A simply supported composite timber beam is loaded as shown in Figure 2(a). The beam cross-section is shown in Figure 2(b). Plot the mid-span flexural stress and strain distribution diagrams of the beam.
A simply supported composite timber beam is loaded as shown in Figure 2(a). The beam cross-section is shown in Figure 2(b). Plot the mid-span flexural stress and strain distribution diagrams of the beam.
Answer
We know that flexural stress and strain have linear diagram. Using bending equation we can determine the stress and strains in given composite timber beam
Let us first convert composite section into timber grade 1 section. The equivalent timber grade 1 section is obtained by multiplying the dimesions of timber grade 2 parallel to N.A by modular ratio
Modular ratio = Elastic Modulus of strong material/Elastic Modulus of weak material
Modular ratio = 30/15
Modular ratio = 2
Now we know that bending stress is given by and
M = Moment at midspan
M = (midspan moment due to udl in simply supported beam = )
M = 45 Kn-m
M = 45 * 106 N-mm
I = Moment of inertia of equivalent timber 1 section
Calculation of 'I' is shown in steps below
Step by step
Solved in 2 steps with 3 images
