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Steel Designers' Manual - 6th Edition (2003)
310 Introduction to manual and computer analysis
9.5.3 The area moment method
The simplest technique of analysing a beam which is indeterminate to a low degree
is by the area moment method.The method is based on two theorems (see Fig. 9.22):
• Area Moment Theorem 1: The change in slope (in radians) between two points
of the deflection curve in a loaded beam is numerically equal to the area under
the M/EI diagram between these two points.
• Area Moment Theorem 2: The vertical intercept on any chosen line between the
tangents drawn to the ends of any portion of a loaded beam, which was originally
straight and horizontal, is numerically equal to the first moment of the area
under the M/EI diagram between the two ends taken about that vertical line.
M
qB - qA
= area of diagram between A and B
EI
M
= Ú d
EI x
B
A
M
D= moment of the diagram between A and B taken about the
EI
vertical line RS
Mx
= Ú d
EI x
B
A
Fig. 9.22 Area moment theorems
I I I I
I I I I
I I M/EI diagram R
deflection curve ______
eB:eA
(9.16)
(9.17)