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In the moment area method, draw the bending moment diagram at the section due to the fixing moment MA and MB at the fixed supports, this diagram is called as
╬╝-diagram
╬╝тА▓-diagram
S ┬╖ F. diagram
none of these
╬╝тА▓-diagram
In the Moment Area Method (often called the Conjugate Beam or Moment Distribution methodology for fixed beams), the total Bending Moment Diagram is decomposed into two parts ┬╖ The ╬╝-diagram represents the bending moment diagram due to external loads assuming the beam is simply supported, while the ╬╝тА▓-diagram represents the bending moment diagram due to the fixing moments (MAтАЛ and MBтАЛ) at the supports.
In the Moment Area Method (often called the Conjugate Beam or Moment Distribution methodology for fixed beams), the total Bending Moment Diagram is decomposed into two parts ┬╖ The ╬╝-diagram represents the bending moment diagram due to external loads assuming the beam is simply supported, while the ╬╝тА▓-diagram represents the bending moment diagram due to the fixing moments (MAтАЛ and MBтАЛ) at the supports.
M=MsimplyтИТsupportedтАЛтИТMfixingтАЛ
тИлEIMтАЛdx=0 (Slope compatibility condition for fixed ends)
The superposition principle is applied to fixed beams ┬╖ Since a fixed beam is statically indeterminate, we treat it as a simply supported beam subjected to actual loads (╬╝-diagram) and then apply the redundant fixing moments at the ends to satisfy the compatibility condition that the slope at fixed supports must be zero ┬╖ The distribution of these fixing moments forms a trapezoidal or rectangular shape known as the ╬╝тА▓-diagram.
The ╬╝-diagram corresponds to the primary structure (simply supported).
The ╬╝тА▓-diagram corresponds to the support reaction moments.
The net bending moment is the algebraic sum of the ╬╝ and ╬╝тА▓ diagrams.
In the Moment Area Method, the area of the ╬╝/EI diagram must equal the area of the ╬╝тА▓/EI diagram for fixed beams.
Simplifies analysis of statically indeterminate beams.
Visual representation helps in understanding stress distribution.
Requires accurate calculation of support moments before plotting ╬╝тА▓.
Limited to linear elastic analysis.
Analysis of fixed-ended beams.
Calculation of slopes and deflections in indeterminate structures.
The ╬╝-diagram is generally parabolic for UDL or triangular for point loads.
The ╬╝тА▓-diagram is usually trapezoidal, representing the constant or linearly varying nature of end moments across the span.
B is correct тАФ The ╬╝тА▓-diagram is the specific terminology used to denote the bending moment diagram created solely by the fixed-end moments MAтАЛ and MBтАЛ in the Moment Area Method.
Always remember that in indeterminate structures, the final bending moment diagram is the superposition of the free bending moment diagram (╬╝) and the restrained bending moment diagram (╬╝тА▓).