PPT: Shear Force & Bending Moment Diagrams (SFD & BMD)

PPT: Shear Force & Bending Moment Diagrams (SFD & BMD) | Strength of Materials (SOM) - Mechanical Engineering PDF Download

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``` Page 1

Shear Force and Bending Moments
Consider a section x-x at a distance 6m from left hand support A
5kN
10kN
8kN
4m 5m 5m 1m
A
C
D
B
R
A
= 8.2 kN R
B
=14.8kN
E
x
x
6 m
Imagine the beam is cut into two pieces at section x-x and is separated, as
shown in figure
Page 2

Shear Force and Bending Moments
Consider a section x-x at a distance 6m from left hand support A
5kN
10kN
8kN
4m 5m 5m 1m
A
C
D
B
R
A
= 8.2 kN R
B
=14.8kN
E
x
x
6 m
Imagine the beam is cut into two pieces at section x-x and is separated, as
shown in figure
To find the forces experienced by the section, consider any one portion of the
beam. Taking left hand portion
Transverse force experienced = 8.2 – 5 = 3.2 kN (upward)
Moment experienced = 8.2 × 6 – 5 × 2 = 39.2 kN-m (clockwise)
If we consider the right hand portion, we get
Transverse force experienced = 14.8 – 10 – 8 =-3.2 kN = 3.2 kN (downward)
Moment experienced  = - 14.8 × 9 +8 × 8 + 10 × 3 = -39.2 kN-m = 39.2 kN-m
(anticlockwise)
5kN
A
8.2 kN
10kN
8kN
B
14.8 kN
4 m
6 m
9 m
1 m
5 m
Page 3

Shear Force and Bending Moments
Consider a section x-x at a distance 6m from left hand support A
5kN
10kN
8kN
4m 5m 5m 1m
A
C
D
B
R
A
= 8.2 kN R
B
=14.8kN
E
x
x
6 m
Imagine the beam is cut into two pieces at section x-x and is separated, as
shown in figure
To find the forces experienced by the section, consider any one portion of the
beam. Taking left hand portion
Transverse force experienced = 8.2 – 5 = 3.2 kN (upward)
Moment experienced = 8.2 × 6 – 5 × 2 = 39.2 kN-m (clockwise)
If we consider the right hand portion, we get
Transverse force experienced = 14.8 – 10 – 8 =-3.2 kN = 3.2 kN (downward)
Moment experienced  = - 14.8 × 9 +8 × 8 + 10 × 3 = -39.2 kN-m = 39.2 kN-m
(anticlockwise)
5kN
A
8.2 kN
10kN
8kN
B
14.8 kN
4 m
6 m
9 m
1 m
5 m
5kN
A
8.2 kN
10kN
8kN
B
14.8 kN
3.2 kN
3.2 kN
39.2 kN-m
39.2 kN-m
Thus the section x-x considered is subjected to forces 3.2 kN and
moment 39.2 kN-m as shown in figure. The force is trying to shear off
the section and hence is called shear force. The moment bends the
section and hence, called bending moment.
Page 4

Shear Force and Bending Moments
Consider a section x-x at a distance 6m from left hand support A
5kN
10kN
8kN
4m 5m 5m 1m
A
C
D
B
R
A
= 8.2 kN R
B
=14.8kN
E
x
x
6 m
Imagine the beam is cut into two pieces at section x-x and is separated, as
shown in figure
To find the forces experienced by the section, consider any one portion of the
beam. Taking left hand portion
Transverse force experienced = 8.2 – 5 = 3.2 kN (upward)
Moment experienced = 8.2 × 6 – 5 × 2 = 39.2 kN-m (clockwise)
If we consider the right hand portion, we get
Transverse force experienced = 14.8 – 10 – 8 =-3.2 kN = 3.2 kN (downward)
Moment experienced  = - 14.8 × 9 +8 × 8 + 10 × 3 = -39.2 kN-m = 39.2 kN-m
(anticlockwise)
5kN
A
8.2 kN
10kN
8kN
B
14.8 kN
4 m
6 m
9 m
1 m
5 m
5kN
A
8.2 kN
10kN
8kN
B
14.8 kN
3.2 kN
3.2 kN
39.2 kN-m
39.2 kN-m
Thus the section x-x considered is subjected to forces 3.2 kN and
moment 39.2 kN-m as shown in figure. The force is trying to shear off
the section and hence is called shear force. The moment bends the
section and hence, called bending moment.
Shear force at a section: The algebraic sum of the vertical forces
acting on the beam either to the left or right of the section is
known as the shear force at a section.
Bending moment (BM) at section: The algebraic sum of the moments
of all forces acting on the beam either to the left or right of the
section is known as the bending moment at a section
3.2 kN
3.2 kN
F
F
Shear force at x-x
M
Bending moment  at x-x
39.2 kN
Page 5

