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Shear force and bending moment diagrams Notes | EduRev

: Shear force and bending moment diagrams Notes | EduRev

``` Page 1

Solid Mechanics

1. Shear force and bending moment
diagrams
Internal Forces in solids

Sign conventions
· Shear forces are given a special symbol on
y
V
1
2
and
z
V
· The couple moment along the axis of the member is
given
x
M T = = Torque
y z
M M = =bending moment.
Page 2

Solid Mechanics

1. Shear force and bending moment
diagrams
Internal Forces in solids

Sign conventions
· Shear forces are given a special symbol on
y
V
1
2
and
z
V
· The couple moment along the axis of the member is
given
x
M T = = Torque
y z
M M = =bending moment.

Solid Mechanics

We need to follow a systematic sign convention for
systematic development of equations and reproducibility of
the equations
The sign convention is like this.
If a face (i.e. formed by the cutting plane) is +ve if its outward
normal unit vector points towards any of the positive coordinate
directions otherwise it is –ve face
· A force component on a +ve face is +ve if it is directed
towards any of the +ve coordinate axis direction. A force
component on a –ve face is +ve if it is directed towards any of
the –ve coordinate axis direction. Otherwise it is –v.
Thus sign conventions depend on the choice of coordinate
axes.
Shear force and bending moment diagrams of beams
Beam is one of the most important structural components.
· Beams are usually long, straight, prismatic members and
always subjected forces perpendicular to the axis of the beam

Two observations:
(1) Forces are coplanar
Page 3

Solid Mechanics

1. Shear force and bending moment
diagrams
Internal Forces in solids

Sign conventions
· Shear forces are given a special symbol on
y
V
1
2
and
z
V
· The couple moment along the axis of the member is
given
x
M T = = Torque
y z
M M = =bending moment.

Solid Mechanics

We need to follow a systematic sign convention for
systematic development of equations and reproducibility of
the equations
The sign convention is like this.
If a face (i.e. formed by the cutting plane) is +ve if its outward
normal unit vector points towards any of the positive coordinate
directions otherwise it is –ve face
· A force component on a +ve face is +ve if it is directed
towards any of the +ve coordinate axis direction. A force
component on a –ve face is +ve if it is directed towards any of
the –ve coordinate axis direction. Otherwise it is –v.
Thus sign conventions depend on the choice of coordinate
axes.
Shear force and bending moment diagrams of beams
Beam is one of the most important structural components.
· Beams are usually long, straight, prismatic members and
always subjected forces perpendicular to the axis of the beam

Two observations:
(1) Forces are coplanar

Solid Mechanics

(2) All forces are applied at the axis of the beam.
Application of method of sections
What are the necessary internal forces to keep the segment of
the beam in equilibrium?
x
y
z
F P
F V
F M
 = 
 = 
 = 
0
0
0

· The shear for a diagram (SFD) and bending moment
diagram(BMD) of a beam shows the variation of shear
Page 4

Solid Mechanics

1. Shear force and bending moment
diagrams
Internal Forces in solids

Sign conventions
· Shear forces are given a special symbol on
y
V
1
2
and
z
V
· The couple moment along the axis of the member is
given
x
M T = = Torque
y z
M M = =bending moment.

Solid Mechanics

We need to follow a systematic sign convention for
systematic development of equations and reproducibility of
the equations
The sign convention is like this.
If a face (i.e. formed by the cutting plane) is +ve if its outward
normal unit vector points towards any of the positive coordinate
directions otherwise it is –ve face
· A force component on a +ve face is +ve if it is directed
towards any of the +ve coordinate axis direction. A force
component on a –ve face is +ve if it is directed towards any of
the –ve coordinate axis direction. Otherwise it is –v.
Thus sign conventions depend on the choice of coordinate
axes.
Shear force and bending moment diagrams of beams
Beam is one of the most important structural components.
· Beams are usually long, straight, prismatic members and
always subjected forces perpendicular to the axis of the beam

Two observations:
(1) Forces are coplanar

Solid Mechanics

(2) All forces are applied at the axis of the beam.
Application of method of sections
What are the necessary internal forces to keep the segment of
the beam in equilibrium?
x
y
z
F P
F V
F M
 = 
 = 
 = 
0
0
0

· The shear for a diagram (SFD) and bending moment
diagram(BMD) of a beam shows the variation of shear

Solid Mechanics

force and bending moment along the length of the
beam.
These diagrams are extremely useful while designing the
beams for various applications.
Supports and various types of beams
(a) Roller Support – resists vertical forces only

(b) Hinge support or pin connection – resists horizontal and
vertical forces

Hinge and roller supports are called as simple supports

(c) Fixed support or built-in end

Page 5

Solid Mechanics

1. Shear force and bending moment
diagrams
Internal Forces in solids

Sign conventions
· Shear forces are given a special symbol on
y
V
1
2
and
z
V
· The couple moment along the axis of the member is
given
x
M T = = Torque
y z
M M = =bending moment.

Solid Mechanics

We need to follow a systematic sign convention for
systematic development of equations and reproducibility of
the equations
The sign convention is like this.
If a face (i.e. formed by the cutting plane) is +ve if its outward
normal unit vector points towards any of the positive coordinate
directions otherwise it is –ve face
· A force component on a +ve face is +ve if it is directed
towards any of the +ve coordinate axis direction. A force
component on a –ve face is +ve if it is directed towards any of
the –ve coordinate axis direction. Otherwise it is –v.
Thus sign conventions depend on the choice of coordinate
axes.
Shear force and bending moment diagrams of beams
Beam is one of the most important structural components.
· Beams are usually long, straight, prismatic members and
always subjected forces perpendicular to the axis of the beam

Two observations:
(1) Forces are coplanar

Solid Mechanics

(2) All forces are applied at the axis of the beam.
Application of method of sections
What are the necessary internal forces to keep the segment of
the beam in equilibrium?
x
y
z
F P
F V
F M
 = 
 = 
 = 
0
0
0

· The shear for a diagram (SFD) and bending moment
diagram(BMD) of a beam shows the variation of shear

Solid Mechanics

force and bending moment along the length of the
beam.
These diagrams are extremely useful while designing the
beams for various applications.
Supports and various types of beams
(a) Roller Support – resists vertical forces only

(b) Hinge support or pin connection – resists horizontal and
vertical forces

Hinge and roller supports are called as simple supports

(c) Fixed support or built-in end

Solid Mechanics

The distance between two supports is known as “span”.
Types of beams
Beams are classified based on the type of supports.
(1) Simply supported beam: A beam with two simple supports

(2) Cantilever beam: Beam fixed at one end and free at other

(3) Overhanging beam

(4) Continuous beam: More than two supports

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