A beam fixed at both ends and subjected to nonuniform bending is a structural element that is supported at both ends and experiences bending forces that vary along its length. This can be caused by unevenly distributed loads or changes in the cross-sectional shape of the beam.
The bending moment for a beam fixed at both ends and subjected to nonuniform bending can be calculated using the equation M = EI(d^2y/dx^2), where E is the modulus of elasticity, I is the moment of inertia, y is the deflection of the beam, and x is the distance along the beam. This equation takes into account the varying bending forces along the length of the beam.
The boundary conditions for a beam fixed at both ends and subjected to nonuniform bending are that the beam is fixed and has zero deflection at both ends. This means that the beam cannot rotate or move vertically at its supports, and the slope of the beam at the supports is also zero.
The load distribution directly affects the bending moment in a beam fixed at both ends. A nonuniform distribution of load will result in a nonuniform bending moment along the beam. The bending moment will be higher where the load is concentrated, and lower where there is less load.
A simply supported beam is supported at two points and experiences bending forces that are uniformly distributed along its length. In contrast, a beam fixed at both ends and subjected to nonuniform bending is fixed at both ends and experiences varying bending forces along its length. This makes it more complex to analyze, but it can also withstand higher loads and has greater stability.