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If the member is hinged at A rather than at B, Equation 2.316 is still valid provided that the subscript A is changed to B.

2.12.4.3 Member with End Restraints

If the member ends are connected by two linear elastic springs, as in Figure 2.120, with spring constants, PkA and Rb at the A and B ends, respectively, the end rotations of the linear springs are MA/PkA and MB/PkB. If we denote the total end rotations at joints A and B by 0A and 0B, respectively, then the corresponding member end rotations, with respect to its chord, will be (0A — MA/PkA) and (0B — MB/PkB). As a result, the slope deflection equations are modified to

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