Shear Force and Bending Moments
Consider a section x-x at a distance 6m from left hand support A
5kN
10kN
8kN
4m 5m 5m 1m
A
C
D
B
R
A
= 8.2 kN R
B
=14.8kN
E
x
x
6 m
Imagine the beam is cut into two pieces at section x-x and is separated, as
shown in figure
To find the forces experienced by the section, consider any one portion of the
beam. Taking left hand portion
Transverse force experienced = 8.2 – 5 = 3.2 kN (upward)
Moment experienced = 8.2 × 6 – 5 × 2 = 39.2 kN-m (clockwise)
If we consider the right hand portion, we get
Transverse force experienced = 14.8 – 10 – 8 =-3.2 kN = 3.2 kN (downward)
Moment experienced  = - 14.8 × 9 +8 × 8 + 10 × 3 = -39.2 kN-m = 39.2 kN-m
(anticlockwise)
5kN
A
8.2 kN
10kN
8kN
B
14.8 kN
4 m
6 m
9 m
1 m
5 m
5kN
A
8.2 kN
10kN
8kN
B
14.8 kN
3.2 kN
3.2 kN
39.2 kN-m
39.2 kN-m
Thus the section x-x considered is subjected to forces 3.2 kN and
moment 39.2 kN-m as shown in figure. The force is trying to shear off
the section and hence is called shear force. The moment bends the
section and hence, called bending moment.
Shear force at a section: The algebraic sum of the vertical forces
acting on the beam either to the left or right of the section is
known as the shear force at a section.
Bending moment (BM) at section: The algebraic sum of the moments
of all forces acting on the beam either to the left or right of the
section is known as the bending moment at a section
3.2 kN
3.2 kN
F
F
Shear force at x-x
M
Bending moment  at x-x
39.2 kN
Moment and Bending moment
Bending Moment (BM): The moment which causes the
bending effect on the beam is called Bending Moment. It is
generally denoted by ‘M’ or ‘BM’.
Moment: It is the product of force and perpendicular
distance between line of action of the force and the point
about which moment is required to be calculated.
```

Strength of Materials (SOM)

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FAQs on PPT: Shear Force & Bending Moment Diagrams (SFD & BMD) - Strength of Materials (SOM) - Mechanical Engineering

 1. What are shear force and bending moment diagrams?
Ans. Shear force and bending moment diagrams are graphical representations that depict the variation of shear force and bending moment along the length of a beam or a structural element. These diagrams provide valuable information about the internal forces and moments acting within the structure, helping engineers analyze its behavior and design accordingly.
 2. How are shear force and bending moment calculated?
Ans. Shear force at any section of a beam can be determined by summing up the vertical forces acting on one side of the section. Bending moment, on the other hand, is calculated by summing up the moments of the forces on one side of the section. By repeating this process for multiple sections along the beam, the complete shear force and bending moment diagrams can be obtained.
 3. What are the typical shapes of shear force and bending moment diagrams?
Ans. The shear force diagram usually consists of a series of straight lines with abrupt changes at points where external loads or reactions are applied. These changes occur due to the transfer of forces across the beam. The bending moment diagram, on the other hand, is typically a curve that changes its slope at points where either concentrated or distributed loads are applied.
 4. How can shear force and bending moment diagrams be used for structural analysis?
Ans. Shear force and bending moment diagrams help engineers determine the critical sections of a structure where the internal forces and moments are at their maximum. By analyzing these diagrams, engineers can assess the structural integrity, identify potential failure points, and optimize the design to ensure that the structure can safely carry the applied loads.
 5. Can shear force and bending moment diagrams be used for different types of structural elements?
Ans. Yes, shear force and bending moment diagrams can be used for various types of structural elements such as beams, frames, trusses, or even entire structures. The principles of calculating and interpreting these diagrams remain the same regardless of the structural element. However, the specific loadings and boundary conditions need to be considered while constructing the diagrams for different types of structures.

Strength of Materials (SOM)

37 videos|39 docs|45 tests

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