At the left end of the beam there is the significant point A

At the left end of the beam there is the significant point A. Predict whether. The value of the bending moment is different than zero. Justify you\'re The value of the slope of the bending moment is different than zero. Justify your answer The value of the curvature of the bending moment is different than zero. Justify your answer

Solution

1) As there is verticle reaction at point A, the value of bending moment at point A is zero.

2) The bending moments at characteristic points can calculated as,

M_a = 0

M_c = A_Y*2a = M_D + Fa

M_d^left = A_Y*3a + C_Y*a = M_D

M_d^{right =} A_Y*3a + C_Y*a - M_D = 0

Therefore, there is maximum bending moment value at point C.

As the value of bending moment is not constant through out the length, the value of slope of bending moment is different than zero.

3)The value of curvature of bending moment diagram at a point depends on the shear force value at that point. If the value of shear force is positive, then the value of slope of the bending moment diagram curve will also be positive and vice versa. So the value of curvature of bending moment diagram is positive for length AC and negative for length CD.