where MFAB and MFBA are fixed-end moments at supports A and B, respectively, due to the applied load. Cab is the rotation as a result of the relative displacement between the member ends A and B given as

where Aab is the relative deflection of the beam ends and yA and yB are the vertical displacements at ends A and B. Fixed-end moments for some loading cases may be obtained from Figure 2.8. The slope deflection equations (Equations 2.21) show that the moment at the end of a member is dependent on member properties EI, length l, and displacement quantities. The fixed-end moments reflect the transverse loading on the member.

2.4.2 Frame Analysis Using Slope Deflection Method

The slope deflection equations may be applied to statically indeterminate frames with or without side sway. A frame may be subjected to side sway if the loads, member properties, and dimensions of the frame are not symmetrical about the centerline. Application of the slope deflection method can be illustrated with the following example.

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