Question

6.3-2 a sandwich beam having steel faces enclosing a plastic core is subjected to a bending momentm 5 ? 5 kn m. the thickness of each steel face ist 5 3 mm with modulus of elasticity e 5 200 gpa s .the height of the plastic core is hp 5 140 mm, andits modulus of elasticity is e 5 800 mpa p . the overall dimensions of the beam are h 5 146 mm andb 5 175 mm.using the transformed-section method, determine the maximum tensile and compressive stressesin the faces and the core.

Answer 1

To find the maximum tensile and compressive stresses in a composite beam with different materials, we use the transformed-section method to evaluate the effective moduli, locate the neutral axis, calculate the moment of inertia, and apply the bending stress formula.

Step-by-step explanation:

To determine the maximum tensile and compressive stresses in the sandwich beam's steel faces and plastic core using the transformed-section method, we must first calculate the ratio of the moduli of elasticity of steel to plastic, and then find the transformed section. The modulus of elasticity of steel (Es) is given as 200 GPa, and for plastic (Ep), it is 800 MPa (or 0.8 GPa). The transformed sectional area of plastic, Ap*, can be found by multiplying the actual plastic area (Ap) by (Es/Ep). Once the transformed section is determined, the location of the neutral axis can be calculated.

Using the neutral axis location, the moment of inertia (I) for the transformed section can be determined. The maximum bending moment (M) is given as 5 kN·m. The maximum stresses can then be found using the bending stress formula σ = M × y/I, where y is the distance from the neutral axis to the point of interest on the beam section. The maximum tensile and compressive stresses occur at the extreme fibers of the steel faces and at the top and bottom of the core.