Question

Consider a uniform load applied to either cantilevered or simply supported beams. When the load distribution in the governing differential equation for the equation of the elastic curve is used, ____ boundary condition(s) is/are require

Answer 1

In the case of a uniform load applied to either cantilevered or simply supported beams, certain boundary conditions are required to solve the governing differential equation for the equation of the elastic curve.

Step-by-step explanation:

In the case of a uniform load applied to either cantilevered or simply supported beams, there are certain boundary conditions that are required in order to solve the governing differential equation for the equation of the elastic curve.

For a cantilevered beam, one boundary condition is that the vertical deflection at the free end of the beam is zero. This means that the beam is fixed and cannot move vertically at the free end.

For a simply supported beam, there are two boundary conditions. The first is that the vertical deflection at each support is zero. This means that the beam is supported and cannot move vertically at the supports. The second boundary condition is that the slope of the beam at each support is zero, which means that the beam is horizontal at the supports.

Answer 2

When analyzing a beam under a uniform load using the differential equation governing the elastic curve (bending equation), different boundary conditions are required depending on whether the beam is cantilevered or simply supported.

At the fixed end (where the beam is attached or built into a support), the slope of the elastic curve is typically zero (θ = 0) because the beam cannot rotate at the fixed support.

In summary, the specific boundary conditions depend on the type of support (cantilevered or simply supported) and the constraints at those support points. These conditions are essential to solve the differential equation governing the elastic curve and obtain the specific equation for the deflection of the beam under the given loading conditions.