In Problem 10.23, let the uniform load be w [F/L] and the maximum allowable distributed fo...

In Problem 10.23, let the uniform load be w [F/L] and the maximum allowable distributed force in the foundation be Pmax = w/8. In terms of k, l, and E, determine the second moment of area Ix of the beam.

Problem 10.23

An infinite beam on an elastic foundation is loaded uniformly over a segment l (Figure P10.23). The maximum allowable distributed force in the foundation at the center of the loaded segment is 15 N/mm. In terms of k, l, and E, determine shape y(z), rotation B(z), internal moment M(z), and internal shear V(z). Sketch each of the four expressions as is done in Figure 10.1 (see Example 10.3). the second moment of area Ix of the beam required to meet the allowable distributed force.

FIGURE P10.23

FIGURE 10.1 Infinite beam on an elastic foundation and loaded at origin.

Example 10.3