Draw qualitatively correct deformed shapes for the beams.  Make sure the support conditions are satisfied.  In particular, at a fixed support the elastic line must have a horizontal tangent.  Note where inflexion points occur.  These are points where the curvature k of the elastic line changes sense, and is zero.  Since  k  = M/EI, the bending moment is zero at an inflexion point, and the  sense of k and M must always be the same.   For each case, draw on the same sketch a qualitatively correct bending moment diagram.   The first case is shown as an example.

The problems shown in the figure are all statically indeterminate to the first degree, and the object of the method of superposition is to determine the statical redundant X by means of a compatibility equation. Depending on the sign convention, the compatibility equation has the form

D_x + D_o = 0

or

D_x = D_o

Your task is only to set up each problem by first adding a deformed shape to the given figure, then drawing two figures alongside the given one showing, respectively, D_x and D_o.  The choice of X is set in each case.  The first case is shown as an example, with the sign convention corresponding to D_x + D_o = 0.  Do the following:

a) Superimpose on the given sketch a qualitatively correct deformed shape.

b) Draw a sketch of the primary structure, i.e. the structure obtained by releasing the restraint associated with X.

    Apply X, and indicate on a sketch of the deformed shape the displacement at the release, D_x, caused by X.

    Write the formula by which D_x may be determined in terms of X.  Assume L and EI where needed.

c) Draw a sketch of the deformed primary structure subjected to the given loading.

   Indicate the displacement at the release,  D_o, caused by the given loading.

   Write the formula by which D_o may be determined in terms of the given loading.