Materials used in structures have a thermal response character, which is noted but rarely developed further in solving problems. The bimetallic strip is presented as an example of where thermal effects can be useful (in thermostats, shape-changing structures etc) and where the coupling between equilibrium, compatibility and the generalised Hooke's Law is evidently demonstrated analytically.

Practical frames have interconnected beams and columns, where moments and forces are transmitted across a local, indeterminate junction. The prospect of a more complex analysis is, however, reduced in certain cases of layout; moreover, it is shown that the simpler layout of a determinate junction proves to be analytically more challenging than the indeterminate case.

The deflection characteristics of a simply-supported beam are calculated directly and summarised alongside a cantilever, in order to define standard cases of deflection coefficients.

The construction of bending moment (and shear force) diagrams is considered using fundamental equilibrium relationships, rather than resorting to remembering standard loading cases. The importance of sign convention, coordinate direction and behaviour at supports is given explicit attention in several examples.

Several techniques based on exploiting symmetry are introduced for reducing the level of calculation in beams and frames that are symmetrical or anti-symmetrical in their original layout. Attention is paid to the performance of stress resultants and kinematical parameters on the plane of symmetry in order to establish quantities which are zero from the outset. This approach reduces, for example, the number of redundancies in statically indeterminate cases.

Rather than solve the usual governing equation of deformation for a deflected cable, its shape is computed indirectly from the applied loading, noting that the two variations must differ by two orders. Solutions by polynomial subsititution are thus appropriate, where coefficicents depend on the specific boundary conditions of the problem. The non-uniform build-up of tensions in a cable wrapped around a rough drum is determined, which then informs a simple experiment for determining the coefficient of friction.

Designing a structure by the method of Lower Bound rarely considers the supports: that often, sizing the 'main beam' is key. One difficulty is how to interpret the nature of supports themselves in a Lower Bound analysis context. Some clarity is given for a nominal multi-span beam where one of its supports is realised differently in three ways.

Often loads applied to a structure do not depend on the deflections they induce. If there is a dependency, they couple the very forces in equilibrium to the displacements they induce, leading to statical indeterminacy. Solving such problems proceeds by assuming a displacement profile dictated by the characteristic behaviour of the loads they couple to. They may be actually very small, but such purpose allows us to express the loads accurately in terms of them whilst considering equilibrium in the undeformed state - a state of pseudo-equilibrium.