UNSYMMETRICAL BENDING
Introduction
18 AAC304 is the subject for the first class in the fifth semester
on aircraft structures. Here, we will be discussing the primary
structural elements of an aircraft, such as the wing, landing
gear, and tail plane. The fuselage structure is also an important
component, consisting of longitudinal stiffening members
called longerons, as well as stringers and bulkheads. These
structural elements are responsible for transmitting and
resisting externally applied loads, providing an aerodynamic
shape, and protecting passengers and payload systems from
environmental conditions.
There are two main types of aircraft structures: semi-
monocoque and monocoque. In semi-monocoque structures,
the outer surface of the shell is supported by longitudinal
stiffening members, rings, or formers, which allow the structure
to resist bending, compressive, and torsional loads. On the
other hand, in monocoque structures, the skin alone must
resist all the applied loads. The wing structure is a good
example of a semi-monocoque structure, with ribs providing
the aerodynamic shape and various structural elements like
skin, fuel tank, and stringers.
When designing aircraft structures, it is important to consider
the aerodynamic moments and loads imposed on the structure.
The structural design engineer must ensure that the structure
can balance these loads and moments. Additionally, aircraft
structural components need to have a high strength-to-weight
ratio or stiffness ratio to minimize weight penalties. This often
results in thin-walled sections with different geometrical cross-
sections such as channel, circular, rectangular, square, and so
on.
The properties of the geometrical cross-section, including the
area moment of inertia, play a vital role in determining the
structural efficiency in resisting bending. Structural
components can be open or closed sections, subjected to axial,
bending, shear, and torsional loads. The efficiency of open or
closed sections in resisting torsion or bending is an important
aspect to be considered.
, When a load is applied perpendicular to the axis of a structural
member, the beam will bend. This bending can be sagging or
hogging, resulting in positive or negative bending moments.
Sagging bending moments cause compression on the top
surface and tension on the bottom surface, while hogging
bending moments have the opposite effect.
In conclusion, aircraft structures need to be designed to resist
various loads and moments while maintaining a high strength-
to-weight or stiffness ratio. The geometry and orientation of
the cross-sections play a crucial role in determining the
structural efficiency. Understanding the bending of beams and
the effects of sagging and hogging bending moments is
essential in aircraft structural design.
Understanding Bending Stress
and Symmetrical Bending
Let's take the example of an eraser to understand bending
stress and symmetrical bending. When we try to bend the
eraser towards our body, the bottom surface gets compressed
while the top surface gets elongated. This results in tension on
the top surface and compression on the bottom surface. On the
other hand, if we try to bend the eraser in the opposite
direction, it bends easily as the moment of inertia is greater
along that axis. The upper fibers get stretched while the lower
fibers get compressed, and there is a neutral plane where the
fibers are neither compressed nor elongated.
When we apply the same pressure to the eraser with the
shorter sides vertical, it requires less effort to bend. This is
because the bending stiffness of the material and the
orientation of the material affect how it behaves when
subjected to bending.
Symmetrical bending refers to the bending of a beam with a
symmetric cross section. In symmetrical bending, the bending
stress can be calculated using the formula: m / I = σv / y =
E / r. Here, m is the maximum bending moment, I is the
moment of inertia, σv is the bending stress, y is the distance
from the neutral axis, and E is the modulus of elasticity.
When a load is applied along the y-axis, causing the beam to
bend about the x-axis, we have positive bending moment.
Introduction
18 AAC304 is the subject for the first class in the fifth semester
on aircraft structures. Here, we will be discussing the primary
structural elements of an aircraft, such as the wing, landing
gear, and tail plane. The fuselage structure is also an important
component, consisting of longitudinal stiffening members
called longerons, as well as stringers and bulkheads. These
structural elements are responsible for transmitting and
resisting externally applied loads, providing an aerodynamic
shape, and protecting passengers and payload systems from
environmental conditions.
There are two main types of aircraft structures: semi-
monocoque and monocoque. In semi-monocoque structures,
the outer surface of the shell is supported by longitudinal
stiffening members, rings, or formers, which allow the structure
to resist bending, compressive, and torsional loads. On the
other hand, in monocoque structures, the skin alone must
resist all the applied loads. The wing structure is a good
example of a semi-monocoque structure, with ribs providing
the aerodynamic shape and various structural elements like
skin, fuel tank, and stringers.
When designing aircraft structures, it is important to consider
the aerodynamic moments and loads imposed on the structure.
The structural design engineer must ensure that the structure
can balance these loads and moments. Additionally, aircraft
structural components need to have a high strength-to-weight
ratio or stiffness ratio to minimize weight penalties. This often
results in thin-walled sections with different geometrical cross-
sections such as channel, circular, rectangular, square, and so
on.
The properties of the geometrical cross-section, including the
area moment of inertia, play a vital role in determining the
structural efficiency in resisting bending. Structural
components can be open or closed sections, subjected to axial,
bending, shear, and torsional loads. The efficiency of open or
closed sections in resisting torsion or bending is an important
aspect to be considered.
, When a load is applied perpendicular to the axis of a structural
member, the beam will bend. This bending can be sagging or
hogging, resulting in positive or negative bending moments.
Sagging bending moments cause compression on the top
surface and tension on the bottom surface, while hogging
bending moments have the opposite effect.
In conclusion, aircraft structures need to be designed to resist
various loads and moments while maintaining a high strength-
to-weight or stiffness ratio. The geometry and orientation of
the cross-sections play a crucial role in determining the
structural efficiency. Understanding the bending of beams and
the effects of sagging and hogging bending moments is
essential in aircraft structural design.
Understanding Bending Stress
and Symmetrical Bending
Let's take the example of an eraser to understand bending
stress and symmetrical bending. When we try to bend the
eraser towards our body, the bottom surface gets compressed
while the top surface gets elongated. This results in tension on
the top surface and compression on the bottom surface. On the
other hand, if we try to bend the eraser in the opposite
direction, it bends easily as the moment of inertia is greater
along that axis. The upper fibers get stretched while the lower
fibers get compressed, and there is a neutral plane where the
fibers are neither compressed nor elongated.
When we apply the same pressure to the eraser with the
shorter sides vertical, it requires less effort to bend. This is
because the bending stiffness of the material and the
orientation of the material affect how it behaves when
subjected to bending.
Symmetrical bending refers to the bending of a beam with a
symmetric cross section. In symmetrical bending, the bending
stress can be calculated using the formula: m / I = σv / y =
E / r. Here, m is the maximum bending moment, I is the
moment of inertia, σv is the bending stress, y is the distance
from the neutral axis, and E is the modulus of elasticity.
When a load is applied along the y-axis, causing the beam to
bend about the x-axis, we have positive bending moment.
