In structural engineering, deflection refers to the displacement of a structural element under a load. The deflection of beams and other structures can be calculated using standard formulas or methods like virtual work. Architects and engineers must consider deflection when selecting materials and designing structures to ensure adequate stiffness. Excessive deflection can be caused by factors like lower modulus of elasticity of concrete or incorrect modeling of creep. Controlling deflection is important for serviceability and preventing adverse effects on strength. There are different types of deflection like axial, lateral, angular, and torsional deflection that depend on the direction and nature of the displacement.

1. Introduction
• In structural engineering, deflection is the degree to which a part of a
structural element is displaced under a load (because it deforms). It may refer
to an angle or a distance.
• The deflection distance of a member under a load can be calculated by
integrating the function that mathematically describes the slope of the
deflected shape of the member under that load.
• Standard formulas exist for the deflection of common beam configurations and
load cases at discrete locations. Otherwise methods such as virtual work, direct
integration, Castigliano's method, Macaulay's method or the direct stiffness
method are used. The deflection of beam elements is usually calculated on the
basis of the Euler–Bernoulli beam equation while that of a plate or shell
element is calculated using plate or shell theory.

2. An example of the use of deflection in this context is in building
construction. Architects and engineers select materials for various
applications.
Examples:The force of this person standing at the end will cause the
beam to bend and deflect from its natural position. In below diagram,
the blue beam is the original position, and the dotted line simulates the
cantilever beam deflection:

3. Max.deflection to span L for beams and slabs.

4. Factors affecting deflection
•Tensile strength. The tensile strength of concrete is an important
property because the slab will crack when the tensile stress in the
extreme fibre is exceeded. ...
•Elastic modulus. ...
•Loading sequence. ...
•Cracking. ...
•Shrinkage curvature

5. What causes excessive deflection?
• There are several probable reasons for the excessive deflection: a lower
value of modulus of elasticity of concrete; neglect of the shear effect
on deflection in the design; incorrect compliance function for the
evolution of creep in time; and a higher influence of relaxation of pre-
stressed steel.

6. What is control of deflection?
• Deflection control is an important serviceability consideration in the
structural design of concrete buildings. The principal material parameters
that influence concrete deflection are modulus of elasticity, modulus of
rupture, creep, and shrinkage.
Is the importance of control of deflection of :
• The structural concrete members shall designed to have adequate
stiffness to limit deflections, which may adversely affect the strength or
serviceability of the structure at working loads.

7. Time-Dependent Deflection of In-Span Hinges in
Restressed Concrete Box Girder Bridges
Deflection Test

8. Types of deflection
Axial Deflection
Axial refers to being parallel to the centerline of the pipe expansion joint.
Compression is the axial deflection which will shorten the bellows length.
Often confusion occurs because thermal expansion in the piping will cause
the pipe expansion joint to be compressed. The specification for a pipe
expansion joint should always state the movements as they affect the pipe
expansion joint, and not as they are produced by the system.

9. Examples:

10. Lateral Deflection
Lateral refers to the direction perpendicular to the centerline of the pipe expansion joint
(in any plane). Other terms for this deflection are PARALLEL OFFSET and TRANSVERSE.
This movement occurs with both of the ends of the pipe expansion joint remaining
parallel to each other, with their centerlines being displaced, or no longer coincident.
The magnitude of the resultant LATERAL DEFLECTION is the square root of the sum of the
squares of the individual deflections. The planes of the various deflections must also be
clearly understood if the pipe expansion joint is to contain structural components such as
hinges, which may inhibit movements in certain directions, and if the individual
deflections can occur separately during the life of the pipe expansion joint.

11. Angular Deflection
When a pipe expansion joint experiences bending about its center, which is on the
centerline and halfway between the ends of the bellows, this deflection is referred to
as ANGULAR. It can occur in any plane that passes through the centerline, but the
plane should be clearly indicated if the pipe expansion joint is more complicated than
the simplest type, i.e., only a bellows with flanges or pipe ends. As in lateral
movements, piping analyses may reveal angular deflections occurring in more than
one plane.

12. Torsional Deflection
Torsion refers to twisting one end of the bellows with respect to the other end, about
the bellows centerline. Pipe expansion joints are not normally expected to accept
torsional deflection since the bellows are essentially inflexible in this direction. The
piping designer should carefully provide the system with restraints so that the pipe
expansion joint is not expected to accept TORSIONAL DEFLECTION. This catalog
contains the calculated torsional spring rate for each pipe expansion joint so that
piping designers and analysts can provide the proper inputs for piping flexibility
computer programs.

13. Thanks