Deflection

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Learning Objectives:

Calculate deflection in statically determinate beams and frames

Various Methods
• • • • Double Integration Method Moment-Area Method Elastic Load Method Conjugate Beam Method

Slope at A negative

Slope at B positive

Deflection at point B

Tangential deviation between points A and B

Change in slope

Change in slope and tangential deviation between points A and B

Moment-Area Method

Beam and moment curve

M/EI curve between points A and B

Moment Area Theorems
•The change in slope between any two points on a smooth continuous elastic curve is equal to the area under the M/EI curve between these points •The tangential deviation at a point B on a smooth continuous elastic curve from the tangent line drawn to the elastic curve at the second point A is equal to the moment about B of the area under the M/EI curve between these two points.

Moment-Area Method

Horizontal, therefore the vertical distance between tangent line and elastic curve are displacements

Cantilever, point of tangency at fixed support

Moment-Area Method

Symmetric members with symmetric loading, point of tangency at intersection of axis of symmetry and elastic curve

Moment-Area Method

Point of tangency at left end of member AB
t BA L tan θ A = θ A in radians tan θ A =

θA=

t BA L

Caution 2.The theorem is applicable for continuous elastic curve 3.Presence of hinge breaks continuity of elastic curve 4.If hinge is present on beam or a frame – then work on either side of hinge (left or right side)

P 9.6 (3rd Edition)

Derive the equations for slope and deflection for the beam shown. Determine the slope at each support and value of deflection at mid span. Hint: Take advantage of symmetry; slope is zero at midspan.

P 9.13

Compute the slope at support A and the deflection at point B. Treat the rocker at D as a roller. Express the answers in terms of EI.

P 9.15 Determine the slop and deflection of point C...
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