What is simple bending?

Short Answer:

Simple bending is the type of bending in which a beam is subjected to both bending moment and shear force due to external loads acting on it. In this case, the bending moment varies along the length of the beam, unlike in pure bending where it remains constant.

In simple words, when a beam is loaded with transverse forces like point loads or uniformly distributed loads, it experiences bending along with shear. This practical condition of bending in beams is called simple bending, and it is the most common form of bending found in real structures.

Detailed Explanation :

Simple Bending

When a beam or structural member is loaded transversely (perpendicular to its axis), it develops bending moments and shear forces at different sections along its length. This combined effect, where the bending moment is not constant and shear force is present, is called simple bending.

In simple bending, the beam bends into a curved shape under the action of external loads such as point loads, distributed loads, or varying loads. The bending moment changes continuously from one section to another, depending on the loading and support conditions.

This type of bending is more realistic and occurs in almost every practical beam used in machines, bridges, and buildings. Hence, the study of simple bending is essential in mechanical and structural engineering.

Definition of Simple Bending

Simple bending can be defined as:

“The bending of a beam when it is subjected to transverse loads such that both bending moment and shear force act on the beam, and the bending moment varies along its length.”

Thus, simple bending is a general form of bending that occurs under ordinary loading conditions.

In short,

  • When bending moment is constant and shear force = 0, it is pure bending.
  • When bending moment varies and shear force ≠ 0, it is simple bending.

Explanation of Simple Bending

When a beam is subjected to external transverse loads (perpendicular to its length), it develops internal forces to maintain equilibrium. These internal forces are:

  1. Shear Force (V):
    It is the internal force that acts along the cross-section of the beam to resist sliding between layers. It is caused by the vertical component of the external load.
  2. Bending Moment (M):
    It is the internal moment that resists the bending action caused by the external load.

In simple bending, both of these — shear force and bending moment — act simultaneously. The bending moment is not constant but varies from one point to another depending on the magnitude and position of the external load.

For example, in a simply supported beam carrying a uniformly distributed load (UDL),

  • The shear force changes linearly along the beam.
  • The bending moment varies parabolically.

This changing moment along the length of the beam results in simple bending.

Distribution of Stresses in Simple Bending

When a beam bends, different fibers of the beam experience different levels of strain and stress:

  • Top fibers (above the neutral axis) experience compressive stress because they shorten.
  • Bottom fibers (below the neutral axis) experience tensile stress because they elongate.
  • The neutral axis is the line within the beam where no stress or strain occurs during bending.

In simple bending, since both bending and shear act together, the stress distribution is slightly modified near the supports (where shear is high). However, the overall pattern remains similar to pure bending — with linear stress variation from tension to compression.

The bending stress at any point in the beam is given by:

Where,

  •  = bending stress (N/mm²)
  •  = bending moment (N·mm)
  •  = distance of the fiber from the neutral axis (mm)
  •  = moment of inertia of the cross-section (mm⁴)

Since  varies along the beam, the bending stress also varies accordingly.

Comparison with Pure Bending

In pure bending, the bending moment is constant along the beam, and no shear force acts on it. This is an ideal condition used to derive the bending equation.
In simple bending, however, the bending moment varies continuously due to the applied loads and the presence of shear force.

So, we can say:

  • Pure bending = theoretical or special condition.
  • Simple bending = practical condition that occurs in most real beams.

Conditions for Simple Bending

For a beam to be in simple bending:

  1. The beam must be subjected to external transverse loads (loads acting perpendicular to its axis).
  2. Both bending moment and shear force must act on the beam.
  3. The bending moment must vary along the length of the beam.
  4. The deflection of the beam should be small compared to its length.
  5. The beam material must behave elastically and follow Hooke’s law.

When these conditions are met, the beam is said to experience simple bending.

Example of Simple Bending

  1. Simply Supported Beam with a Point Load:
    When a simply supported beam carries a single concentrated load at its center, both shear force and bending moment vary along the beam. The maximum bending moment occurs at the midpoint, while the shear force is maximum at the supports.
  2. Cantilever Beam with a Uniform Load:
    In this case, the bending moment varies along the length of the beam, being maximum at the fixed end and zero at the free end. The shear force also changes from maximum to zero along the beam.

These examples are common in practical applications like bridge decks, machine frames, and structural supports.

Applications of Simple Bending

Simple bending occurs in most structural and mechanical components, such as:

  1. Beams in Buildings and Bridges:
    These beams carry loads from slabs and distribute them to columns.
  2. Machine Elements:
    Levers, axles, shafts, and arms experience simple bending under external forces.
  3. Vehicle Frames and Chassis:
    Bending moments due to road loads cause simple bending.
  4. Cranes and Load-Carrying Arms:
    These parts bend under variable loads, showing the effects of simple bending.
  5. Structural Members:
    Trusses and girders often have portions under simple bending.

Significance of Simple Bending in Engineering

  1. Realistic Representation:
    Most beams in real-world applications undergo simple bending rather than pure bending.
  2. Design and Safety:
    Knowledge of simple bending helps engineers determine safe load-carrying capacities of beams.
  3. Understanding Shear and Moment Distribution:
    It helps in drawing shear force and bending moment diagrams for design purposes.
  4. Prediction of Maximum Stress:
    Allows calculation of maximum bending stresses to prevent material failure.
  5. Structural Optimization:
    Engineers can design lighter and stronger beams by understanding stress variation in simple bending.
Conclusion

In conclusion, simple bending refers to the bending of a beam when it is subjected to transverse loads, producing both bending moment and shear force. The bending moment in this case varies along the beam’s length, and the beam experiences a combination of bending and shear stresses. Unlike pure bending, simple bending represents real-life conditions in which beams and structural elements operate. It is a fundamental concept in mechanical and structural engineering, forming the basis for beam design, stress analysis, and safe construction of load-bearing structures.