Question 6.3: A simply supported laminated composite beam (Figure 6.4) of ...
A simply supported laminated composite beam (Figure 6.4) of length 0.1 m and width 5 mm made of graphite/epoxy has the following layup: [0/90/–30/30]_2. A uniform load of 200 N/m is applied on the beam. What is the maximum deflection of the beam? Find the local stresses at the top of the third ply (–30°) from the top. Assume that each ply is 0.125 mm thick and the properties of unidirectional graphite/epoxy are as given in Table 2.1.
TABLE 2.1
Typical Mechanical Properties of a Unidirectional Lamina (SI System of Units)
Property | Symbol | Units | Glass/ epoxy |
Boron/ epoxy |
Graphite/ epoxy |
Fiber volume fraction | V_f | 0.45 | 0.50 | 0.70 | |
Longitudinal elastic modulus | E_1 | GPa | 38.6 | 204 | 181 |
Transverse elastic modulus | E_2 | GPa | 8.27 | 18.50 | 10.30 |
Major Poisson’s ratio | V_{12} | 0.26 | 0.23 | 0.28 | |
Shear modulus | G_{12} | GPa | 4.14 | 5.59 | 7.17 |
Ultimate longitudinal tensile strength | (\sigma_1^T)_{ult} | MPa | 1062 | 1260 | 1500 |
Ultimate longitudinal compressive strength | (\sigma_1^C)_{ult} | MPa | 610 | 2500 | 1500 |
Ultimate transverse tensile strength | (\sigma_2^T)_{ult} | MPa | 31 | 61 | 40 |
Ultimate transverse compressive strength | (\sigma_2^C)_{ult} | MPa | 118 | 202 | 246 |
Ultimate in-plane shear strength | (\tau_{12})_{ult} | MPa | 72 | 67 | 68 |
Longitudinal coefficient of thermal expansion | \alpha_1 | μm/m/°C | 8.6 | 6.1 | 0.02 |
Transverse coefficient of thermal expansion | \alpha_2 | μm/m/°C | 22.1 | 30.3 | 22.5 |
Longitudinal coefficient of moisture expansion | \beta_1 | m/m/kg/kg | 0.00 | 0.00 | 0.00 |
Transverse coefficient of moisture expansion | \beta_2 | m/m/kg/kg | 0.60 | 0.60 | 0.60 |
Source: Tsai, S.W. and Hahn, H.T., Introduction to Composite Materials, CRC Press, Boca Raton, FL, Table 1.7, p. 19; Table 7.1, p. 292; Table 8.3, p. 344. Reprinted with permission.
TABLE 1.7
Chemical Composition of E-Glass and S-Glass Fibers
Material | % Weight | |
E-Glass | S-Glass | |
Silicon oxide | 54 | 64 |
Aluminum oxide | 15 | 25 |
Calcium oxide | 17 | 0.01 |
Magnesium oxide | 4.5 | 10 |
Boron oxide | 8 | 0.01 |
Others | 1.5 | 0.8 |
Our explanations are based on the best information we have, but they may not always be right or fit every situation.
Learn more on how we answer questions.