For finding the Value of X, For that first draw the FBD, Taking moment about point A UDL = 2000 X 2 = 4000 acting at a distance of (X + 1) from point A.
MA = 4000 ⋅ (X + 1) - RB ⋅ (2 + X) + 1000 ⋅ (X + 3) = 0
4000 + 4000X - 8000 - 4000X - 1000X -3000 = 0
1000X = 1000 X = 1m
Calculation for Banding Moment diagram
Here total three-section line, which cut AC, CB and BD
Distance of section 1-1 from point A is X1
Distance of section 2-2 from point A is X2
Distance of section 3-3 from point A is X3
Consider left portion of the beam
Consider section 1-1, taking moment about section 1-1
BM1-1 = 1000.X1
It is Equation of straight line (Y = mX + C), inclined linear
Inclined linear means value of bending moment at both nearest point of the section is varies with X1 = 0 to X1 = 1
At X1 = 0 BMA = 0 ...(8)
At X1 = 1 BMC = 1000 ...(9)
i.e. inclined line 0 to 1000 (Inclined line)
Consider section 2-2, taking moment about section 2-2
BM2-2 = 1000.X2 -2000(X2-1)
It is Equation of parabola (Y = mX2 + C),
Parabola means value of bending moment at both nearest point of the section is varies with X2 = 1 to X2 = 3 and make a curve.
At X2 = 1 BMC = 1000 ...(8)
At X2 = 3 BMB = –1000 ...(9)
i.e. Curve between 1000 to -1000
Consider section 3-3, taking moment about section 3-3
BM3-3 = 1000.X3 –4000(X3 – 2) + 4000(X3 – 3)
It is Equation of straight line (Y = mX + C), inclined linear
Inclined linear means value of bending moment at both nearest point of the section is varies with X3 = 3 to X3 = 4
At X3 = 3 BMB = –1000 ...(8)
At X3 = 4 BMB = 0 ...(9)
i.e. Curve between -1000 to 0
Plot the BMD with the help of above value, BMD is show in fig,
