Final answer:
To find the largest couple that can be applied to a nylon beam, one must use the bending stress formula, taking into account the allowable tensile and compressive stresses for nylon, along with the beam's moment of inertia and cross-sectional area.
Step-by-step explanation:
The question asks to determine the largest couple M that can be applied to a nylon beam, given the allowable stress in tension (24 MPa) and compression (29.5 MPa). To answer this, one would typically use the bending stress formula derived from the bending moment equations in mechanics of materials. The formula σ = M*y/I (where σ is the stress, M is the moment, y is the distance from the neutral axis, and I is the moment of inertia) would be employed, ensuring that the maximum tensile and compressive stresses do not exceed the given allowable stress limits for nylon. This process involves calculations that are not presented in the provided context, hence specific numerical values cannot be ascertained without additional information such as the beam's geometry and material properties.
It must be noted that determining the largest couple requires knowledge of the beam's cross-sectional area, the moment of inertia about the neutral axis, and the most distant fiber from the neutral axis. One must also consider the assumptions of linear elastic behavior and pure bending in the derivation of the bending stress formula.