Calculate deflection in statically determinate beams and frames
• • • • 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
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.
Horizontal, therefore the vertical distance between tangent line and elastic curve are displacements
Cantilever, point of tangency at fixed support
Symmetric members with symmetric loading, point of tangency at intersection of axis of symmetry and elastic curve
Point of tangency at left end of member AB
t BA L tan θ A = θ A in radians tan θ A =
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.
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...