Problem: A lamina with fiber angle θ is subjected to in-plane stresses (σx=-3S, σy=4S and ζxy=4S) as shown in the figure below. Determine the local stresses, strains, engineering constant and the maximum load S that can be applied to this lamina by using hand calculation and Matlab. It should be noted that the selection of angle of lamina, material type and engineering constant as well as failure theory is based on the last four digit of student number. These parameters are given in Tables 1 and 2. Each student needs to specify correctly these parameters on the report. Zero marks are given for using the wrong parameters.
Questions 1-7 (Hand calculation and check with Matlab).
If this lamina is subject to three stresses (σx=-3 MPa, σy=4 MPa and ζxy=4 MPa), determine:
Q1. The compliance matrix [S] and reduced stiffness matrix [Q]
Q2. The transformed compliance matrix and transformed reduced stiffness matrix
Q3. Local stresses
Q4. Global strains
Q5. Local strains
Q6. Find the engineering constant of lamina
Q7. Find the maximum load, S, that can be applied
Questions 8-9 (Matlab)
Q8. Calculate the engineering constant of lamina in increment of 100 in the range ( 0 ≤ θ ≤ 90° ) and plot this calculation.
Q9. Calculate the maximum load, S which can be applied, in increment of 100 in the range ( 0 ≤ θ ≤ 90° ) and plot this calculation.
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