1 Deflection Diagrams and The Elastic Curve 1
1 Deflection Diagrams and The Elastic Curve 1
1 Deflection Diagrams and The Elastic Curve 1
1-1
Deflection of structures can occur from various
sources such as
Loads
Temperatures
Fabrication errors
Settlement
Represents the elastic curve for the points at centroids of the cross-
sectional area along each of the members
1.
2.
3.
M
A B C D
4.
P
A B C D
5.
P
A B C
6.
A B C D
1-2
1-3
INTEGRATION METHOD used to determine the slope
and deflection of a beam.
Elastic deformation – beam’s slope is very small
Only deflection due to bending
Additional deflection due to shear generally represents few
percent of the bending deformation.
1. Draw an exaggerated view of the beam’s elastic curve. Recall that
points of zero slope and zero displacement occur at fixed support,
and zero displacement occurs at pin and roller supports.
2. Establish the x and y coordinate axes. The x-axis must be parallel
to the undeflected beam and its origin at the left side of the beam,
with a positive direction to the right.
3. If several discontinuous loads are present, establish x-coordinates
that are valid for each region of the beam between the
discontinuities.
4. In all cases, the associated positive y-axis should be directed
upward.
For each region in which there is an x-coordinate, express the