Advanced strenght of materials

Consider the cantilevered beam of length L, modulus E, and inertia I on elastic foundation (in blue) with stiffness k and a concentrated force P at the end. P z y(z) The boundary conditions are given by: • Solve for y(z) using the methods outlined in class and in the text. Use separate sheets of paper and put work one side only. Clearly show all steps in your analysis, including all of the details for the calculus and algebra required to obtain results. For example, to obtain second and third derivatives, you must show the first derivative work and the steps in collecting like terms to simply results for the next step in the solution. Another example is in determining the constants in the general solution by applying the boundary conditions, where each step in determining them such as solving coupled algebraic equations must be presented. Neglecting to include all steps in the solution of any part of the process will result in points taken off your score. • Express the solution as the dimensionless ratio Y as a function of Z and βL given as Where: • Z is the dimensionless parameter • βL is the dimensionless parameter obtained from your student ID according to the relationship with ID = 6894 • The reference group is the deflection at the tip of a cantilevered beam that does not have any elastic foundation under it where the deflection distribution relative to its tip is given as • For your specific value of βL, provide a plot of Y(Z,βL) vs. Z and V(Z) vs. Z on the same page comparing the solution for the beam with the elastic foundation with the solution for the beam without the elastic foundation. Use different line types or colors to identify the two curves along with a legend and axes labels.