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Beams that are built of more than one material are called composite beams. Examples are bimetallic beams, which consists of two different metals bonded together, sandwich beams, and reinforced concrete beams.
Composite beams may be analysed by the same bending theory as used for the analysis of ordinary beams, because the assumption that the cross-section that are plane before bending remain plane after bending is valid in pure bending regardless of the material. From this assumption, it follows that the longitudinal strains vary linearly from top to bottom of the beam. The position of the neutral axis need not necessarily be at the centroid of the cross-sectional area. In the case of a sandwich beam, the cross-section is doubly symmetric and the neutral axis is located t the mid-height of the cross-section.
A flitch beam is a sandwich type of composite beam, consisting of timber and steel as shown in figure-1.
Figure 1: Flitched Beam Cross-section
The timber and steel act together. A timber joist is strengthened by addition of a steel plate on the top and bottom, the three members being securely bolted together at the intervals.
The bolting together that ensures there is no slip between the steel and the timber at the section AA and BB. Thus, strain in the steel at AA = strain in the timber at AA.
Now, stress in steel at AA = , and
Stress in timber at AA = .
Stress in steel = m x stress in timber
If = 210000 and = 7000
Using this relationship, the beam of two materials can be considered as an equivalent timber beam or equivalent steel beam as shown in figure 2 and 3.
Figure 2: Equivalent Timber Beam
Figure 3: Equivalent Steel Beam
It should be noted that, in forming these equivalent beams, the width only has been altered. Any alteration in the vertical dimensions of the timber or steel would affect the values of the strain and therefore only horizontal dimensions may be altered in forming the equivalent sections.
The strength of the real beam may now be calculated by determining the strength of the equivalent timber bam or the equivalent steel beam in the usual manner, treating the section as a normal homogeneous one.