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Jaydeep Patel
School of Technology,
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Beams
Members that are slender and support loads applied
perpendicular to their longitudinal axis.
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Forces are acting on the girder
or on the beam due to
supported loads over it.
These forces are balanced by
the reactions given by the walls
or by the pillars to the beam or
girder.
Wall supports or the pillar
supports provide reactions to
the beam to keep the forces
acting on the beam in
equilibrium.
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Types of Beams
Depends on the support configuration
Simply Supported Beam:
When both end of a beam are
simply supported it is called
simply supported beam Such a
beam can support load in the
direction normal to its axis.
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Cantilever Beam:
If a beam is fixed at one end and is
free at the other end, it is called
cantilever beam.
Over-hanging Beam:
If a beam is projecting beyond the
support. It is called an over-hanging
beam.
The overhang may be only on one
side or may be on both sides.
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Beam with One End Hinged and the
Other on Rollers:
If one end of a beam is hinged and other
end is on rollers, the beam can resist load in
any direction
Propped Cantilever:
It is a beam with one end fixed and
the other end simply supported.
Continuous Beam:
A beam is said to be continuous, if it is
supported at more than two points.
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Statically Determinate or
Indeterminate beams
In the case of simply supported beams, beams with one end
hinged and the other on rollers, cantilever and over-hanging
beams, it is possible to determine the reactions for given loadings by
using the equations of equilibrium only.
In the other cases, the number of independent equilibrium equations are
less than the number of unknown reactions and hence it is not possible
to analyse them by using equilibrium equations alone.
The beams which can be analysed using only equilibrium equations
are known as Statically Determinate beams and those which cannot
be analysed are known as Statically Indeterminate beams.
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Types of Loading
Concentrated Loads:
If a load is acting on a beam over a very small
length, it is approximated as acting at the mid
point of that length and is represented by an
arrow as shown in Fig.
Uniformly Distributed Load (UDL):
• Over considerably long distance such load has got
uniform intensity.
• It is represented as shown in Fig (a),(b).
• For finding reaction, this load may be assumed as total
load acting at the centre of gravity of the loading
(middle of the loaded length).
• For example, in the beam shown in Fig., the given
load may be replaced by a 20 × 4 = 80 kN
concentrated load acting at a distance 2 m from the
left support.
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UniformlyVarying Load:
• The load shown in Fig. varies uniformly from C to D.
• Its intensity is zero at C and is 20 kN/m at D.
• In the load diagram, the ordinate represents the load intensity and the abscissa
represents the position of load on the beam.
• Hence the area of the triangle represents the total load and the centroid of the triangle
• Represents the centre of gravity of the load. Thus, total load in this case is (½)× 3 × 20
= 30 kN and the centre of gravity of this loading is at (1/3) × 3 = 1 m from D, i.e., 1 +
3 – 1 = 3 m from A.
• For finding the reactions, we can assume that the given load is equivalent to 30 kN
acting at 3 m from A.
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General Loadings:
Figure shows a general loading.
Here the ordinate represents the intensity
of loading and abscissa represents position
of the load on the beam.
For simplicity in analysis such loadings are
replaced by a set of equivalent
concentrated loads.
External Moment:
• A beam may be subjected to external
moment at certain points.
• In Fig. the beam is subjected to clockwise
moment of 30 kN-m at a distance of 2 m from
the left support.
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