[[wiki-architecture]] · [[Architectural Concepts and History]] · [[ARCHITECTURE]] · [[000]]
# Bending stiffness
The bending stiffness (
K
{\displaystyle K}
) is the resistance of a member against bending deflection/deformation. It is a function of the Young's modulus
E
{\displaystyle E}
, the second moment of area
I
{\displaystyle I}
of the beam cross-section about the axis of interest, length of the beam and beam boundary condition. Bending stiffness of a beam can analytically be derived from the equation of beam deflection when it is applied by a force.
K
=
p
w
{\displaystyle K={\frac {\mathrm {p} }{\mathrm {w} }}}
where
p
{\displaystyle \mathrm {p} }
is the applied force and
w
{\displaystyle \mathrm {w} }
is the deflection. According to elementary beam theory, the relationship between the applied bending moment
M
{\displaystyle M}
and the resulting curvature
κ
{\displaystyle \kappa }
of the beam is:
M
=
E
I
κ
≈
E
I
d
2
w
d
x
2
{\displaystyle M=EI\kappa \approx EI{\frac {\mathrm {d} ^{2}w}{\mathrm {d} x^{2}}}}
where
w
{\displaystyle w}
is the deflection of the beam and
x
{\displaystyle x}
is the distance along the beam. Double integration of the above equation leads to computing the deflection of the beam, and in turn, the bending stiffness of the beam.
Bending stiffness in beams is also known as Flexural rigidity.
== See also ==
Applied mechanics
Beam theory
Bending
Stiffness
== References ==
- [[Building Construction]]
- [[Building Construction/Area Programming]]
- [[Building Construction/Construction & Materials]]
- [[Building Construction/Construction & Materials/Building Material]]
- [[Building Construction/Construction & Materials/Building Material/Concrete and Cement]]
- [[Building Construction/Construction & Materials/Building Material/Glass and Glazing]]
- [[Building Construction/Construction & Materials/Building Material/Insulation Materials]]
- [[Building Construction/Construction & Materials/Building Material/Metals and Alloys]]
- [[Building Construction/Construction & Materials/Building Material/Natural Stone]]
- [[Building Construction/Construction & Materials/Building Material/Polymers and Composites]]