Recall that the Influence function (or Green’s function), G(x, ¿) is a solution to the differential equation d4y dx4 from a 1N force at x =8(x − )—and thus gives the deflection of a beam under a point

Question1 .

Recall that the Influence function (or Green’s function), G(x, ¿) is a solution to the differential
equation d4y dx4 from a 1N force at x =8(x − )—and thus gives the deflection of a beam under a point load coming EI(x) ξ.

You can use this fact, combined with what you know about constants and integration, to use the Influence function to find the deflection for any point load (not just a point load from a 1N force).

Question 2.

Suppose we have a uniform beam that: is 3.51 metres long, has a flexural rigidity of 33133Nm2, and is supported with a simple support on the left end, and an elastic support (with spring constant ko = – 18345) on the right end.

Find the Influence function of the beam for the beam and use it to find the folowing deflection of the beam in millimetres at various points on the beam under different point loads, according to the table, below. Fill out the table with your answers