An infinitely long beam rests on an elastic foundation and is loaded by two equal forces P spaced at a distance L. The beam has bending stiffness EI and the foundation has a spring constant k.
a. Find the distance L such that the deflection y under one of the forces is the same as the deflection midway between the two forces.
b. For unit values of P, EI, and k, and with the origin midway between the two forces, write an expression for the deflection y as a function of position z. Evaluate your expression for deflection at z=± L/2.
c. Plot the expression derived in (b) over the domain - 4.0 ≤ βz ≤ 4.0.
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