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2 - Moment Area Method

The moment area method is a graphical technique developed by Otto Mohr and formalized by Charles E. Greene to determine the slope and deflection of elastic curves in bending. It relates the change in slope between two points on the curve to the area under the moment of inertia diagram between those points. Similarly, the vertical deviation between tangent lines at two points equals the moment of that area about one point. Examples are given of using the method to calculate slope at different points and deflection at one point for beams with given properties under loading.

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John Ray Cuevas
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716 views16 pages

2 - Moment Area Method

The moment area method is a graphical technique developed by Otto Mohr and formalized by Charles E. Greene to determine the slope and deflection of elastic curves in bending. It relates the change in slope between two points on the curve to the area under the moment of inertia diagram between those points. Similarly, the vertical deviation between tangent lines at two points equals the moment of that area about one point. Examples are given of using the method to calculate slope at different points and deflection at one point for beams with given properties under loading.

Uploaded by

John Ray Cuevas
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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ce132p structural theory 2

--MOMENT AREA METHOD


1-4
Developed by Otto Mohr

Later stated formally by Charles E. Greene in 1873

Provide semi-graphical technique in determining


the slope of the elastic curve

deflection due to bending

Advantageous:
Beam subjected to series of concentrated load

Segments having different moment of inertia


The change in slope between any two
points on the elastic curve equals the
area of the M/EI diagram between
these two points.
B/A is referred to as the angle of the tangent at B is measured with
respect to the tangent at A.
Angle is measured counterclockwise from tangent A to tangent B if
the are of M/EI diagram is positive.
Negative clockwise
Measured as radians
The vertical deviation of the tangent at a point
(A) on the elastic curve with respect to the
tangent extended from another point (B)
equals the moment of the area under the
M/EI diagram between the two points (A and
B). This moment is computed about point A
(the point on the elastic curve), where the
deviation tA/B is to be determined.
A B
B/ A tB / A
Determine the slope at points B and C of the beam.
E = 200 GPa and I = 360 x 106 mm4.

Ans. B = -0.00521 rad and C = -0.00694 rad


Determine the slope at point C of the beam.
E = 200 GPa and I = 6 x 106 mm4.

Ans. C = 0.112 rad


Determine the deflection at point C of the beam.
E = 200 GPa and I = 250 x 106 mm4.

Ans. C = -0.143 m
Next topic: CONJUGATE BEAM METHOD

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