Example of Shear force and bending moment diagram:

Q: Draw the Shear Force and bending moment diagram for the simply supported beam loaded as shown in the figure given below. 

Sol.: Let reaction at support A and B be, R_A  and R_B  First find support reaction

For that,

Taking moment about the point A,

ΣM_A = 0

2 X 1 + 4 X 2 + 2 X 3 - R_B  X 4 = 0

R_B = 4KN                                                                                           ...(2)

From equation (1), R_A  = 4KN                                                                                                                       ...(3)

Calculation for Shear force Diagram

Draw the section line, here total four section line, which break the load RA and 2KN(Between A and C),

2KN and 4KN(Between C and D),

4KN and 2KN (Between D and E) and

2KN and RB(Between E and B) Consider left portion of beam Take section 1-1

Force on left of section 1-1 is RA

SF_1-1 = 4KN (constant value)

Constant value means value of shear force at both the nearest point of section is equal that is

SFA = SFC  = 4KN                                                                               ...(4)

Take section 2-2

Forces on left of section 2-2 is RA  and 2KN

SF_2-2 = 4 - 2 = 2KN (constant value)

Constant value means value of shear force at both the nearest point of section is equal that is

SF_C = SF_D  = 2KN                                                                                                                        ...(5)

Take section 3-3

Forces on left of section 3-3 is R_A, 2KN, 4KN

SF_3-3 = 4 - 2 - 4 = -2KN (constant value)

The constant value means that value of shear force at both the nearest point of the section is equal that is

SF_D = SF_E  = -2KN                                                                                                                      ...(6)

Take section 4-4

Forces on left of the section 4-4 is R_A, 2KN, 4KN, 2KN

SF_4-4 = 4 - 2 - 4 - 2 = - 4KN (constant value)

The constant value means that value of shear force at both the nearest point of section is equal that is

SF_E = SF_B  = -4KN                                                                                                                      ...(7)

Plot the SF_D with the help of above shear force values.

Calculation for bending moment Diagram

Let

The distance of section 1-1 from A is X₁

The distance of section 2-2 from A is X₂

The distance of section 3-3 from A is X₃

The distance of section 4-4 from A is X₄

Take left portion of the beam

Take section 1-1, taking moment about section 1-1

BM_1-1 = 4.X₁

It is the Equation of straight line (Y = mX + C), inclined linear.

Inclined linear means that the value of bending moment at both the nearest point of section is varies with

It is Equation of the straight line (Y = mX + C), inclined linear.

Inclined linear means that the value of bending moment at both the nearest point of section varies with

Plot the BMD with the help of obtained bending moment values.