This video shows how you can calculate deflection and slope of a cantilever beam with a point load at the free end using the double integration method.

Differential Equation of the Elastic Curve :-    • How to Calculate Beam Deflections & S...  
Sign Convention: Bending Moment, Axial Force & Shear Force:    • Sign Convention: Bending Moment, Shea...  
1/R = M/EI:    • How to Derive Bending Equation | Flex...  
How to Derive Bending Equation aka Flexural Formula:    • How to Derive Bending Equation | Flex...  
Strain (ε), Stress (σ) and Radius of Curvature (R):    • Strain (ε), Stress (σ) and Radius of ...  

M - Bending moment
L - Length of the beam
F - Force applied to the free end of the centilever beam
dy/dx - Slope

E - Modulus of elasticity
I - Moment of inertia
EI - Flexural stiffness

0:23 - Differential equation of the elastic curve


Assumptions used to derive the differential equation of elastic curve:
1) Beam is stressed within the elastic limit i.e. stress is proportional to strain (Hooks law).
2) Beam curvature is very small.
3) Deflection resulting from the shear deformation of the material or shear stresses is neglected.
4) Simple bending theory (i.e. bending equation) is valid.

Theory behind the bending equation derivation has been developed for pure bending. Important points:
a) Plane sections remain after bending.
b) Beam material is homogenous and isotropic.
c) Beam is symmetrical about the plane of bending.
d) The stress-strain relationship is linear and elastic.
e) Young’s modulus remains the same for tension and compression.
f) Beam is initially straight and shape remains the same along the beam.

Pure bending: Stresses in an element caused by a bending moment applied to the element without axial, shear or torsion forces acting on the element.

#Slope #Deflection #PointLoad #CantileverBeam

Design to Eurocodes:
EN 1990 (EC0) - Basis of structural design
Design to Eurocode 1 - EN 1991 (EC1) - Actions on structures
Design to Eurocode 2 - (EN 1992 EC2) - Design of concrete structures including concrete bridges
Design to Eurocode 3 - (EN 1993 EC3) - Design of steel structures including steel bridges
Design to Eurocode 4 - (EN 1994 EC4) - Design of composite steel & concrete structures including composite bridges
Design to Eurocode 7 - (EN 1997 EC7) - Geotechnical design

Terms of use in addition to "Standard YouTube Licence": http://www.eurocoded.com/mod/page/vie...