# 9.1 Introduction

The *slope-deflection method* is an alternate way to analyse indeterminate structures. In many ways, it can be thought of as the opposite of the force method.

In the force method, we first identified redundant forces for the analysis and solved for them. In the slope-deflection method, we will first identify unrestrained degrees-of-freedom (DOFs, which are rotations or deflections) and solve for them. In the force-method, we found the redundant forces in terms of the deflections or rotations at the redundant force locations. In the slope-deflection method, we will find the deflections/rotations of the unrestrained DOFs in terms of the forces and moments at the DOF locations. In the force method, we solved for the unknown redundant forces by applying compatibility conditions at the redundant force locations. In the slope-deflection method, we will solve the deflections/rotations of the unrestrained DOFs by applying equilibrium conditions at the DOF locations. So, to in whenever we used a force or moment in the force method, we will use a deflection or rotation in the slope-deflection method, and vice versa.

The consequence of this is that, while the force method required us to solve a system of equations with as many equations/unknowns as there were redundants, for the slope-deflection method we will need to solve a system of equations with as many equations/unknowns as there are degrees-of-freedom (DOFs). So, where the force method was good at analysing indeterminate structures with a low number of degrees of indeterminacy, the slope-deflection method will be good for analysing highly-constrained structures, with a lot of degrees of indeterminacy, and not much freedom of movement (not many DOFs).