PHYS 270 Chapter Notes - Chapter 7: Differential Equation, Statically Indeterminate, Statistical Graphics
Document Summary
Second order boundary-value problem: chapter 6 showed the symmetric bending of beams. If you can find the deflection in the y direction of one point on the cross section, we can determine the deflection of all points on the cross section. The deflection at a cross section is independent of y and z coordinates. Deflection can be a function of x shown below: the deflected curve represented by v(x) is called the elastic curve, as one moves across the beam, applied load can change. This ultimately results in different functions of x that represent internal moment mz. One for each side of x1 totals four integration constants: assuming the beam neither breaks nor kinks. The displacement functions must statisfy the following conditions: v1 and v2 are displacement functions of left and riht xj, called continuity conditions. In statically indeterminate beams, the internal moment found from static equilibrium will contain some unknown reactions in the moment expression.
