TABLE OF CONTENTS | Q: | 8.1 By means of drawing free body diagrams of the beam tip and the tip nonstructural mass that include inertia forces, derive the tip boundary conditions for the cantilevered beam of Example 8.5, which are  Recall that for this doubly symmetric cross section (the area product of inertia is zero) the internal elastic shear force is EIw ? ? and the internal elastic bending moment is EIw ? ?. |
| Q: | 8.2 (a) Redo Example 8.4 when the applied downward loading per unit length is spatially uniform but increases linearly with time. That is, let the simply supported, undamped beam be subject to the following force per unit of beam length  where f 0 has units of force per length. (b) Use the result of part (a) to get the response to a triangular-shaped pulse that peaks at time t = t 1 and that is symmetrical about t = t 1. |
| Q: | 8.3 Determine the complete response of a uniform, simply supported beam of length L and stiffness coefficient EI, originally at rest, when it is subjected to an x, z plane lateral loading per unit of beam length that varies sinusoidally in both space and time. In other words, solve the beam bending equation when the upwardly acting, externally applied loading per unit length for the time period 0 ? t ? t 1 is  and is zero otherwise. Hint: Be... |
