MECHANICS OF MATERIALS
COURSE PROJECTANALYSIS OF COMPOSITE BEAMS
Project Members:
Aditya Bhat (CE21B005)
Anupama Rajan (CE21B019)
Dhawal Shukla (CE21B043)
Harshal Prajapat (CE21B057)
INTRODUCTION
COMPOSITE BEAM
 It is a type of beam made from two types of material to increase the strength
and stiffness of the beam.
 Engineers design beam beams in this manner to develop a more efficient
means for carrying applied loads.
 The flexure formula cannot be applied directly to determine normal stress in
a composite beam.
 Thus, a method will be developed to transform a beam X- section into one
made of a single material then we can apply the flexure formula.
 STRESS BEHAVIOUR OF COMPOSITE BEAMS
We consider a composite beam made up of two materials of types A and B and of
rectangular cross-section area and young modulus of elasticity EA and EB.
let a differential area dA in material type A at a distance of y from the neutral axis
NA, the longitudinal force acting on dA is
dF=sigma *dA
sigma=E*€ where €a =y/
The same force equation can be written by
Or
where n is
ratio.
known as the modular
From these equations, we can convert this composite beam as a single material
beam A type then the area of B material converted to n times their original area of
cross-section. The Neutral axis (NA) of the section shell passes through the centroid
of the transformed section.
Area
transformation
Stress distribution in beams with composite materials
If we want to calculate the magnitude of stress at points P and Q in materials A and
B then we can determine them from the transformed section as
In reality, the magnitude of stress developed at P should be given by
Multiplying
and dividing by EA, we get
Where
denotes the magnitude of stress at P in the transformed section.to get
the real stress we need to multiply by the modular ratio
.where EA is the
modulus of elasticity of material in terms of which the entire area transformed.
 Longitudinal shear
▪ The longitudinal shear stress in a beam occurs along the longitudinal axis
and is visualized by a slip in the layers of the beam
▪ Longitudinal or horizontal shear occurs due to the bending of the beam.
The fibres above shorten in length and those below the neutral axis
elongate under sagging bending moments. Therefore, the fibres tend to
slip over each other and the effect is maximum at the neutral axis.
▪ In general, a beam will support both shear and moment. The shear V is the
result of a transverse shear-stress distribution that acts over the beam’s
cross-section. Due to the complementary property of shear, however, this
stress will create corresponding longitudinal shear stresses which will act
along the longitudinal planes of the beam as shown in fig.
The behaviour of Aluminium and Steel composite beam
 Displacement
▪ As we increase the percentage of aluminium in steel as to make a
composite beam the ratio of max displacement of the cantilever beam and
simply supported beam max to max constant.
▪ According to our simulation we observed that in the cantilever beam max
displacement occurs at the free end of the beam but in the case of a
simply supported beam max displacement is at the centre of the beam.
DISPLACEMENT ANALYSIS
Al%
0
cantilever beam
simply supported ratio
max
4.22
0.169
25.011
min
0
0
0
25
50
75
100
max
6.538
0.2617
24.98
min
0
0
0
max
7.904
0.3179
24.86
min
0
0
0
max
8.09
0.3265
24.77
min
0
0
0
max
12.82
0.5152
24.65
min
0
0
0
 Data was taken from our simulation module.
 Stress
▪ Composite beams have greater max stress as compared to pure beams.
▪ As we increase the % of aluminium in composite beam stress increases in
both cantilevered and simply supported beam cases.
▪ Max stress in the cantilever beam is observed near the fixed end, whereas
in the simply supported beam it is at the centre.
Stress Analysis
Al%
0
25
50
75
100
cantilever beam
simply supported
ratio
max
4.22
0.169
25.011
min
0
0
0
max
17.78
2.439
7.04
min
0.01413
0.09083
0.155
max
19.11
2.667
7.16
min
0.1027
0.1048
0.97
max
22.57
2.66
8.48
min
0.1704
0.02513
6.78
max
13.54
1.862
7.27
min
0.2219
0.007743
28.65
▪ Data was taken from the simulation module
 Strain
▪
Strain Analysis
Al%
0
25
50
75
100
cantilever beam
simply supported
ratio
Max 10-5
4.22
0.169
25.011
Min 10-7
0
0
0
Max 10-5
11.72
1.42
8.25
Min 10-7
2.6
8.26
0.31
Max 10-5
13.76
1.87
7.32
Min 10-7
15.31
6.189
2.47
Max 10-5
13.85
1.92
7.21
Min 10-7
23.86
1.437
16.6
Max 10-5
17.2
2.435
7.66
Min 10-7
57.69
1.247
46.26