Pure bending ( Theory of simple bending) is a condition of stress where a
bending moment is applied to a beam without the simultaneous presence of
axial
Axial may refer to:
* one of the anatomical directions describing relationships in an animal body
* In geometry:
:* a geometric term of location
:* an axis of rotation
* In chemistry, referring to an axial bond
* a type of modal frame, in music
* ...
,
shear, or
torsional forces.
Pure bending occurs only under a constant bending moment (M) since the shear force (V), which is equal to
, has to be equal to zero. In reality, a state of pure bending does not practically exist, because such a state needs an absolutely weightless member. The state of pure bending is an approximation made to derive formulas.
Kinematics of pure bending
#In pure bending the axial lines bend to form
circumferential lines and
transverse line
The transverse plane (also known as the horizontal plane, axial plane and transaxial plane) is an anatomical plane that divides the body into superior and inferior sections. It is perpendicular to the coronal and sagittal planes.
List of cli ...
s remain straight and become
radial lines.
#Axial lines that do not extend or contract form a neutral surface.
Assumptions made in the theory of Pure Bending
#The material of the beam is homogeneous
1 and isotropic
2.
#The value of Young's
Modulus of Elasticity is same in tension and compression.
#The
transverse sections
Transverse may refer to:
*Transverse engine, an engine in which the crankshaft is oriented side-to-side relative to the wheels of the vehicle
*Transverse flute, a flute that is held horizontally
* Transverse force (or ''Euler force''), the tangen ...
which were plane before bending, remain plane after bending also.
#The beam is initially straight and all longitudinal filaments bend into circular arcs with a common centre of curvature.
#The radius of curvature is large as compared to the dimensions of the cross-section.
#Each layer of the beam is free to expand or contract, independently of the layer, above or below it.
Notes:
1 Homogeneous means the material is of same kind throughout.
2 Isotropic means that the elastic properties in all directions are equal.
References
*E P Popov; Sammurthy Nagarajan; Z A Lu.
Mechanics of Material. Englewood Cliffs, N.J. : Prentice-Hall, ©1976, p. 119, "Pure Bending of Beams", {{ISBN, 978-0-13-571356-3
Force
Solid mechanics
Structural system