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Chapter 4.1:Shear and
Moment Diagram
Chapter 5:
Stresses in
Beams
Chapter 6:
Classical
Methods
Beam Types
Generally, beams are classified according to how the
beam is supported and according to cross-
section variance.
A beam maybe determinate or indeterminate
depending on the support conditions.
Determinacy pertains to the complexity of analysis of
a particular beam with loadings.
Determinate beams are beams whose support
reactions may easily be determined from
equations of equilibrium.
Indeterminate beams are beams whose support
reactions cannot all be determined from conditions
of equilibrium.
“Determinate Beams”
1. Simply Supported
2. Cantilever
3. Overhanging Beams
“Indeterminate Beams”1. Propped Beams
2. Restrained Beams
3. Continuous Beams
“Beam Shear and Bending Moment”
Beam shear simply relates the transverse loads and reactions
along the beam.
Bending Moment is the moment reaction of the beam against
flexure or bending.
To determine the beam shear and bending moment along any
part of the beam, pass a cutting plane normal to the beam.
Shear and Moment Equations and Diagrams
Shear and Moment on beams can be determined from using
equations or from diagrams – the latter being the preferred
option.
Again, in order to determine the shear and moment for specific
parts or segments of the beam, a cutting plane must be
passed through beam.
To determine the shear at the cut section, employ summation
of forces. To determine moment at the cut section, take
summation of moment about the cut section itself.
For the diagrams, it is important to remember that the shear
diagram is higher than the load diagram by one
mathematical degree.
Consequently, the moment diagram is also higher than the
shear diagram by one mathematical degree.
“Beam Shear and Bending Moment”
However, some conventions must be established:
( + ) Positive
( - ) Negative
Conventions and other rules regarding the shear and moment
diagram are best discussed in the proceeding examples.
For Positive (+) Conventions, (1) Shear Forces that tend to bend a beam element clockwise.(2) Bending moments that tend to bend a beam element
concave upward (the beam “smiles”).
( + ) Positive
Conventions and other rules regarding the shear and moment
diagram are best discussed in the proceeding examples.
( - ) Negative
For Negative (-) Conventions, (1) Shear Forces that tend to bend a beam element counter clockwise.(2) Bending moments that tend to bend a beam element
concave downward (the beam “sad face”).
Example : Determine the shear and moment equations of
the beam given below and draw the shear andmoment diagrams.
A CB
14 kN
2 m 3 m 2 m
D
28kN
Example : Determine the shear and moment equations of
the beam given below and draw the shear andmoment diagrams.
A B
16 kN.m
3 m 1 m
C
Example : Determine the shear and moment equations of
the beam given below and draw the shear andmoment diagrams.
A CA
20 kN
2 m 4 m
15 kN/mB
Example : Determine the shear and moment equations of
the beam given below and draw the shear andmoment diagrams.
A B
20 kN/m
3m
Example : Determine the shear and moment equations of
the beam given below and draw the shear andmoment diagrams.
A B
20 kN/m
3m
10 kN/m
Example : Determine the shear and moment equations of
the beam given below and draw the shear andmoment diagrams.
10 kN/m
A B
2m
10 kN.m
1m
Example : Determine the shear and moment equations of
the beam given below and draw the shear andmoment diagrams.
A DA
2 m 4 m
20 kN/mB C
2 m
Example : Determine the shear and moment equations of
the beam given below and draw the shear andmoment diagrams.
20 kN/m
A B
2m
10 kN
2m
10kN/m1m 1m
C
D E
Example : Determine the shear and moment equations of
the beam given below and draw the shear andmoment diagrams.
10 kN/m
10 kN/m5 kN
4m 3m 3m1m1m
AB
C
D
E F
Example : Determine the shear and moment equations of
the beam given below and draw the shear andmoment diagrams.
10 kN/m
A B
2m
1m
20 kN/m
Example : Draw the load and the bending moment
diagrams that correspond to the given shear forcediagram. Assume that no couples are applied to thebeam.
48 kN
-20 kN
28 kN
8 kN
-32 kN
X (m)
V (kN)
2m 2m 2m1m1m
Example : Draw the load and the bending moment
diagrams that correspond to the given shear forcediagram.
10 kN
20 kN
-30 kN
X (m)
V (kN)
2m 1m1.5 m
0.5 m1m
