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Homework7 sol

# Homework7 sol - Use material properties given below E1 =...

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Fall 2010 - Introduction to Composite Materials – 3 credits Cross-Listed Course: MAE 4550, CEE 4770, MSE 5550, TAM 4550/5550 HW 7. Failure Criteria and Design Date Due: November 2, 2010 Consider a tube made of [±45/0 3 ] s carbon fiber composite. The tube is subjected to an axial force P (tension) and a positive Torque T (the vector T at the left end is along the positive axis x, which is the axis of the tube. The mean radius of the tube is 30mm and the thickness of each layer is 0.25mm. Compute stress matrix {σ} x and {σ} 1 for the following cases: (i) T=1 kN.m (ii) P=1 kN (iii) T=1 kN.m and P=1 kN (just do superposition) For each case clearly draw the distribution of {σ} x and {σ} 1 in each layer or group of layers. Note that {σ} x is in global coordinate system and {σ} 1 is in local (or material) coordinate system

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Unformatted text preview: Use material properties given below: E1 = 125 Gpa E2 = 10 GPa v12 = 0.25 G12 = 5 GPa SOLUTION This solution is almost exactly the same as homework 6 solution except for: i) T=1kN.m The torque will contribute to Nxy, which needs to be in units of Force/unit length. Nxy=Torque/(circumference*radius) = T/(2*π*r 2 ) Next, find Q, , and in the same way as in homework 6. Since the laminate is symmetric, [B] = 0. Since there is no moment, we don’t need to worry about solving for [D] and [κ] = 0 Then, It follows that To find stress in the material coordinates, ii) The process for this section is the exact same, but the N vector is based on the axial force/unit length… Nx=P/(2*π*r 2 ) iii) This step is simply superposition of the previous two solutions....
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