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...