Analysis Lecture 3

Analysis Lecture 3 - TOPIC 3 EQUILIBRIUM METHOD MOMENT...

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CIVL2007 Theory and Design of Structures II Analytical Component (16 February 2007) page 61 TOPIC 3: EQUILIBRIUM METHOD MOMENT DISTRIBUTION METHOD - LECTURE NOTES - Applications of the Moment Distribution Method The moment distribution method is suited to statically indeterminate beams and frames (sway and non-sway). Continuous Beams Non-Sway Frames Sway Frames
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CIVL2007 Theory and Design of Structures II Analytical Component (16 February 2007) page 62 General Comments The Moment Distribution Method was presented by Hardy Cross in 1930. It is recognised as one of the most notable advances in structural engineering of the twentieth century and was the dominant method of analysing indeterminate structures until the advent of the computer. The Moment Distribution Method still has an important place in the structural engineering world for the quick analysis of structures with low degrees of indeterminacy (static) in addition to an effective tool in teaching equilibrium based methods of structural analysis to students of engineering. Characteristics Iterative solution Solution is approximate but can be refined to any degree of accuracy by conducting more iterations Very effective in analysing plane frames with a high degree of static indeterminacy Distinguishes between non-sway and sway frames (joint translation) General Principles Displacement method of analysis When a structure carries load it deforms The load carried is shared by members in a structure The load path depends on the relative member stiffness Stiffness = load/deformation (e.g. kN/m) or moment/rotation (e.g. kNm/rad) Moment distribution considers primarily the rotational stiffness (moment/rotation) of members in a structure
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CIVL2007 Theory and Design of Structures II Analytical Component (16 February 2007) page 63 Prerequisites of the Moment Distribution Method The moment distribution method begins by assuming each joint of a structure is fixed. By unlocking and locking each joint in succession, the internal moments at the joints are distributed and balanced until the joints have rotated to their final positions. The process of alternately clamping and releasing joints until equilibrium is achieved is known as the Moment Distribution Method . Moment Distribution Method for Beams A derivation of the moment distribution method applied to beams is now given followed by a worked example. Theory Consider the 2-span continuous beam below. The beam is clamped at end A and C and free to rotate at B. A B C (a) FEM AB FEM BA = M B (b) θ B θ b M BA M BC M B (c) M BA M BA (d) M BC M CB
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CIVL2007 Theory and Design of Structures II Analytical Component (16 February 2007) page 64 Initially assume joint B is also clamped, therefore end moments at A and B are produced, i.e. FEM AB and FEM BA , respectively.
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