BEAM DEFLECTION PPT

1. STRENGTH OF MATERIAL-I
CHAPTER 3
DEFLECTION IN BEAM
Prepared by
S.MEHALA,
A/P CIVIL

2. Why Deflection a problem?
• While beam deflection itself has no bearing on the
capacity or safety of your rack, it can affect the
rack load and those interacting with the system.
As beams deflect, loads can tilt toward each
other, increasing the likelihood of contact. This
can cause product damage or pose a risk during
loading and unloading

3. Method to find Deflection in beam
• The deflections of the beam can be computed by
the following methods.
• Double integration method
• Macaulay's Method
• Moment Area method
• Conjugate Beam Method

4. Double integration method
This method entails obtaining the deflection of a
beam by integrating the differential equation of
the elastic curve of a beam twice and using
boundary conditions to determine the constants of
integration. The first integration yields the slope,
and the second integration gives the deflection

5. Macaulay's Method
• Macaulay's method (the double integration
method) is a technique used in structural analysis
to determine the deflection of Euler-Bernoulli
beams. Use of Macaulay's technique is very
convenient for cases of discontinuous and/or
discrete loading.

6. Moment Area method
• The moment-area method is one of the most effective
methods for obtaining the bending displacement in
beams and frames. In this method, the area of the
bending moment diagrams is utilized for computing the
slope and or deflections at particular points along the
axis of the beam or frame. Two theorems known as the
moment area theorems are utilized for calculation of the
deflection. One theorem is used to calculate the change
in the slope between two points on the elastic curve.
The other theorem is used to compute the vertical
distance (called tangential deviation) between a point
on the elastic curve and a line tangent to the elastic
curve at a second point

7. Conjugate Beam Method
• Conjugate beam is defined as the imaginary beam
with the same dimensions (length) as that of the
original beam but load at any point on the
conjugate beam is equal to the bending moment at
that point divided by EI. The conjugate-beam
method is an engineering method to derive the
slope and displacement of a beam.

8. SHORTCUT TO FIND DEFLECTION