Please show steps clearly as I REALLY want/need to understand this problem. Lami
ID: 1939816 • Letter: P
Question
Please show steps clearly as I REALLY want/need to understand this problem.
Laminated fiber composites are materials with a matrix made of a polymer resin or a metal with hard, strong fibers embedded in the it. These fibers are usually aligned along a particular direction. Sheets of these materials can be used in such a way that the direction of the fibers is not parallel to the coordinate system suggested by the geomnetry of the piece or component made with the composite, as shown in the figure. Note that the fibers are contained in the x-y plane, but are inclined 45degree with respect to y. The natural coordinate system for these composites is with one axis parallel to the fibers and another two axes perpendicular to them. In this particular case, it is known that the composite will fail if one or all of the following limits are exceeded: tensile normal stress along the fibers: 400 MPa. Tensile normal stress perpendicular to the fibers: 150 MPa. Shear stress parallel to the fiber: 50 MPa (any sense). Shear stress perpendicular to the fiber: 100 MPa (any sense). Compression normal stresses do not occur in the particular application considered here. Assuming that all these stresses occur simultaneously in the x'y'z coordinate system in a manner consistent with equilibrium, find: The stresses that can be applied in the xyz coordinate system without producing failure of the composite. Note that you know sigma' in this case and you need to find out sigma. Hint: Remember that sigma' = RsigmaT. In addition, the rotation matrix is orthogonal, i.e., RRT = 1.20 points.Explanation / Answer
Try using calculus with the laws of refraction and/or reflection.