ΤΕΧΝΟΛΟΓΙΑ ΚΑΙ ΜΗΧΑΝΙΚΗ ΣΥΝΘΕΤΩΝ...
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1 ΤΕΧΝΟΛΟΓΙΑ ΚΑΙ ΜΗΧΑΝΙΚΗ ΣΥΝΘΕΤΩΝ ΥΛΙΚΩΝ Ακαδ. Έτος 2015-2016 1. Two cylindrical pressure vessels made of the same unidirectional lamina but with different fiber orientations were loaded as shown in Fig. 1 and gave the following strain readings: Fig. 1 Cylinder A Diameter: D = 100 mm Thickness: h = 5 mm Hoop wound (i.e., fibers in the circumferential direction) Internal pressure: p = 20 MPa Measured strains: ε x = 8 x 10 -3 , ε y = ε θ = 2.75 x 10 -3 Cylinder B Diameter: D = 100 mm Thickness: h = 5 mm Helically wound at θ = 45 ο Axial load: P = 147 kN Measured strain: ε x = 7 x 10 -3 Assuming v 12 = 0.3, determine lamina moduli E 1 , E 2 , and G 12 . 2. A thin-wall tube made of a unidirectional lamina with a fiber direction θ to its axis is loaded in torsion as shown in Fig. 2. Using the maximum strain theory , plot torsional strength, T f , versus θ (for 0 ο ≤ θ ≤ 90 ο ) for the following material properties: E 1 =10E 2 , v 12 * = 0.25, F 1t = F 1c = 2F 2c = 4F 6 =10F 2t = 1000 MPa. Fig. 2 Note : F 1t and F 1c are the longitudinal tensile and compressive strengths, F 2t and F 2c are the transverse tensile and compressive strengths and F 6 (F 12 ) is the in-plane shear strength.
Transcript of ΤΕΧΝΟΛΟΓΙΑ ΚΑΙ ΜΗΧΑΝΙΚΗ ΣΥΝΘΕΤΩΝ...
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ΤΕΧΝΟΛΟΓΙΑ ΚΑΙ ΜΗΧΑΝΙΚΗ ΣΥΝΘΕΤΩΝ ΥΛΙΚΩΝ Ακαδ. Έτος 2015-2016
1. Two cylindrical pressure vessels made of the same unidirectional lamina but with different fiber orientations were loaded as shown in Fig. 1 and gave the following strain readings:
Fig. 1
Cylinder A
Diameter: D = 100 mm Thickness: h = 5 mm Hoop wound (i.e., fibers in the circumferential direction) Internal pressure: p = 20 MPa Measured strains: εx= 8 x 10-3, εy = εθ = 2.75 x 10-3
Cylinder B
Diameter: D = 100 mm Thickness: h = 5 mm Helically wound at θ = 45ο Axial load: P = 147 kN Measured strain: εx= 7 x 10-3
Assuming v12 = 0.3, determine lamina moduli E1, E2, and G12.
2. A thin-wall tube made of a unidirectional lamina with a fiber direction θ to its axis is loaded in torsion as shown in Fig. 2. Using the maximum strain theory, plot torsional strength, Tf, versus θ (for 0ο ≤ θ ≤ 90ο) for the following material properties:
E1 =10E2, v12* = 0.25, F1t = F1c = 2F2c = 4F6 =10F2t = 1000 MPa.
Fig. 2
Note: F1t and F1c are the longitudinal tensile and compressive strengths,
F2t and F2c are the transverse tensile and compressive strengths and F6 (F12) is the in-plane shear strength.
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3. A laminate is balanced if it consists of pairs of layers with identical thickness and elastic properties but having +θ and -θ orientations of their principal material axes with respect to the laminate principal axes.
A balanced cross-ply laminate possessing mid-plane symmetry is made-up of laminae having the following properties:
EL = 15 GPa, ET = 6 GPa, GLT = 3 GPa, νLT = 0.5
The laminate is subjected to a normal axial stress of 15 MPa and a shear stress of 1.0 MPa.
(a) Calculate the normal and shear stresses in the 0o and 90o plies.
(b) Calculate the residual stresses in the cross-ply laminate that is fabricated at 125oC and cooled to 25oC. Given αL = 7.0 × 10-6/oC and αT = 23.0 × 10-6/oC. How will the residual stresses be affected by interchanging locations of 0o and 90o plies?
4. Α laminate of [0/±45/90]s lay-up is loaded under in-plane biaxial loading :
Nx = No
Ny = 2No
Nxy = 0
and the resulting strains are: εx = 1.3 × 10-3, εy = 5.1 × 10-3.
Determine Poisson's ratio νxy.
5. An unsymmetric cross-ply laminate [04/904]2, which is originally in the form of a flat plate, is bent and glued at the seam to form a tube of 5 cm radius such that the outermost ply has fibers in the hoop direction.
Calculate the ply stresses and strains when the tube is subjected to a torque of 0.5 N∙m. Assume that each lamina is 0.125 mm thick and has the following properties:
EL = 138 GPa, ET = 8.96 GPa, GLT = 7.1 GPa, νLT = 0.3
(Hint: Use the partially inverted form of the stiffness matrix to obtain mid-plane strains).
