Problem 5.4. Bending of reinforced I beam Figure 5.13 depicts an aluminum I beam of height h = 0.25 m, width b = 0.2 m, flange thickness ta = 16 mm, and web thickness tw = 12 mm. The beam is reinforced by two layers of unidirectional composite material of thickness tc = 5 mm. The section is subjected to a
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Problem 5.4. Bending of reinforced I beam
Figure 5.13 depicts an aluminum I beam of height h = 0.25 m, width b = 0.2 m, flange thickness ta = 16 mm, and web thickness tw = 12 mm. The beam is reinforced by two layers of unidirectional composite material of thickness tc = 5 mm. The section is subjected to an axial force N1 = 250 kN and bending moment M3 = 200 kN·m. The Young’s moduli for the aluminum and unidirectional composite are Ea = 73 GPa and Ec = 140 GPa, respectively. (1) Compute the axial and bending stiffnesses of the cross section. (2) Find the distribution of axial stress over the cross-section. Sketch it along the ¯ı2 axis. Sketch it across the tops of both flanges. (3) Find the magnitude and location of the maximum axial stress in the aluminum and composite layers. (4) Assume the applied loads grow in a proportional manner, i.e. the applied loads are λN1 and λM3. If the allowable stress for the aluminum and unidirectional composite are σallowa = 400 MPa and σallowc = 1500 MPa, respectively, find the maximum loading factor, λMax. (5) Sketch the distribution of axial strain along the ¯ı2 axis, and describe its distribution over the entire cross-section.
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