What is stress due to self-weight?

Short Answer:

Stress due to self-weight is the internal resistance developed within a body because of its own weight. When a long vertical member such as a rod, column, or wire is hanging or standing under gravity, it experiences stress caused by the weight of the material below each section.

This type of stress increases from the top to the bottom of the member since the lower parts carry the weight of the material above. It is calculated by multiplying the material’s density and gravitational acceleration by the height of the member and is generally small compared to external loads.

Detailed Explanation :

Stress due to Self-Weight

When a structural or mechanical member such as a rod, bar, or column is placed vertically, it is subjected to its own weight due to gravity. This causes an internal resistance or stress within the material, which is known as stress due to self-weight. In most practical situations, especially when the member is short and lightweight, this stress is very small and often neglected. However, in tall structures or very long rods, the effect of self-weight becomes significant and must be considered during design.

Concept of Stress due to Self-Weight

Every material has a mass, and when it is under the influence of gravity, it exerts a force known as weight. In a vertical member, each small portion of the material supports the weight of all the portions below it. This causes an internal stress distribution that increases from the top to the bottom of the member.

If the member is uniform and has a constant cross-sectional area, the stress varies linearly with depth, being zero at the top and maximum at the bottom. This stress is a type of tensile stress in hanging members (like a vertical wire) and a compressive stress in standing members (like a column).

Derivation of Formula

Consider a uniform vertical bar of:

  • Length =
  • Cross-sectional area =
  • Density of material =
  • Gravitational acceleration =

Let us find the stress at a distance  from the top.

  1. The weight of the portion of the bar below the section is:
  1. The stress at that section is the load per unit area:
  1. Simplifying, we get:

This shows that the stress increases linearly with the depth .

The maximum stress occurs at the bottom of the member where :

Explanation of Parameters

  1. Density () – This represents the mass per unit volume of the material. Denser materials such as steel or copper will produce higher stress due to their own weight compared to lighter materials like aluminum or wood.
  2. Gravitational acceleration (g) – Usually taken as , it represents the force with which the Earth attracts all masses towards its center.
  3. Length (L) – The height of the member directly affects the stress; longer members experience greater stress at the bottom because they support more weight.
  4. Cross-sectional area (A) – In the case of uniform cross-section, the area does not affect the stress value since it cancels out during derivation. However, it affects the total force experienced by each section.

Nature of Stress in Different Members

  • In a hanging bar or wire:
    The stress due to self-weight is tensile because the weight tries to elongate the material.
  • In a standing column or rod:
    The stress due to self-weight is compressive because the weight of the upper parts compresses the material below.

Thus, the type of stress depends on the orientation and the loading condition of the body.

Example Calculation

Let’s consider a steel wire of:

  • Length = 20 m
  • Density = 7850 kg/m³

The stress due to self-weight at the bottom is:

or

This value shows that the stress due to self-weight is usually small compared to stresses caused by external loads (which are often tens or hundreds of MPa). Therefore, it can be neglected in short members but must be considered in tall structures like towers or long suspension cables.

Importance of Considering Self-Weight Stress

  1. In Tall Buildings and Towers:
    For very tall structures, such as skyscrapers, the self-weight of the concrete or steel components becomes a major factor in design.
  2. In Long Shafts or Wires:
    In vertical shafts or elevator cables, self-weight can significantly affect elongation and safety.
  3. In Structural Columns:
    It is essential to account for compressive stress due to self-weight to prevent buckling or collapse.
  4. In Engineering Design:
    Ignoring self-weight in long members can lead to underestimation of stress, resulting in unsafe designs.

Effect on Deformation

The elongation or shortening due to self-weight can also be calculated using the formula:

where  is the modulus of elasticity of the material.

This expression helps to determine how much a bar will stretch or compress under its own weight.

Conclusion

Stress due to self-weight is the internal resistance developed within a material because of its own gravitational force. It increases linearly with the height of the body and reaches its maximum at the lowest point. While often small for short members, this stress becomes crucial in tall or heavy structures. Engineers must consider it during design to ensure that the structure remains safe, stable, and within permissible stress limits.