parts &  let's assume that the resultant of loads (F) and reactions to the left of section xx is vertically upwards.                         (fig.  1.2) For equilibrium of the section, the resultant of loads and reactions to the right of section xx has to be equal to ''F" but vertically downwards. This force is known as shear force...