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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