A cantilever beam is a rigid bar or beam fixed at one end and free at the other. This document discusses calculating the deflection and slope of a cantilever beam with an end load using the double integration method. It defines slope as the angle between the tangent line and original axis, and deflection as the distance between the beam's positions before and after loading. An example problem is presented of finding these values for a cantilever beam fixed at point A carrying a load at the free end B.

1. (Double Integration Method)
MUNEEBA MARYAM
Deflection and Slope of
Cantilever Beam With End
Load

2. • BEAM:
A beam is a long thick bar of wood, metal, or concrete, especially one used to support the roof of a
building.
• SLOPE OF A BEAM:
slope at any section in a deflected beam is defined as the
angle in radians which the tangent at the section makes
with the original axis of the beam.
• Deflection of a Beam :
The deflection at any point on the axis of the beam is the distance between its position before and
after loading
• CANTILEVER BEAM
A cantilever beam is a rigid bar or beam whose one end is free while the other end is fixed to a
support. There are four kind of loads studied on cantilever beams
1. End load
2. Intermediate load
3. Uniform distributed load
4. Triangular Distributed Load

3. Cantilever beam with end load.
A cantilever AB of length L fixed at a point A and
free at point B, carrying a point load at free end
B. AB shows the position of cantilever before any load is applied
Whereas AB’ shows the
position of the cantilever
after loading. B’ is the
elastic curve and θ is the
slope. X is the distance
from point B and y is
deflection from B to B’

4. For Deflection and Slope By Double
Integration Method

12. Let’s consider an example

13. There are many other methods of finding Slope and
Deflection of beam,
1.Double integration method
2.Moment Area method
3.Macaulay’s Method
4.Conjugate bream method
5.Strain energy method
Application of Cantilever Beam
The cantilever Beam is applicable in the following cases,
✓ Construction of Building.
✓ Constructing a cantilever Bridge.
✓ For overhanging Roof projects such as a stadium Roofs,
Shelters.
✓ For making furniture, shelving.