2 (Su + Sj ) — (kL)2 L2

— (Sii + Sij ) L Sii

where Sü and Sj are the member stiffness coefficients obtained from the elastic beam-column stability functions (Chen and Lui 1987). These coefficients may be expressed as

kL sin(kL) — (kL)2 cos(kL) 2 — 2 cos(kL) — kL sin(kL) (kL)2 cosh(kL) — kL sinh(kL) 2 — 2 cosh(kL) + kL sinh(kL)

where kL L^P/EI and P is positive in compression and negative in tension.

The fixed-end force vector rf is a 6 x 1 matrix that can be computed from the in-span loading in the beam-column. If curvature shortening is ignored, rf1 = rf4 = 0, rf3 = MFA, and rf6 = MFB. MFA and MFB can be obtained from Table 2.5 for different in-span loading conditions. rf2 and rf5 can be obtained from the equilibrium of forces.

If the axial force in the member is small, Equation 2.331 can be simplified by ignoring the higher-order terms of the power series expansion of the trigonometric functions. The resulting element stiffness matrix becomes

0 0

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